Identifier
-
Mp00183:
Skew partitions
—inner shape⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St000395: Dyck paths ⟶ ℤ
Values
[[2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,1],[1]] => [1] => [1,0] => [1,0] => 1
[[2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[2,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[2,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[2,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[3,2,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[2,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[3,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[2,2,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[2,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[2,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[3,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,2],[1]] => [1] => [1,0] => [1,0] => 1
[[5,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[5,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[3,3,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,3,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,2,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,3,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[3,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[3,2,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[3,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[3,3,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[4,3,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[2,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[3,2,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,2],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[2,2,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[3,3,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[3,2,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[4,3,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,2,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[3,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,3],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[4,3,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,3],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[2,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[3,3,2,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,3,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[3,2,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,3,2,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,3,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[2,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,2],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[3,3,2,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,3,2],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[3,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,2],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[4,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,3,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[2,2,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[3,3,2,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
>>> Load all 1392 entries. <<<[[4,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[2,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[3,2,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[6,1],[1]] => [1] => [1,0] => [1,0] => 1
[[5,2],[1]] => [1] => [1,0] => [1,0] => 1
[[6,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[6,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3],[1]] => [1] => [1,0] => [1,0] => 1
[[5,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[6,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,3,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[5,3,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,2,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[6,3,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[4,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,3,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[6,3,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[4,2,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,3,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[5,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[6,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,4],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[6,4],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[3,3,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,4,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,3,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[6,4,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[3,3,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[3,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,4,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[4,2,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,3,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,4,2],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[3,3,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[3,2,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,2,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,3,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,4,2,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[4,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,4,3],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,3,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,4,3],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[3,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,3,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,3,2,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,4,3,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[4,2,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,3,2,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,4,3,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[3,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,3,3,2],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,3,2,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,4,3,2],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[4,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,3,3,2],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,4,3,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[3,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[3,2,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,3,2,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[3,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[4,2,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[6,5],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[[4,4,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,5,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[5,4,1],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[6,5,1],[5,1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[3,3,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,5,2],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[4,3,2],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,2],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,5,2],[5,2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 7
[[3,3,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,2,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[4,4,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,5,2,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[4,3,1,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,2,1],[4,1,1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[5,4,1,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,5,2,1],[5,2,1]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 8
[[3,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,3],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[4,3,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,3],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,5,3],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 8
[[2,2,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[3,3,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,3,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,4,2,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,3,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[3,2,2,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,3,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[4,3,2,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,3,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,4,2,1],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,5,3,1],[5,3,1]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[[3,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,3,2],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[4,4,2,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,3,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[4,3,2,2],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,3,2],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[5,4,2,2],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[6,5,3,2],[5,3,2]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[[2,2,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[3,3,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[3,3,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,4,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[3,2,1,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[4,3,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[[4,3,1,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 8
[[5,4,2,1,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[4,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,4],[4,4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 8
[[5,4,4],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,5,4],[5,4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 9
[[3,3,3,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,4,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[4,4,3,1],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,4,1],[4,4,1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[[4,3,3,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,4,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[5,4,3,1],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,5,4,1],[5,4,1]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 10
[[2,2,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,4,2],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[3,3,2,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,3,2],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,4,2],[4,4,2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[[3,2,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,4,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[4,3,2,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,3,2],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[6,5,4,2],[5,4,2]] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
[[2,2,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[3,3,3,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[3,3,2,1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[4,4,3,1,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,4,2,1],[4,4,2,1]] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[[3,2,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,3,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[4,3,2,1,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[[5,4,3,1,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[3,3,3,3],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,4,3],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[4,4,3,3],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,4,3],[4,4,3]] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[[4,3,3,3],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,4,4,3],[4,3,3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[[5,4,3,3],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[6,5,4,3],[5,4,3]] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[[2,2,2,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[3,3,3,2,1],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,4,3,1],[3,3,3,1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 10
[[3,3,2,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[4,4,3,2,1],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,4,3,1],[4,4,3,1]] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[[3,2,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[4,3,3,2,1],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,4,4,3,1],[4,3,3,1]] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[[4,3,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,4,3,2,1],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,3,3,3,2],[2,2,2,2]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 8
[[3,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,4,4,3,2],[3,3,3,2]] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 11
[[3,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,3,3,2],[3,3,2,2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[[4,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[5,5,4,3,2],[4,4,3,2]] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 13
[[3,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,3,3,3,2],[3,2,2,2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 9
[[4,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,4,4,3,2],[4,3,3,2]] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[[4,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,4,3,3,2],[4,3,2,2]] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[[5,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 9
[[2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 8
[[3,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[[2,2,1,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 7
[[3,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[[3,3,2,1,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[[4,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[2,1,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[3,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[[3,2,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[4,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[3,2,1,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[[4,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,3,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[7,1],[1]] => [1] => [1,0] => [1,0] => 1
[[6,2],[1]] => [1] => [1,0] => [1,0] => 1
[[7,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[6,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[6,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[7,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3],[1]] => [1] => [1,0] => [1,0] => 1
[[6,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[7,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,3,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[6,3,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[6,2,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[7,3,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[6,3,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[6,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[7,3,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,2,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[5,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[6,3,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[6,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[6,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[7,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,4],[1]] => [1] => [1,0] => [1,0] => 1
[[5,4],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[6,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[7,4],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[4,4,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,1],[1]] => [1] => [1,0] => [1,0] => 1
[[5,4,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[6,4,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,3,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[7,4,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[4,3,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,4,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[5,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[6,4,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,2,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[6,3,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[7,4,2],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[4,3,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,3,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,4,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,2,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[5,3,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,3,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[6,4,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,2,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[6,3,2,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[6,3,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[7,4,2,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[6,4,3],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[6,3,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[7,4,3],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[4,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,3,3,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,3,2,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[6,4,3,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,2,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[6,3,3,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,3,2,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[7,4,3,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[4,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[5,3,3,2],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[5,3,2,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[6,4,3,2],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[6,3,3,2],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[6,3,2,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[7,4,3,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[4,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[4,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[5,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,2,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[5,3,2,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[6,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[4,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[5,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[5,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[6,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,2,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[6,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[6,3,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[7,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,5],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[6,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[7,5],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[[4,4,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,5,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[6,5,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,4,1],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[7,5,1],[5,1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[3,3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,5,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[4,3,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,4,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,5,2],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[5,3,2],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[6,4,2],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[7,5,2],[5,2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 7
[[3,3,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,5,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,3,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,4,2,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,5,2,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,3,1,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[6,4,2,1],[4,1,1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[6,4,1,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[7,5,2,1],[5,2,1]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 8
[[3,3,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,5,3],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[4,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,4,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,5,3],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[5,3,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,4,3],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[7,5,3],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 8
[[3,3,3,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,3,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,2,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,5,3,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[3,2,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,3,3,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,4,3,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,2,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,5,3,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[4,2,2,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,3,3,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,3,2,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,4,3,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[6,4,2,1],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[7,5,3,1],[5,3,1]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[[3,3,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,3,2],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,2,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,5,3,2],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[4,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,4,3,2],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,4,2,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,5,3,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[5,3,2,2],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[6,4,3,2],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[6,4,2,2],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[7,5,3,2],[5,3,2]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[[3,3,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,3,2,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[3,3,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,2,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,5,3,2,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[3,2,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,3,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[4,3,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,4,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[4,2,1,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[5,3,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[6,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[[5,3,1,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 8
[[6,4,2,1,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[6,5,4],[4,4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 8
[[6,4,4],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[7,5,4],[5,4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 9
[[4,3,3,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,4,4,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,4,3,1],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[6,5,4,1],[4,4,1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[[5,3,3,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,4,4,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[6,4,3,1],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[7,5,4,1],[5,4,1]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 10
[[3,2,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,3,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,4,4,2],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[4,3,2,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,4,3,2],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[6,5,4,2],[4,4,2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[[4,2,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,3,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,4,4,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[5,3,2,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,4,3,2],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[7,5,4,2],[5,4,2]] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
[[3,2,2,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,3,3,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[4,3,2,1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[5,4,3,1,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[6,5,4,2,1],[4,4,2,1]] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[[4,2,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,3,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,3,2,1,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[[6,4,3,1,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[4,3,3,3],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[5,4,4,3],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[5,4,3,3],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[6,5,4,3],[4,4,3]] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[[5,3,3,3],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[6,4,4,3],[4,3,3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[[6,4,3,3],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[7,5,4,3],[5,4,3]] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[[3,2,2,2,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,3,3,2,1],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[5,4,4,3,1],[3,3,3,1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 10
[[4,3,2,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[5,4,3,2,1],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[6,5,4,3,1],[4,4,3,1]] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[[4,2,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,3,3,2,1],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[6,4,4,3,1],[4,3,3,1]] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[[5,3,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[6,4,3,2,1],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[4,3,3,3,2],[2,2,2,2]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 8
[[4,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[5,4,4,3,2],[3,3,3,2]] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 11
[[4,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[5,4,3,3,2],[3,3,2,2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[[5,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[6,5,4,3,2],[4,4,3,2]] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 13
[[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[5,3,3,3,2],[3,2,2,2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 9
[[5,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[6,4,4,3,2],[4,3,3,2]] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[[5,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[6,4,3,3,2],[4,3,2,2]] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[[6,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[3,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[3,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[4,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 9
[[3,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 8
[[4,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[5,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[[3,2,1,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 7
[[4,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[5,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[[4,3,2,1,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[[5,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[3,1,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[5,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[[4,2,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[5,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[4,2,1,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[[5,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,3,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[6,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[6,6],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[[7,6],[6]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
[[5,5,1],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[6,6,1],[5,1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[6,5,1],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[[7,6,1],[6,1]] => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[[4,4,2],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,5,2],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,6,2],[5,2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 7
[[5,4,2],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[6,5,2],[5,1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[7,6,2],[6,2]] => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8
[[4,4,1,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,5,2,1],[4,1,1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[5,5,1,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,6,2,1],[5,2,1]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 8
[[5,4,1,1],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[6,5,2,1],[5,1,1]] => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[[6,5,1,1],[5,1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[[3,3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,5,3],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,6,3],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 8
[[4,3,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,3],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,5,3],[5,2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 7
[[7,6,3],[6,3]] => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 9
[[3,3,2,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,3,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[4,4,2,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,5,3,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,5,2,1],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,6,3,1],[5,3,1]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[[4,3,2,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,3,1],[4,1,1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[5,4,2,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,5,3,1],[5,2,1]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 8
[[6,5,2,1],[5,2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 7
[[4,4,2,2],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,5,3,2],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[5,5,2,2],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[6,6,3,2],[5,3,2]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[[5,4,2,2],[4,1,1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[6,5,3,2],[5,2,2]] => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 9
[[6,5,2,2],[5,2,1]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 8
[[3,3,1,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,2,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[4,4,2,1,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,5,3,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[[4,4,1,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,5,2,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 8
[[5,5,2,1,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[4,3,1,1,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,2,2,1],[4,1,1,1]] => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[[5,4,2,1,1],[4,1,1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[[5,4,1,1,1],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,5,2,1,1],[5,2,1]] => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 8
[[4,4,4],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,4],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,6,4],[5,4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 9
[[5,4,4],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,5,4],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 8
[[7,6,4],[6,4]] => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 10
[[3,3,3,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,4,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,4,3,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,4,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[5,5,3,1],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,6,4,1],[5,4,1]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 10
[[4,3,3,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,4,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,4,3,1],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,5,4,1],[5,3,1]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[[6,5,3,1],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 8
[[2,2,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,4,2],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[3,3,2,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,3,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,4,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[4,4,2,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,3,2],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[6,6,4,2],[5,4,2]] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
[[3,2,2,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,3,2],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,4,2],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[4,3,2,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,3,2],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[6,5,4,2],[5,3,2]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[[5,4,2,2],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,5,3,2],[5,3,1]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[[2,2,2,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,4,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[3,3,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,3,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,4,3,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,4,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[4,4,2,1,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,3,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[[5,5,3,1,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[3,2,2,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,3,2,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[4,3,3,1,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,4,2,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[[4,3,2,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,3,2,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 8
[[5,4,3,1,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,4,2,1,1],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,5,3,1,1],[5,3,1]] => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 9
[[4,4,3,3],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,5,4,3],[4,3,3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[[5,5,3,3],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[6,6,4,3],[5,4,3]] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[[5,4,3,3],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[6,5,4,3],[5,3,3]] => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11
[[6,5,3,3],[5,3,2]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[[3,3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,3,3,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[4,4,3,2,1],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,5,4,3,1],[4,3,3,1]] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[[4,4,2,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,3,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,5,3,2,1],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[4,3,2,2,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,3,3,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[[5,4,3,2,1],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[5,4,2,2,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[6,5,3,2,1],[5,3,2]] => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,4,3,3,2],[3,2,2,2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 9
[[4,4,3,2,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,5,4,3,2],[4,3,3,2]] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[[4,4,2,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,5,3,3,2],[4,3,2,2]] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[[5,5,3,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[4,3,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[5,4,3,3,2],[4,2,2,2]] => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 10
[[5,4,3,2,2],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[[5,4,2,2,2],[4,2,1,1]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 8
[[2,2,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[3,3,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,4,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[[3,3,2,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[4,4,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[3,3,1,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[[4,4,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,4,2,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[3,2,1,1,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,2,2,2,1],[3,1,1,1,1]] => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[[4,3,2,2,1,1],[3,1,1,1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[4,3,2,1,1,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,3,2,1,1],[4,2,2,1]] => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 9
[[4,3,1,1,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,2,2,1,1],[4,2,1,1]] => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 8
[[5,4,2,1,1,1],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,5,5],[4,4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 8
[[6,6,5],[5,5]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 10
[[6,5,5],[5,4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 9
[[7,6,5],[6,5]] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11
[[4,4,4,1],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,5,1],[4,4,1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[[5,5,4,1],[4,4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 8
[[6,6,5,1],[5,5,1]] => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11
[[5,4,4,1],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,5,5,1],[5,4,1]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 10
[[6,5,4,1],[5,4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 9
[[3,3,3,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,4,2],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,5,2],[4,4,2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[[4,4,3,2],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,4,2],[4,4,1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[[6,6,5,2],[5,5,2]] => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 12
[[4,3,3,2],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,4,2],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[6,5,5,2],[5,4,2]] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
[[5,4,3,2],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,5,4,2],[5,4,1]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 10
[[3,3,3,1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,4,2,1],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[4,4,4,1,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,5,2,1],[4,4,2,1]] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[[4,4,3,1,1],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,4,2,1],[4,4,1,1]] => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 10
[[5,5,4,1,1],[4,4,1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[[4,3,3,1,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,4,2,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[[5,4,4,1,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[5,4,3,1,1],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,5,4,1,1],[5,4,1]] => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 10
[[3,3,3,3],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,4,3],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,5,3],[4,4,3]] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[[4,4,3,3],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,4,3],[4,4,2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[[6,6,5,3],[5,5,3]] => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 13
[[4,3,3,3],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,4,3],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[6,5,5,3],[5,4,3]] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[[5,4,3,3],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[6,5,4,3],[5,4,2]] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
[[2,2,2,2,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,3,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[3,3,3,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,4,3,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[4,4,4,2,1],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,5,3,1],[4,4,3,1]] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[[3,3,2,2,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,3,3,1],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[4,4,3,2,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,4,3,1],[4,4,2,1]] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[[5,5,4,2,1],[4,4,2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[[3,2,2,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3,3,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,3,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,4,3,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,4,4,2,1],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[4,3,2,2,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,3,3,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[[5,4,3,2,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[6,5,4,2,1],[5,4,2]] => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11
[[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,4,3,2],[3,3,2,2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[[4,4,4,2,2],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[5,5,5,3,2],[4,4,3,2]] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 13
[[4,4,3,2,2],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[5,5,4,3,2],[4,4,2,2]] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 12
[[5,5,4,2,2],[4,4,2,1]] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[[4,3,3,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,4,4,3,2],[4,3,2,2]] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[[5,4,4,2,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,4,3,2,2],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[[2,2,2,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 7
[[3,3,3,2,1,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,4,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[[3,3,3,1,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,4,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[[4,4,4,2,1,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[3,3,2,1,1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,3,2,2,1],[3,3,1,1,1]] => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 9
[[4,4,3,2,1,1],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[4,4,3,1,1,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,4,2,1,1],[4,4,2,1]] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[[3,2,2,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[[4,3,3,2,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,3,3,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,4,2,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[4,3,2,1,1,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,3,2,1,1],[4,3,1,1]] => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 9
[[5,4,3,1,1,1],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[4,4,4,4],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[5,5,5,4],[4,4,4]] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 12
[[5,5,4,4],[4,4,3]] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[[6,6,5,4],[5,5,4]] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
[[5,4,4,4],[4,3,3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[[6,5,5,4],[5,4,4]] => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 13
[[6,5,4,4],[5,4,3]] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[[3,3,3,3,1],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,4,4,1],[3,3,3,1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 10
[[4,4,4,3,1],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[5,5,5,4,1],[4,4,4,1]] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 13
[[4,4,3,3,1],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,4,4,1],[4,4,3,1]] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[[5,5,4,3,1],[4,4,3]] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[[4,3,3,3,1],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,4,4,4,1],[4,3,3,1]] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[[5,4,4,3,1],[4,3,3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[[5,4,3,3,1],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[6,5,4,3,1],[5,4,3]] => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[[2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,4,4,4,2],[3,3,3,2]] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 11
[[3,3,3,2,2],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,4,3,2],[3,3,3,1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 10
[[5,5,5,4,2],[4,4,4,2]] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 14
[[3,3,2,2,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,3,3,2],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[5,5,4,4,2],[4,4,3,2]] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 13
[[4,4,3,2,2],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,4,3,2],[4,4,3,1]] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[[3,2,2,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,3,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,4,4,4,2],[4,3,3,2]] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[[4,3,3,2,2],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,4,4,3,2],[4,3,3,1]] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[[4,3,2,2,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,3,3,2],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,4,3,2,2],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,3,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 8
[[3,3,3,3,1,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,4,4,4,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[[3,3,3,2,1,1],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,4,3,2,1],[3,3,3,1,1]] => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 11
[[4,4,4,3,1,1],[3,3,3,1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 10
[[3,3,2,2,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,3,3,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[[4,4,3,3,1,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[4,4,3,2,1,1],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,4,3,1,1],[4,4,3,1]] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[[3,2,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,3,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[4,3,3,3,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[4,3,3,2,1,1],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,4,4,3,1,1],[4,3,3,1]] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[[4,3,2,2,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,3,3,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,4,3,2,1,1],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 8
[[4,4,4,4,3],[3,3,3,3]] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 12
[[4,4,4,3,3],[3,3,3,2]] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 11
[[5,5,5,4,3],[4,4,4,3]] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 15
[[4,4,3,3,3],[3,3,2,2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[[5,5,4,4,3],[4,4,3,3]] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 14
[[5,5,4,3,3],[4,4,3,2]] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 13
[[4,3,3,3,3],[3,2,2,2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 9
[[5,4,4,4,3],[4,3,3,3]] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 13
[[5,4,4,3,3],[4,3,3,2]] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[[5,4,3,3,3],[4,3,2,2]] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,3,3,3,3,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 9
[[3,3,3,3,2,1],[2,2,2,2]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 8
[[4,4,4,4,3,1],[3,3,3,3,1]] => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 13
[[3,3,3,2,2,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,4,4,3,3,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[[4,4,4,3,2,1],[3,3,3,2]] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 11
[[3,3,2,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,3,3,3,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[[4,4,3,3,2,1],[3,3,2,2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[[4,4,3,2,2,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[5,5,4,3,2,1],[4,4,3,2]] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 13
[[3,2,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,3,3,3,3,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[[4,3,3,3,2,1],[3,2,2,2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 9
[[4,3,3,2,2,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,4,4,3,2,1],[4,3,3,2]] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[[4,3,2,2,2,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,4,3,3,2,1],[4,3,2,2]] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[[5,4,3,2,2,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[3,3,3,3,3,2],[2,2,2,2,2]] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 10
[[3,3,3,3,2,2],[2,2,2,2,1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 9
[[4,4,4,4,3,2],[3,3,3,3,2]] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 14
[[3,3,3,2,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 8
[[4,4,4,3,3,2],[3,3,3,2,2]] => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 13
[[4,4,4,3,2,2],[3,3,3,2,1]] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[[3,3,2,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 7
[[4,4,3,3,3,2],[3,3,2,2,2]] => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 12
[[4,4,3,3,2,2],[3,3,2,2,1]] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[[4,4,3,2,2,2],[3,3,2,1,1]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[[3,2,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[4,3,3,3,3,2],[3,2,2,2,2]] => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 11
[[4,3,3,3,2,2],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[[4,3,3,2,2,2],[3,2,2,1,1]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[4,3,2,2,2,2],[3,2,1,1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 11
[[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 10
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 9
[[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 9
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 8
[[3,3,3,2,1,1,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 12
[[2,2,1,1,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 8
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 7
[[3,3,2,2,1,1,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 11
[[3,3,2,1,1,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[[4,4,3,2,1,1,1],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[2,1,1,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[3,2,2,2,1,1,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 10
[[3,2,2,1,1,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 9
[[4,3,3,2,1,1,1],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[3,2,1,1,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 8
[[4,3,2,2,1,1,1],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[4,3,2,1,1,1,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,3,2,1,1,1],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[2,2,1,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[2,2,2,1,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,2,1,1,1,1],[1]] => [1] => [1,0] => [1,0] => 1
[[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,2,2,1,1,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2,1,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,1,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,3,2,1,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,2,1,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[4,3,3,1,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,3,1,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,3,1,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,3,2,2,1],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,2,2,1],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,3,3,2,1],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,3,2,1],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,3,2,1],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,4,2,1],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,4,2,1],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[4,3,3,3,1],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,3,3,1],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,3,3,1],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,4,3,1],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,4,3,1],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,3,1],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[4,4,4,4,1],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[5,4,4,1],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,4,1],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,4,1],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 7
[[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 8
[[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[5,3,2,2],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[5,4,2,2],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 9
[[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,3,3,2],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[5,4,3,2],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,3,2],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 10
[[5,4,4,2],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,4,2],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[6,4,2],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,5,5,2],[4,4,1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[[6,5,2],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 10
[[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 9
[[5,3,3,3],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[[5,4,3,3],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,5,3,3],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 11
[[5,4,4,3],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[5,5,4,3],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[6,4,3],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,5,5,3],[4,4,2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[[6,5,3],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,6,3],[5,2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 7
[[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 12
[[5,4,4,4],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[5,5,4,4],[4,3,3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[[6,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,5,4],[4,4,3]] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[[6,5,4],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,6,4],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 8
[[7,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,5,5,5],[4,4,4]] => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 12
[[6,6,6],[5,5]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 10
[[7,7],[6]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 12
[[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 15
[[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 16
[[6,6,6,6],[5,5,5]] => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 15
[[7,7,7],[6,6]] => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 12
[[8,8],[7]] => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[[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] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[[3,3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[2,2,2,2,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,5],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[3,3,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,3],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,5],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,2],[1]] => [1] => [1,0] => [1,0] => 1
[[2,2,2,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,2,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,2,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[2,2,2,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,4],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,1],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,3,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,1],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,1],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[6,6],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[5,5,5],[4,3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 7
[[6,5],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,5,5],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[6,6],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,4,4],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[6,4],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,5,4],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[4,4,4,4],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[5,4,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,4,4,4],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[5,5,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,5,5],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[6,5],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,5,5],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[6,6],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,5,5],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 7
[[6,3],[1]] => [1] => [1,0] => [1,0] => 1
[[5,5,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,4,3],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,5,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[5,3,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[[4,3,3,3],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[4,4,3,3],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[5,4,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,5,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4,3],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,4,4],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[6,4],[1]] => [1] => [1,0] => [1,0] => 1
[[5,5,4],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[4,4,4,4],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,4,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,4,4],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,5,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,5,5],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[6,5],[1]] => [1] => [1,0] => [1,0] => 1
[[5,5,5],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[6,6],[1]] => [1] => [1,0] => [1,0] => 1
[[5,5,5],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,4,4,4],[3,1,1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[[5,4,4],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4,4],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[5,5,4],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4,4],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[5,5,5],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[5,5,2],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,2],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,5,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,3,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,3,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,3,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,4,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,2],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,5,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[2,2,2,2,2,2],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,2,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[2,2,2,2,2,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,2,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,2,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,3,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,3,3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3,2],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,2],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,4,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3,2],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,3,2],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3,3],[2,2,2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => 6
[[5,5,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,4,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,5,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,3,3],[2,2,1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => 5
[[5,3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[3,3,3,3,3],[2,1,1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[[4,3,3,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[3,3,3,3,3],[1,1,1]] => [1,1,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => 3
[[4,4,3,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4,3],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,5,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,4,4],[3,3]] => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 6
[[5,5,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,4,4],[3,2]] => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 5
[[5,4,4],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,4],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[5,5,4],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[5,5,5],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,5,5],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,4],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,4,4],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,4],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[5,5,4],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,4],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[5,5,5],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3,3],[2,2]] => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 4
[[4,3,3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,3,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,3,3],[2,1]] => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[[4,3,3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3,3],[1,1]] => [1,1] => [1,1,0,0] => [1,0,1,0] => 2
[[4,4,3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,4,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,3],[1]] => [1] => [1,0] => [1,0] => 1
[[3,3,3,3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[3,3,3,3,3],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[4,4,4,4],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,4],[1]] => [1] => [1,0] => [1,0] => 1
[[5,5,5,1],[1]] => [1] => [1,0] => [1,0] => 1
[[4,4,4,4,1],[1]] => [1] => [1,0] => [1,0] => 1
[[7,7],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[[6,6,6],[5,4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 9
[[6,6,6],[4,4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 8
[[7,7],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[5,5,5,5],[4,4,3]] => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 11
[[5,5,5,5],[4,3,3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 10
[[5,5,5,5],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[6,6,6],[5,3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 8
[[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 11
[[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 10
[[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 9
[[5,5,5,5],[4,4,2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 10
[[5,5,5,5],[4,3,2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 9
[[5,5,5,5],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[6,6,6],[4,2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 6
[[5,5,5,5],[4,2,2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 8
[[5,5,5,5],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 9
[[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 8
[[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 10
[[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 9
[[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 8
[[5,5,5,5],[4,4,1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 9
[[5,5,5,5],[4,3,1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 8
[[5,5,5,5],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[5,5,5,5],[4,2,1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 7
[[5,5,5,5],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 8
[[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 7
[[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => 4
[[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 8
[[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 6
[[4,4,4,4,4],[3,3,3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 9
[[4,4,4,4,4],[3,3,2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 8
[[4,4,4,4,4],[3,2,2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 7
[[4,4,4,4,4],[3,3,1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 7
[[4,4,4,4,4],[3,2,1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 6
[[5,5,5,5],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[3,3,3,3,3,3],[2]] => [2] => [1,0,1,0] => [1,1,0,0] => 2
[[4,4,4,4,3],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[5,5,5,4],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[4,4,4,4,4],[3,1]] => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 4
[[5,5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[4,4,4,4,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[8,8],[6]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
[[7,7,7],[6,5]] => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11
[[6,6,6,6],[5,5,4]] => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 14
[[5,5,5,5,5],[4,4,4,3]] => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 15
[[4,4,4,4,4,4],[3,3,3,3,2]] => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 14
[[3,3,3,3,3,3,3],[2,2,2,2,2,1]] => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 11
[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
[[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 10
[[5,5,5,5,5],[4,3,2,2]] => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11
[[5,5,5,5,5],[4,3,3,1]] => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 11
[[5,5,5,5,5],[4,3,3,2]] => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[[5,5,5,5,5],[4,3,3,3]] => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 13
[[5,5,5,5,5],[4,4,2,1]] => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 11
[[5,5,5,5,5],[4,4,2,2]] => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 12
[[5,5,5,5,5],[4,4,3,1]] => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[[5,5,5,5,5],[4,4,3,2]] => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 13
[[5,5,5,5,5],[4,4,3,3]] => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 14
[[5,5,5,5,5],[4,4,4,1]] => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 13
[[5,5,5,5,5],[4,4,4,2]] => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 14
[[5,5,5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[5,5,5,5,5,5],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[4,4,4,4,4,4],[3]] => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 3
[[6,6,6,6,6,6],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[[6,6,6,6,6],[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 5
[[5,5,5,5,4],[4]] => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 4
[[5,5,5,5,5],[4,1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[[5,5,5,5,1],[1]] => [1] => [1,0] => [1,0] => 1
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Description
The sum of the heights of the peaks of a Dyck path.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Delest-Viennot-inverse
Description
Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\beta^{(-1)}\circ\gamma)(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\beta^{(-1)}\circ\gamma)(D)$.
Map
inner shape
Description
The inner shape of a skew partition.
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