Identifier
-
Mp00311:
Plane partitions
—to partition⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
St000996: Permutations ⟶ ℤ
Values
[[1]] => [1] => [1,0,1,0] => [2,1] => 1
[[1],[1]] => [1,1] => [1,0,1,1,0,0] => [2,1,3] => 1
[[2]] => [2] => [1,1,0,0,1,0] => [1,3,2] => 1
[[1,1]] => [2] => [1,1,0,0,1,0] => [1,3,2] => 1
[[1],[1],[1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [2,1,3,4] => 1
[[2],[1]] => [2,1] => [1,0,1,0,1,0] => [2,3,1] => 2
[[1,1],[1]] => [2,1] => [1,0,1,0,1,0] => [2,3,1] => 2
[[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,2,4,3] => 1
[[2,1]] => [3] => [1,1,1,0,0,0,1,0] => [1,2,4,3] => 1
[[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => [1,2,4,3] => 1
[[1],[1],[1],[1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,5] => 1
[[2],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,4,1,3] => 2
[[2],[2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,3,2,4] => 1
[[1,1],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [2,4,1,3] => 2
[[1,1],[1,1]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,3,2,4] => 1
[[3],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [3,1,4,2] => 2
[[2,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [3,1,4,2] => 2
[[1,1,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [3,1,4,2] => 2
[[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1
[[3,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1
[[2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1
[[2,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1
[[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,2,3,5,4] => 1
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,4,5,6] => 1
[[2],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => 2
[[2],[2],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [2,3,1,4] => 2
[[1,1],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [2,5,1,3,4] => 2
[[1,1],[1,1],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [2,3,1,4] => 2
[[3],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [2,1,4,3] => 2
[[3],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => 2
[[2,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [2,1,4,3] => 2
[[2,1],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => 2
[[2,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => 2
[[1,1,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [2,1,4,3] => 2
[[1,1,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => 2
[[4],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => 2
[[3,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => 2
[[2,2],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => 2
[[2,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => 2
[[1,1,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,5,3] => 2
[[5]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 1
[[4,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 1
[[3,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 1
[[3,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 1
[[2,2,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 1
[[2,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 1
[[1,1,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,3,4,6,5] => 1
[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => 1
[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => 2
[[2],[2],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => 2
[[2],[2],[2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => 1
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,6,1,3,4,5] => 2
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => 2
[[1,1],[1,1],[1,1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,3,2,4,5] => 1
[[3],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => 2
[[3],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 3
[[3],[3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => 1
[[2,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => 2
[[2,1],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 3
[[2,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 3
[[2,1],[2,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => 1
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => 2
[[1,1,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => 3
[[1,1,1],[1,1,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,2,4,3,5] => 1
[[4],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => 2
[[4],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[3,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => 2
[[3,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[3,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[2,2],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => 2
[[2,2],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[2,2],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[2,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => 2
[[2,1,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[2,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[1,1,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => 2
[[1,1,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => 2
[[5],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 2
[[4,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 2
[[3,2],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 2
[[3,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 2
[[2,2,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 2
[[2,1,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 2
[[1,1,1,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,4] => 2
[[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[5,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[4,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[4,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[3,2,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[3,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[2,2,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[2,1,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[1,1,1,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,2,3,4,5,7,6] => 1
[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => 1
[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => 2
[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => 2
[[2],[2],[2],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => 2
[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,7,1,3,4,5,6] => 2
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,5,1,3,4,6] => 2
>>> Load all 1123 entries. <<<[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => 2
[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => 2
[[3],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => 3
[[3],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => 2
[[3],[3],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => 2
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => 2
[[2,1],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => 3
[[2,1],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => 2
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => 3
[[2,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => 2
[[2,1],[2,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => 2
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,3,4,5] => 2
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,4,5,1,3] => 3
[[1,1,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => 2
[[1,1,1],[1,1,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => 2
[[4],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 2
[[4],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[4],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
[[3,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 2
[[3,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[3,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[3,1],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
[[3,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
[[2,2],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 2
[[2,2],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[2,2],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[2,2],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 2
[[2,1,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[2,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[2,1,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
[[2,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,5,4] => 2
[[1,1,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,4,1,5,2] => 3
[[1,1,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => 2
[[5],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[[5],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[4,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[[4,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[4,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[3,2],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[[3,2],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[3,2],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[3,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[[3,1,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[3,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[2,2,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[[2,2,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[2,2,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[2,1,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[[2,1,1,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[2,1,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[1,1,1,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,5] => 2
[[1,1,1,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,2,3,6,4] => 2
[[6],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[5,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[4,2],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[4,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[3,3],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[3,2,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[3,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[2,2,2],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[2,2,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[2,1,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[1,1,1,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => 2
[[7]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[6,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[5,2]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[5,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[4,3]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[4,2,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[4,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[3,3,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[3,2,2]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[3,2,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[3,1,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[2,2,2,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[2,2,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[2,1,1,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[1,1,1,1,1,1,1]] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,8,7] => 1
[[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => 1
[[2],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => 2
[[2],[2],[1],[1],[1],[1]] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => 2
[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => 2
[[2],[2],[2],[2]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => 1
[[1,1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7] => 2
[[1,1],[1,1],[1],[1],[1],[1]] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,6,1,3,4,5,7] => 2
[[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => 2
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,4,5,6] => 1
[[3],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => 2
[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => 3
[[3],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => 3
[[3],[3],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => 2
[[3],[3],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 2
[[2,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => 2
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => 3
[[2,1],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => 3
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => 3
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => 3
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => 2
[[2,1],[2,1],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 2
[[2,1],[2,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 2
[[1,1,1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,3,4,5,6] => 2
[[1,1,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,5,6,1,3,4] => 3
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,3,5,1,4] => 3
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [2,1,4,3,5] => 2
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => 2
[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => 2
[[4],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[4],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[4],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 3
[[4],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => 1
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => 2
[[3,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[3,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[3,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[3,1],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 3
[[3,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 3
[[3,1],[3,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => 1
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => 2
[[2,2],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[2,2],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[2,2],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[2,2],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 3
[[2,2],[2,2]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => 1
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => 2
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[2,1,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[2,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[2,1,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 3
[[2,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 3
[[2,1,1],[2,1,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => 1
[[1,1,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => 2
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => 3
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4] => 2
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,4,5,2] => 3
[[1,1,1,1],[1,1,1,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,5,4,6] => 1
[[5],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 2
[[5],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[5],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[4,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 2
[[4,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[4,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[4,1],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[4,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[3,2],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 2
[[3,2],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[3,2],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[3,2],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[3,2],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[3,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 2
[[3,1,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[3,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[3,1,1],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[3,1,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[3,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[2,2,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 2
[[2,2,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[2,2,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[2,2,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[2,2,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 2
[[2,1,1,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[2,1,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[2,1,1,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[2,1,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => 2
[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,5,1,2,6,3] => 3
[[1,1,1,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => 2
[[6],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[6],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[5,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[5,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[5,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[4,2],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[4,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[4,2],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[4,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[4,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[4,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[3,3],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[3,3],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[3,3],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[3,2,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[3,2,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[3,2,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[3,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[3,1,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[3,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[2,2,2],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[2,2,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[2,2,2],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[2,2,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[2,2,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[2,2,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[2,1,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[2,1,1,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[2,1,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[1,1,1,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => 2
[[1,1,1,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,2,3,4,7,5] => 2
[[7],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[6,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[5,2],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[5,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[4,3],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[4,2,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[4,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[3,3,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[3,2,2],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[3,2,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[3,1,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[2,2,2,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[2,2,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[2,1,1,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[1,1,1,1,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => 2
[[8]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[7,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[6,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[6,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[5,3]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[5,2,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[5,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[4,4]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[4,3,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[4,2,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[4,2,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[4,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[3,3,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[3,3,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[3,2,2,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[3,2,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[3,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[2,2,2,2]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[2,2,2,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[2,2,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[2,1,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[1,1,1,1,1,1,1,1]] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,9,8] => 1
[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => 1
[[2],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => 2
[[2],[2],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => 2
[[2],[2],[2],[1],[1],[1]] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => 2
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => 2
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,9,1,3,4,5,6,7,8] => 2
[[1,1],[1,1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,7,1,3,4,5,6,8] => 2
[[1,1],[1,1],[1,1],[1],[1],[1]] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,5,1,3,4,6,7] => 2
[[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => 2
[[3],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => 2
[[3],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => 3
[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => 3
[[3],[2],[2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => 2
[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => 2
[[3],[3],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 3
[[3],[3],[3]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => 1
[[2,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => 2
[[2,1],[2],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => 3
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => 3
[[2,1],[2],[2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => 2
[[2,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => 3
[[2,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => 3
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => 2
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => 2
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 3
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 3
[[2,1],[2,1],[2,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => 1
[[1,1,1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,1,8,3,4,5,6,7] => 2
[[1,1,1],[1,1],[1],[1],[1],[1]] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,6,7,1,3,4,5] => 3
[[1,1,1],[1,1],[1,1],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,6,1,3,5] => 3
[[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,6,2,4,5] => 2
[[1,1,1],[1,1,1],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => 2
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5] => 3
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,4,3,5,6] => 1
[[4],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => 2
[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[4],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[4],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 3
[[4],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[4],[4],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => 2
[[3,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => 2
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[3,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[3,1],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 3
[[3,1],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 3
[[3,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[3,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[3,1],[3,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => 2
[[2,2],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => 2
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[2,2],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 3
[[2,2],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[2,2],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[2,2],[2,2],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => 2
[[2,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => 2
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[2,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 3
[[2,1,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[2,1,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 3
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[2,1,1],[2,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => 2
[[1,1,1,1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,3,7,4,5,6] => 2
[[1,1,1,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,5,1,6,3,4] => 3
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => 3
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => 3
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2] => 3
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,1,2,5,3,6] => 2
[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 2
[[5],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[5],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[5],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[5],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 2
[[4,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[4,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[4,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[4,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[4,1],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[4,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[4,1],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[4,1],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 2
[[3,2],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[3,2],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[3,2],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[3,2],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[3,2],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[3,2],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[3,2],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[3,2],[2,2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 2
[[3,1,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[3,1,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[3,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[3,1,1],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[3,1,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[3,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[3,1,1],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[3,1,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 2
[[2,2,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[2,2,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[2,2,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[2,2,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[2,2,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[2,2,1],[2,2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[2,2,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[2,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 2
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[2,1,1,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[2,1,1,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[2,1,1,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[2,1,1,1],[1,1,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[1,1,1,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,6,5] => 2
[[1,1,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,5,1,2,6,4] => 3
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => 2
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,5,2,6,3] => 3
[[1,1,1,1,1],[1,1,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => 2
[[6],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[6],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[6],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[5,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[5,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[5,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[5,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[5,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[4,2],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[4,2],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[4,2],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[4,2],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[4,2],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[4,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[4,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[4,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[4,1,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[4,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[4,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,3],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[3,3],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[3,3],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[3,3],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,3],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,2,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[3,2,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[3,2,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[3,2,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,2,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,2,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,1,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[3,1,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[3,1,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[3,1,1,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,1,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[3,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[2,2,2],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[2,2,2],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[2,2,2],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[2,2,2],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[2,2,2],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[2,2,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[2,2,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[2,2,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[2,2,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[2,2,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[2,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[2,1,1,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[2,1,1,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[2,1,1,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[2,1,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[1,1,1,1,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => 2
[[1,1,1,1,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,6,1,2,3,7,4] => 3
[[1,1,1,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,2,6,3,4,7,5] => 2
[[7],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[7],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[6,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[6,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[6,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[5,2],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[5,2],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[5,2],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[5,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[5,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[5,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[4,3],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[4,3],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[4,3],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[4,2,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[4,2,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[4,2,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[4,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[4,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[4,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,3,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[3,3,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,3,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,2,2],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[3,2,2],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,2,2],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,2,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[3,2,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,2,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,1,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[3,1,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[3,1,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[2,2,2,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[2,2,2,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[2,2,2,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[2,2,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[2,2,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[2,2,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[2,1,1,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[2,1,1,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[2,1,1,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[1,1,1,1,1,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => 2
[[1,1,1,1,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,2,3,4,5,8,6] => 2
[[8],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[7,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[6,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[6,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[5,3],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[5,2,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[5,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[4,4],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[4,3,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[4,2,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[4,2,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[4,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[3,3,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[3,3,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[3,2,2,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[3,2,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[3,1,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[2,2,2,2],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[2,2,2,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[2,2,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[2,1,1,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[1,1,1,1,1,1,1,1],[1]] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => 2
[[9]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[8,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[7,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[7,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[6,3]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[6,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[6,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[5,4]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[5,3,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[5,2,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[5,2,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[5,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[4,4,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[4,3,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[4,3,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[4,2,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[4,2,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[4,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[3,3,3]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[3,3,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[3,3,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[3,2,2,2]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[3,2,2,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[3,2,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[3,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[2,2,2,2,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[2,2,2,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[2,2,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[2,1,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[1,1,1,1,1,1,1,1,1]] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9] => 1
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => 1
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => 2
[[2],[2],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => 2
[[2],[2],[2],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => 2
[[2],[2],[2],[2],[1],[1]] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => 2
[[2],[2],[2],[2],[2]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => 1
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,10,1,3,4,5,6,7,8,9] => 2
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,8,1,3,4,5,6,7,9] => 2
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,6,1,3,4,5,7,8] => 2
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,1,3,5,6,7] => 2
[[1,1],[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,4,5,6,7] => 1
[[3],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => 2
[[3],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => 3
[[3],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => 3
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => 3
[[3],[3],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => 2
[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => 3
[[3],[3],[2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => 2
[[3],[3],[3],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => 2
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => 2
[[2,1],[2],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => 3
[[2,1],[2],[2],[1],[1],[1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => 3
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => 3
[[2,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => 3
[[2,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => 3
[[2,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => 3
[[2,1],[2,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => 2
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => 3
[[2,1],[2,1],[2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => 2
[[2,1],[2,1],[1,1],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => 3
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => 2
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => 2
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,1,9,3,4,5,6,7,8] => 2
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,7,8,1,3,4,5,6] => 3
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,5,7,1,3,4,6] => 3
[[1,1,1],[1,1],[1,1],[1,1],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,3,6,1,4,5] => 3
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,3,4,5,7] => 2
[[1,1,1],[1,1,1],[1,1],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => 3
[[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => 2
[[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => 2
[[4],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => 2
[[4],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[4],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 3
[[4],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[4],[3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 2
[[4],[4],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => 2
[[4],[4],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[3,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => 2
[[3,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[3,1],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[3,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[3,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 3
[[3,1],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[3,1],[3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 2
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 3
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[3,1],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 2
[[3,1],[3,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => 2
[[3,1],[3,1],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[3,1],[3,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[2,2],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => 2
[[2,2],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[2,2],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[2,2],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[2,2],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 3
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[2,2],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 2
[[2,2],[2,2],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => 2
[[2,2],[2,2],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[2,2],[2,2],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[2,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => 2
[[2,1,1],[2],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[2,1,1],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[2,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[2,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[2,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[2,1,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 3
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[2,1,1],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 2
[[2,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 3
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 2
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => 2
[[2,1,1],[2,1,1],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,1,3,8,4,5,6,7] => 2
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,6,1,7,3,4,5] => 3
[[1,1,1,1],[1,1],[1,1],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => 3
[[1,1,1,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => 2
[[1,1,1,1],[1,1,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,6,3,4] => 3
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => 4
[[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => 2
[[1,1,1,1],[1,1,1,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => 2
[[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => 2
[[5],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 2
[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[5],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[5],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[5],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[5],[4],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[5],[5]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 1
[[4,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 2
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[4,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[4,1],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[4,1],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[4,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[4,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[4,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[4,1],[4],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[4,1],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[4,1],[4,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 1
[[3,2],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 2
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[3,2],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[3,2],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[3,2],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[3,2],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[3,2],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[3,2],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[3,2],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[3,2],[2,2],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[3,2],[3,2]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 1
[[3,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 2
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[3,1,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[3,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[3,1,1],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[3,1,1],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[3,1,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[3,1,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[3,1,1],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[3,1,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[3,1,1],[3,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 1
[[2,2,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 2
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[2,2,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[2,2,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[2,2,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[2,2,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[2,2,1],[2,2],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[2,2,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[2,2,1],[2,2,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 1
[[2,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 2
[[2,1,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[2,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[2,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[2,1,1,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[2,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[2,1,1,1],[2,1,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 1
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,3,4,7,5,6] => 2
[[1,1,1,1,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,5,1,3,6,4] => 3
[[1,1,1,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,4,1,2,6,5] => 3
[[1,1,1,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => 3
[[1,1,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,5,2,6,3] => 3
[[1,1,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,2,5,6,3] => 3
[[1,1,1,1,1],[1,1,1,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,2,3,4,6,5,7] => 1
[[6],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[6],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[6],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[6],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[6],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[5,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[5,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[5,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[5,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[5,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[5,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[5,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[5,1],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[5,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[4,2],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[4,2],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[4,2],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[4,2],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[4,2],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[4,2],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[4,2],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[4,2],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[4,2],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[4,2],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[4,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[4,1,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[4,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[4,1,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[4,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[4,1,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[4,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[4,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[4,1,1],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[4,1,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[4,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,3],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[3,3],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[3,3],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[3,3],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[3,3],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[3,3],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,3],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,3],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,3],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,2,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[3,2,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[3,2,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[3,2,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[3,2,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[3,2,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,2,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,2,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,2,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,2,1],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,2,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[3,1,1,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[3,1,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[3,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[3,1,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[3,1,1,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,1,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,1,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[3,1,1,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,1,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[3,1,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[2,2,2],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[2,2,2],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[2,2,2],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[2,2,2],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[2,2,2],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[2,2,2],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[2,2,2],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[2,2,2],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[2,2,2],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[2,2,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[2,2,1,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[2,2,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[2,2,1,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[2,2,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[2,2,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[2,2,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[2,2,1,1],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[2,2,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[2,2,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[2,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[2,1,1,1,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[2,1,1,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[2,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[2,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[2,1,1,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[2,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[2,1,1,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[2,1,1,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => 2
[[1,1,1,1,1,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,6,1,2,3,7,5] => 3
[[1,1,1,1,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,5,2,3,4,7,6] => 2
[[1,1,1,1,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,6,2,3,7,4] => 3
[[1,1,1,1,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,2,3,6,4,7,5] => 2
[[7],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[7],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[7],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[6,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[6,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[6,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[6,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[6,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[5,2],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[5,2],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[5,2],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[5,2],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[5,2],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[5,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[5,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[5,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[5,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[5,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[5,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,3],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[4,3],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[4,3],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[4,3],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,3],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,2,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[4,2,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[4,2,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[4,2,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,2,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,2,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[4,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[4,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[4,1,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[4,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,3,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[3,3,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,3,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,3,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,3,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,3,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,2,2],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[3,2,2],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,2,2],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,2,2],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,2,2],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,2,2],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,2,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[3,2,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,2,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,2,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,2,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,2,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[3,1,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,1,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[3,1,1,1,1],[3]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,1,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[3,1,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[2,2,2,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[2,2,2,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[2,2,2,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[2,2,2,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[2,2,2,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[2,2,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[2,2,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[2,2,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[2,2,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[2,2,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[2,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[2,1,1,1,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[2,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[2,1,1,1,1,1],[2,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[2,1,1,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[1,1,1,1,1,1,1],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => 2
[[1,1,1,1,1,1,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,7,1,2,3,4,8,5] => 3
[[1,1,1,1,1,1,1],[1,1,1]] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,2,7,3,4,5,8,6] => 2
[[8],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[8],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[7,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[7,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[7,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[6,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[6,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[6,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[6,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[6,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[6,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[5,3],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[5,3],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[5,3],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[5,2,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[5,2,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[5,2,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[5,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[5,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[5,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,4],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[4,4],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,4],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,3,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[4,3,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,3,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,2,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[4,2,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,2,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,2,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[4,2,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,2,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[4,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[4,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,3,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[3,3,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,3,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,3,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[3,3,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,3,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,2,2,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[3,2,2,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,2,2,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,2,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[3,2,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,2,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[3,1,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[3,1,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,2,2,2],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[2,2,2,2],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,2,2,2],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,2,2,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[2,2,2,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,2,2,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,2,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[2,2,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,2,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[2,1,1,1,1,1,1],[2]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[2,1,1,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[1,1,1,1,1,1,1,1],[1],[1]] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => 2
[[1,1,1,1,1,1,1,1],[1,1]] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,8,2,3,4,5,6,9,7] => 2
[[9],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[8,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[7,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[7,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[6,3],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[6,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[6,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[5,4],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[5,3,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[5,2,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[5,2,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[5,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[4,4,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[4,3,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[4,3,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[4,2,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[4,2,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[4,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[3,3,3],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[3,3,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[3,3,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[3,2,2,2],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[3,2,2,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[3,2,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[3,1,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[2,2,2,2,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[2,2,2,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[2,2,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[2,1,1,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[1,1,1,1,1,1,1,1,1],[1]] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => 2
[[10]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[9,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[8,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[8,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[7,3]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[7,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[7,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[6,4]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[6,3,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[6,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[6,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[6,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[5,5]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[5,4,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[5,3,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[5,3,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[5,2,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[5,2,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[5,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,4,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,4,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,3,3]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,3,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,3,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,2,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,2,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,2,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[4,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,3,3,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,3,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,3,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,3,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,2,2,2,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,2,2,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,2,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[3,1,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[2,2,2,2,2]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[2,2,2,2,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[2,2,2,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[2,2,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[2,1,1,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[[1,1,1,1,1,1,1,1,1,1]] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,2,3,4,5,6,7,8,9,11,10] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,5 8,16 17,27,4 16,58,12 30,95,35 34,158,90 52,261,177,10
$F_{1} = q$
$F_{2} = 3\ q$
$F_{3} = 4\ q + 2\ q^{2}$
$F_{4} = 8\ q + 5\ q^{2}$
$F_{5} = 8\ q + 16\ q^{2}$
$F_{6} = 17\ q + 27\ q^{2} + 4\ q^{3}$
$F_{7} = 16\ q + 58\ q^{2} + 12\ q^{3}$
$F_{8} = 30\ q + 95\ q^{2} + 35\ q^{3}$
$F_{9} = 34\ q + 158\ q^{2} + 90\ q^{3}$
$F_{10} = 52\ q + 261\ q^{2} + 177\ q^{3} + 10\ q^{4}$
Description
The number of exclusive left-to-right maxima of a permutation.
This is the number of left-to-right maxima that are not right-to-left minima.
This is the number of left-to-right maxima that are not right-to-left minima.
Map
to partition
Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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