Identifier
-
Mp00311:
Plane partitions
—to partition⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St000980: Dyck paths ⟶ ℤ
Values
[[1]] => [1] => [1,0,1,0] => [1,0,1,0] => 0
[[1],[1]] => [1,1] => [1,0,1,1,0,0] => [1,0,1,1,0,0] => 0
[[2]] => [2] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 0
[[1,1]] => [2] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => 0
[[1],[1],[1]] => [1,1,1] => [1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0] => 0
[[2],[1]] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 0
[[1,1],[1]] => [2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 0
[[3]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => 0
[[2,1]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => 0
[[1,1,1]] => [3] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => 0
[[1],[1],[1],[1]] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 0
[[2],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => 0
[[2],[2]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 0
[[1,1],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => 0
[[1,1],[1,1]] => [2,2] => [1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 0
[[3],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[[2,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[[1,1,1],[1]] => [3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[[4]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[[3,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[[2,2]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[[1,1,1,1]] => [4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[[1],[1],[1],[1],[1]] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[2],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[[2],[2],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => 0
[[1,1],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[[1,1],[1,1],[1]] => [2,2,1] => [1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0] => 0
[[3],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[[3],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 0
[[2,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[[2,1],[2]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 0
[[2,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 0
[[1,1,1],[1],[1]] => [3,1,1] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[[1,1,1],[1,1]] => [3,2] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 0
[[4],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[3,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[2,2],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[1,1,1,1],[1]] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[5]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[1,1,1,1,1]] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[2],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[[2],[2],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[[2],[2],[2]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[[1,1],[1,1],[1],[1]] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[[1,1],[1,1],[1,1]] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[[3],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[3],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 0
[[3],[3]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[[2,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[2,1],[2],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 0
[[2,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 0
[[2,1],[2,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[[1,1,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[1,1,1],[1,1],[1]] => [3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 0
[[1,1,1],[1,1,1]] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[[4],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[4],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[3,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[3,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[3,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,2],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[2,2],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,2],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1],[2]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[1,1,1,1],[1],[1]] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[1,1,1,1],[1,1]] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[5],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[1,1,1,1,1],[1]] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[6]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[5,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,3]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,2,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[2,2,2]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[2,2,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[2,1,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[1,1,1,1,1,1]] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[2],[2],[1],[1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[[2],[2],[2],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
>>> Load all 851 entries. <<<[[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 0
[[3],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[3],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[3],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[3],[3],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[2,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[2,1],[2],[2]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[2,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[2,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[2,1],[2,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[1,1,1],[1],[1],[1],[1]] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[1,1,1],[1,1],[1,1]] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[1,1,1],[1,1,1],[1]] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[4],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[4],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[4],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[[3,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[3,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[3,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[3,1],[3]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[[3,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[[2,2],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[2,2],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,2],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,2],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[[2,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1],[2],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1],[2,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[[2,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[[1,1,1,1],[1],[1],[1]] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[[1,1,1,1],[1,1],[1]] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[1,1,1,1],[1,1,1]] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 0
[[5],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1],[2]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[1,1,1,1,1],[1],[1]] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[1,1,1,1,1],[1,1]] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[6],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,2],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,3],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,2],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,1,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[1,1,1,1,1,1],[1]] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[2],[2],[2],[1],[1]] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[[2],[2],[2],[2]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[3],[2],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[3],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[3],[3],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[3],[3],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[2,1],[2],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[2],[2],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[2,1],[1,1],[1],[1],[1]] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[2,1],[2,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[2,1],[2,1],[2]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[2,1],[2,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[[1,1,1],[1,1,1],[1,1]] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 0
[[4],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[4],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[4],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[4],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[4],[4]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[3,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[3,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[3,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[3,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[3,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[3,1],[3],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[3,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[3,1],[3,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[2,2],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,2],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[2,2],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,2],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[2,2],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,2],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[2,2],[2,2]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[2,1,1],[1],[1],[1],[1]] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,1,1],[2],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[2,1,1],[2],[2]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[2,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1],[2,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[2,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[2,1,1],[2,1,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[1,1,1,1],[1,1],[1],[1]] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[1,1,1,1],[1,1],[1,1]] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[[1,1,1,1],[1,1,1],[1]] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[1,1,1,1],[1,1,1,1]] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[5],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[5],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[4,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[4,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,2],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,2],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[3]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1],[2],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[2,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[1,1,1,1,1],[1],[1],[1]] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[1,1,1,1,1],[1,1],[1]] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[1,1,1,1,1],[1,1,1]] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[6],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[6],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,3],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,1,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,2],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,2],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,2],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1,1],[1],[1]] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,1,1,1,1],[2]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[1,1,1,1,1,1],[1,1]] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[7],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[6,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[5,2],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[5,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,3],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,2,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,3,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,2,2],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,2,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,1,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[2,2,2,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[2,2,1,1,1],[1]] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[2],[2],[2],[2],[1]] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[3],[2],[2],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[3],[2],[2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[3],[3],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[3],[3],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[3],[3],[3]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[2,1],[2],[2],[1],[1]] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[2],[2],[2]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[2,1],[2,1],[1],[1],[1]] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[2,1],[2],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[2,1],[2,1],[2,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[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] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 0
[[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[4],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[4],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[4],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[4],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[4],[4],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[3,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[3,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[3,1],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[3,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[3,1],[3],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[3,1],[3],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[3,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[3,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[3,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[3,1],[3,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[2,2],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,2],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[2,2],[1,1],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,2],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[2,2],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[2,2],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[2,2],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[2,2],[2,2],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[2,1,1],[2],[1],[1],[1]] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,1,1],[2],[2],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[2,1,1],[2,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[2,1,1],[2,1],[2]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[2,1,1],[2,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[2,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[2,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[2,1,1],[2,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[1,1,1,1],[1,1],[1,1],[1]] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[[1,1,1,1],[1,1,1],[1],[1]] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[5],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[5],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[5],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[5],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[4,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[4,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[4,1],[4]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[4,1],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[3,2],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,2],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,2],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[3,2],[2,2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[3,1,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[3],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[3,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[3,1,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[2,2,1],[1],[1],[1],[1]] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[2,2]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[2,2,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1],[2],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[2],[2]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[1,1],[1],[1]] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[2,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[2,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[2,1,1,1],[1,1,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[1,1,1,1,1],[1,1],[1,1]] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[1,1,1,1,1],[1,1,1],[1]] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[1,1,1,1,1],[1,1,1,1]] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[[6],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[6],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[6],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[5,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[5,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,2],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,2],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,2],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,3],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,3],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,3],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2,1],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,1,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1,1],[3]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,2],[1],[1],[1]] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,2],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,2],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,2],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,2],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1,1],[1,1],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,1,1,1,1],[2],[1]] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1,1],[2,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1,1],[1,1,1]] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[7],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[7],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[6,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[6,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[6,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,2],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[5,2],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,2],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,1,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[5,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,3],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,3],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,3],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,2,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,2,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,2,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,1,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,3,1],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,3,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,3,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2,2],[1],[1]] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,2,2],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2,2],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,2,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2,1,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,1,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[2,2,2,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,2,1],[1,1]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[2,2,1,1,1],[2]] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[2],[2],[2],[2],[2]] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[[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] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[3],[2],[2],[2],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[3],[3],[2],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[3],[3],[2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[3],[3],[3],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[2,1],[2],[2],[2],[1]] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[2,1],[2,1],[2],[1],[1]] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[2,1],[2],[2]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[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] => [1,1,0,0,1,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[4],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[4],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[4],[3],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[4],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[4],[3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[[4],[4],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[4],[4],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[3,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[3,1],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[3,1],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[3,1],[3],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[3,1],[3],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[3,1],[3],[3]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[[3,1],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[3,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[3,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[3,1],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[[3,1],[3,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[3,1],[3,1],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[3,1],[3,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[2,2],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[2,2],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[2,2],[1,1],[1,1],[1,1]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[2,2],[2,1],[1],[1],[1]] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,2],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2,2],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2,2],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[[2,2],[2,2],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,2],[2,2],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[2,2],[2,2],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[2,1,1],[2],[2],[1],[1]] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[2,1,1],[2],[2],[2]] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,1,1],[2,1],[2],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2,1,1],[2,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2,1,1],[2,1],[2,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[[2,1,1],[2,1,1],[1],[1]] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[2,1,1],[2,1,1],[2]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[2,1,1],[2,1,1],[1,1]] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[[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] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[1,1,1,1],[1,1,1],[1,1],[1]] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,1,0,0] => 0
[[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] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[5],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[5],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[5],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[5],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[5],[4],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[5],[5]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[4,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[4,1],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[4,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[4,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[4,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[4,1],[4],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[4,1],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[4,1],[4,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[3,2],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[1,1],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[3,2],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,2],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[3,2],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,2],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,2],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[3,2],[2,2],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[3,2],[3,2]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[3,1,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1],[3],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[3],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1],[3,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[3,1,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[3,1,1],[3,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[2,2,1],[2],[1],[1],[1]] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[1,1],[1,1],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[1,1,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1],[2,2],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[2,2,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[2,2,1],[2,2,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[2],[2],[1]] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1],[2,1],[1],[1]] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[2,1],[2]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[2,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[1,1,1],[1,1]] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[2,1,1,1],[2,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[2,1,1,1],[1,1,1,1],[1]] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[2,1,1,1],[2,1,1,1]] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[[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] => [1,0,1,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,0,0,0,1,0,1,0] => 0
[[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] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[[6],[1],[1],[1],[1]] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[6],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[6],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[6],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[6],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[5,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[5,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[5,1],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[5,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,2],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,2],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,2],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,2],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[4,2],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[4,2],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,1,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[4,1,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[4,1,1],[4]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[4,1,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[4,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,3],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[1,1],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,3],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,3],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,3],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[3,3],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[3,2,1],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2,1],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,2,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2,1],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,2,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[3,2,1],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[3,2,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[3,1,1,1],[3],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[3,1,1,1],[3,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[3,1,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[2,2,2],[2],[1],[1]] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,2],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,2],[1,1],[1,1]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,2],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,2],[1,1,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,2],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[2,2,2],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,2,1,1],[2,1],[1]] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,2,1,1],[2,2]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[2,2,1,1],[1,1,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[2,1,1,1,1],[2],[2]] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[2,1,1,1,1],[2,1,1]] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[[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] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[[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] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[[7],[1],[1],[1]] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[7],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[6,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[6,1],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[5,2],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[5,2],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[5,1,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,3],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[4,3],[1,1],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[4,2,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,3,1],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[3,2,2],[2],[1]] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[[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] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[[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] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
F1=1
F2=3
F3=6
F4=13
F5=24
F6=48
Description
The number of boxes weakly below the path and above the diagonal that lie below at least two peaks.
For example, the path 111011010000 has three peaks in positions 03,15,26. The boxes below 03 are 01,02,12, the boxes below 15 are 12,13,14,23,24,34, and the boxes below 26 are 23,24,25,34,35,45.
We thus obtain the four boxes in positions 12,23,24,34 that are below at least two peaks.
For example, the path 111011010000 has three peaks in positions 03,15,26. The boxes below 03 are 01,02,12, the boxes below 15 are 12,13,14,23,24,34, and the boxes below 26 are 23,24,25,34,35,45.
We thus obtain the four boxes in positions 12,23,24,34 that are below at least two peaks.
Map
bounce path
Description
Sends a Dyck path D of length 2n to its bounce path.
This path is formed by starting at the endpoint (n,n) of D and travelling west until encountering the first vertical step of D, then south until hitting the diagonal, then west again to hit D, etc. until the point (0,0) is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint (n,n) of D and travelling west until encountering the first vertical step of D, then south until hitting the diagonal, then west again to hit D, etc. until the point (0,0) is reached.
This map is the first part of the zeta map Mp00030zeta map.
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.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!