Identifier
-
Mp00036:
Gelfand-Tsetlin patterns
—to semistandard tableau⟶
Semistandard tableaux
Mp00077: Semistandard tableaux —shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000319: Integer partitions ⟶ ℤ (values match St000320The dinv adjustment of an integer partition.)
Values
[[1,1],[1]] => [[1],[2]] => [1,1] => [1] => 0
[[2,1],[1]] => [[1,2],[2]] => [2,1] => [1] => 0
[[2,1],[2]] => [[1,1],[2]] => [2,1] => [1] => 0
[[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1] => 0
[[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1] => 0
[[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1] => 0
[[3,1],[1]] => [[1,2,2],[2]] => [3,1] => [1] => 0
[[3,1],[2]] => [[1,1,2],[2]] => [3,1] => [1] => 0
[[3,1],[3]] => [[1,1,1],[2]] => [3,1] => [1] => 0
[[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [2] => 1
[[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => [1] => 0
[[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => [1] => 0
[[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1] => [1] => 0
[[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => [1] => 0
[[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1] => [1] => 0
[[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => [1] => 0
[[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => [1] => 0
[[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => [1] => 0
[[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,1] => 0
[[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1] => 0
[[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1] => 0
[[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1] => 0
[[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1] => 0
[[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1] => 0
[[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1] => 0
[[4,1],[1]] => [[1,2,2,2],[2]] => [4,1] => [1] => 0
[[4,1],[2]] => [[1,1,2,2],[2]] => [4,1] => [1] => 0
[[4,1],[3]] => [[1,1,1,2],[2]] => [4,1] => [1] => 0
[[4,1],[4]] => [[1,1,1,1],[2]] => [4,1] => [1] => 0
[[3,2],[2]] => [[1,1,2],[2,2]] => [3,2] => [2] => 1
[[3,2],[3]] => [[1,1,1],[2,2]] => [3,2] => [2] => 1
[[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1] => [1] => 0
[[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1] => [1] => 0
[[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [3,1] => [1] => 0
[[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1] => [1] => 0
[[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1] => [1] => 0
[[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1] => [1] => 0
[[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [3,1] => [1] => 0
[[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1] => [1] => 0
[[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1] => [1] => 0
[[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [3,1] => [1] => 0
[[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [3,1] => [1] => 0
[[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1] => [1] => 0
[[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1] => [1] => 0
[[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1] => [1] => 0
[[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1] => [1] => 0
[[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => [2] => 1
[[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2] => [2] => 1
[[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => [2] => 1
[[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2] => [2] => 1
[[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2] => [2] => 1
[[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [2] => 1
[[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1] => [1] => 0
[[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1] => [1] => 0
[[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1] => [1] => 0
[[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => [1] => 0
[[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => [1] => 0
[[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,1] => 0
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1] => 0
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1] => 0
[[5,1],[1]] => [[1,2,2,2,2],[2]] => [5,1] => [1] => 0
[[5,1],[2]] => [[1,1,2,2,2],[2]] => [5,1] => [1] => 0
[[5,1],[3]] => [[1,1,1,2,2],[2]] => [5,1] => [1] => 0
[[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1] => [1] => 0
[[5,1],[5]] => [[1,1,1,1,1],[2]] => [5,1] => [1] => 0
[[4,2],[2]] => [[1,1,2,2],[2,2]] => [4,2] => [2] => 1
[[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,2] => [2] => 1
[[4,2],[4]] => [[1,1,1,1],[2,2]] => [4,2] => [2] => 1
[[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3] => [3] => 2
[[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [4,1] => [1] => 0
>>> Load all 1055 entries. <<<[[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [4,1] => [1] => 0
[[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [4,1] => [1] => 0
[[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1] => [1] => 0
[[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [4,1] => [1] => 0
[[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [4,1] => [1] => 0
[[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1] => [1] => 0
[[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [4,1] => [1] => 0
[[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [4,1] => [1] => 0
[[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [4,1] => [1] => 0
[[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [4,1] => [1] => 0
[[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [4,1] => [1] => 0
[[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [4,1] => [1] => 0
[[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [4,1] => [1] => 0
[[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1] => [1] => 0
[[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [4,1] => [1] => 0
[[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,2] => [2] => 1
[[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,2] => [2] => 1
[[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,2] => [2] => 1
[[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [3,2] => [2] => 1
[[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,2] => [2] => 1
[[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,2] => [2] => 1
[[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [3,2] => [2] => 1
[[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [3,2] => [2] => 1
[[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [3,2] => [2] => 1
[[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [3,2] => [2] => 1
[[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [3,2] => [2] => 1
[[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,2] => [2] => 1
[[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [3,2] => [2] => 1
[[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,2] => [2] => 1
[[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [3,2] => [2] => 1
[[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1] => [1,1] => 0
[[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [2,2,1] => [2,1] => 1
[[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [2,2,1] => [2,1] => 1
[[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [2,2,1] => [2,1] => 1
[[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1] => [1] => 0
[[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1] => [1] => 0
[[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,2] => [2] => 1
[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => [2] => 1
[[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2] => [2] => 1
[[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => [2] => 1
[[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2] => [2] => 1
[[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2] => [2] => 1
[[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [2] => 1
[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1] => [1,1] => 0
[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1] => [1,1,1] => 0
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => [1] => 0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,1] => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1] => 0
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1] => 0
[[6,1],[1]] => [[1,2,2,2,2,2],[2]] => [6,1] => [1] => 0
[[6,1],[2]] => [[1,1,2,2,2,2],[2]] => [6,1] => [1] => 0
[[6,1],[3]] => [[1,1,1,2,2,2],[2]] => [6,1] => [1] => 0
[[6,1],[4]] => [[1,1,1,1,2,2],[2]] => [6,1] => [1] => 0
[[6,1],[5]] => [[1,1,1,1,1,2],[2]] => [6,1] => [1] => 0
[[6,1],[6]] => [[1,1,1,1,1,1],[2]] => [6,1] => [1] => 0
[[5,2],[2]] => [[1,1,2,2,2],[2,2]] => [5,2] => [2] => 1
[[5,2],[3]] => [[1,1,1,2,2],[2,2]] => [5,2] => [2] => 1
[[5,2],[4]] => [[1,1,1,1,2],[2,2]] => [5,2] => [2] => 1
[[5,2],[5]] => [[1,1,1,1,1],[2,2]] => [5,2] => [2] => 1
[[4,3],[3]] => [[1,1,1,2],[2,2,2]] => [4,3] => [3] => 2
[[4,3],[4]] => [[1,1,1,1],[2,2,2]] => [4,3] => [3] => 2
[[5,1,0],[1,0],[0]] => [[2,3,3,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[1,0],[1]] => [[1,3,3,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[1,1],[1]] => [[1,3,3,3,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[2,0],[0]] => [[2,2,3,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[2,0],[1]] => [[1,2,3,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[2,0],[2]] => [[1,1,3,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[2,1],[1]] => [[1,2,3,3,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[2,1],[2]] => [[1,1,3,3,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[3,0],[0]] => [[2,2,2,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[3,0],[1]] => [[1,2,2,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[3,0],[2]] => [[1,1,2,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[3,0],[3]] => [[1,1,1,3,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[3,1],[1]] => [[1,2,2,3,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[3,1],[2]] => [[1,1,2,3,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[3,1],[3]] => [[1,1,1,3,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[4,0],[0]] => [[2,2,2,2,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[4,0],[1]] => [[1,2,2,2,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[4,0],[2]] => [[1,1,2,2,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[4,0],[3]] => [[1,1,1,2,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[4,0],[4]] => [[1,1,1,1,3],[3]] => [5,1] => [1] => 0
[[5,1,0],[4,1],[1]] => [[1,2,2,2,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[4,1],[2]] => [[1,1,2,2,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[4,1],[3]] => [[1,1,1,2,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[4,1],[4]] => [[1,1,1,1,3],[2]] => [5,1] => [1] => 0
[[5,1,0],[5,0],[0]] => [[2,2,2,2,2],[3]] => [5,1] => [1] => 0
[[5,1,0],[5,0],[1]] => [[1,2,2,2,2],[3]] => [5,1] => [1] => 0
[[5,1,0],[5,0],[2]] => [[1,1,2,2,2],[3]] => [5,1] => [1] => 0
[[5,1,0],[5,0],[3]] => [[1,1,1,2,2],[3]] => [5,1] => [1] => 0
[[5,1,0],[5,0],[4]] => [[1,1,1,1,2],[3]] => [5,1] => [1] => 0
[[5,1,0],[5,0],[5]] => [[1,1,1,1,1],[3]] => [5,1] => [1] => 0
[[5,1,0],[5,1],[1]] => [[1,2,2,2,2],[2]] => [5,1] => [1] => 0
[[5,1,0],[5,1],[2]] => [[1,1,2,2,2],[2]] => [5,1] => [1] => 0
[[5,1,0],[5,1],[3]] => [[1,1,1,2,2],[2]] => [5,1] => [1] => 0
[[5,1,0],[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1] => [1] => 0
[[5,1,0],[5,1],[5]] => [[1,1,1,1,1],[2]] => [5,1] => [1] => 0
[[4,2,0],[2,0],[0]] => [[2,2,3,3],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[2,0],[1]] => [[1,2,3,3],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[2,0],[2]] => [[1,1,3,3],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[2,1],[1]] => [[1,2,3,3],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[2,1],[2]] => [[1,1,3,3],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[2,2],[2]] => [[1,1,3,3],[2,2]] => [4,2] => [2] => 1
[[4,2,0],[3,0],[0]] => [[2,2,2,3],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[3,0],[1]] => [[1,2,2,3],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[3,0],[2]] => [[1,1,2,3],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[3,0],[3]] => [[1,1,1,3],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[3,1],[1]] => [[1,2,2,3],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[3,1],[2]] => [[1,1,2,3],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[3,1],[3]] => [[1,1,1,3],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[3,2],[2]] => [[1,1,2,3],[2,2]] => [4,2] => [2] => 1
[[4,2,0],[3,2],[3]] => [[1,1,1,3],[2,2]] => [4,2] => [2] => 1
[[4,2,0],[4,0],[0]] => [[2,2,2,2],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[4,0],[1]] => [[1,2,2,2],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[4,0],[2]] => [[1,1,2,2],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[4,0],[3]] => [[1,1,1,2],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[4,0],[4]] => [[1,1,1,1],[3,3]] => [4,2] => [2] => 1
[[4,2,0],[4,1],[1]] => [[1,2,2,2],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[4,1],[2]] => [[1,1,2,2],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[4,1],[3]] => [[1,1,1,2],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[4,1],[4]] => [[1,1,1,1],[2,3]] => [4,2] => [2] => 1
[[4,2,0],[4,2],[2]] => [[1,1,2,2],[2,2]] => [4,2] => [2] => 1
[[4,2,0],[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,2] => [2] => 1
[[4,2,0],[4,2],[4]] => [[1,1,1,1],[2,2]] => [4,2] => [2] => 1
[[4,1,1],[1,1],[1]] => [[1,3,3,3],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[2,1],[1]] => [[1,2,3,3],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[2,1],[2]] => [[1,1,3,3],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[3,1],[1]] => [[1,2,2,3],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[3,1],[2]] => [[1,1,2,3],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[3,1],[3]] => [[1,1,1,3],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[4,1],[1]] => [[1,2,2,2],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[4,1],[2]] => [[1,1,2,2],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[4,1],[3]] => [[1,1,1,2],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1],[4,1],[4]] => [[1,1,1,1],[2],[3]] => [4,1,1] => [1,1] => 0
[[3,3,0],[3,0],[0]] => [[2,2,2],[3,3,3]] => [3,3] => [3] => 2
[[3,3,0],[3,0],[1]] => [[1,2,2],[3,3,3]] => [3,3] => [3] => 2
[[3,3,0],[3,0],[2]] => [[1,1,2],[3,3,3]] => [3,3] => [3] => 2
[[3,3,0],[3,0],[3]] => [[1,1,1],[3,3,3]] => [3,3] => [3] => 2
[[3,3,0],[3,1],[1]] => [[1,2,2],[2,3,3]] => [3,3] => [3] => 2
[[3,3,0],[3,1],[2]] => [[1,1,2],[2,3,3]] => [3,3] => [3] => 2
[[3,3,0],[3,1],[3]] => [[1,1,1],[2,3,3]] => [3,3] => [3] => 2
[[3,3,0],[3,2],[2]] => [[1,1,2],[2,2,3]] => [3,3] => [3] => 2
[[3,3,0],[3,2],[3]] => [[1,1,1],[2,2,3]] => [3,3] => [3] => 2
[[3,3,0],[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3] => [3] => 2
[[3,2,1],[2,1],[1]] => [[1,2,3],[2,3],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1],[2,1],[2]] => [[1,1,3],[2,3],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1],[2,2],[2]] => [[1,1,3],[2,2],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1],[3,1],[1]] => [[1,2,2],[2,3],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1],[3,1],[2]] => [[1,1,2],[2,3],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1],[3,1],[3]] => [[1,1,1],[2,3],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1],[3,2],[2]] => [[1,1,2],[2,2],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1],[3,2],[3]] => [[1,1,1],[2,2],[3]] => [3,2,1] => [2,1] => 1
[[2,2,2],[2,2],[2]] => [[1,1],[2,2],[3,3]] => [2,2,2] => [2,2] => 1
[[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1] => [1] => 0
[[4,1,0,0],[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [4,1] => [1] => 0
[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]] => [3,2] => [2] => 1
[[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]] => [3,2] => [2] => 1
[[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,2] => [2] => 1
[[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [3,2] => [2] => 1
[[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [3,1,1] => [1,1] => 0
[[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1] => [1,1] => 0
[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [2,2,1] => [2,1] => 1
[[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [2,2,1] => [2,1] => 1
[[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => 0
[[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => 0
[[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => 0
[[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => 0
[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5,5],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,5],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,5],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,5],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,5],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[5]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1] => [1] => 0
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1] => [1] => 0
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,5]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,2] => [2] => 1
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => [2] => 1
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,5],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[5]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1] => [1,1] => 0
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1] => [1,1] => 0
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4],[5]] => [1,1,1,1] => [1,1,1] => 0
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4],[5]] => [1,1,1,1] => [1,1,1] => 0
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4],[5]] => [1,1,1,1] => [1,1,1] => 0
[[1,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3],[5]] => [1,1,1,1] => [1,1,1] => 0
[[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1] => [1,1,1] => 0
[[2,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,6],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,6],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,6],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,6],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,6],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,6],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[6]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => [1] => 0
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => [1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[6]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => [1,1] => 0
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => [1,1] => 0
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6],[7]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[7]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[7]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[7]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[7]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[7]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => [1] => 0
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => [1] => 0
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5]] => [4,1] => [1] => 0
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4]] => [4,1] => [1] => 0
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3]] => [4,1] => [1] => 0
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2]] => [4,1] => [1] => 0
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5]] => [3,2] => [2] => 1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5]] => [3,2] => [2] => 1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4]] => [3,2] => [2] => 1
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5]] => [3,2] => [2] => 1
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4]] => [3,2] => [2] => 1
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5]] => [3,1,1] => [1,1] => 0
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5]] => [3,1,1] => [1,1] => 0
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5]] => [3,1,1] => [1,1] => 0
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4]] => [3,1,1] => [1,1] => 0
[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3]] => [3,1,1] => [1,1] => 0
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5]] => [2,2,1] => [2,1] => 1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5]] => [2,2,1] => [2,1] => 1
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4]] => [2,2,1] => [2,1] => 1
[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3]] => [2,2,1] => [2,1] => 1
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5]] => [2,1,1,1] => [1,1,1] => 0
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5]] => [2,1,1,1] => [1,1,1] => 0
[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5]] => [2,1,1,1] => [1,1,1] => 0
[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4]] => [2,1,1,1] => [1,1,1] => 0
[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [1,1,1,1] => 0
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5,6],[2]] => [5,1] => [1] => 0
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5,6],[3]] => [5,1] => [1] => 0
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5,6],[4]] => [5,1] => [1] => 0
[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,6],[5]] => [5,1] => [1] => 0
[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5],[6]] => [5,1] => [1] => 0
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5,6],[2,4]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5,6],[3,4]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,6],[2,5]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,6],[3,5]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,6],[4,5]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2,6]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3,6]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4,6]] => [4,2] => [2] => 1
[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5,6]] => [4,2] => [2] => 1
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5,6],[2],[3]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5,6],[2],[4]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5,6],[3],[4]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,6],[2],[5]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,6],[3],[5]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,6],[4],[5]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2],[6]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3],[6]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4],[6]] => [4,1,1] => [1,1] => 0
[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5],[6]] => [4,1,1] => [1,1] => 0
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4,6]] => [3,3] => [3] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4,6]] => [3,3] => [3] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5,6]] => [3,3] => [3] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5,6]] => [3,3] => [3] => 2
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5,6]] => [3,3] => [3] => 2
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,6],[2,5],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2,5],[4]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3,5],[4]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2,4],[5]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3,4],[5]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2,6],[3]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,6],[4]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,6],[4]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,6],[5]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,6],[5]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,6],[5]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4],[6]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4],[6]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5],[6]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5],[6]] => [3,2,1] => [2,1] => 1
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5],[6]] => [3,2,1] => [2,1] => 1
[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5,6],[2],[3],[4]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,6],[2],[3],[5]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2],[4],[5]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3],[4],[5]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3],[6]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4],[6]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4],[6]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5],[6]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5],[6]] => [3,1,1,1] => [1,1,1] => 0
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => [1,1,1] => 0
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3,6]] => [2,2,2] => [2,2] => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4,6]] => [2,2,2] => [2,2] => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4,6]] => [2,2,2] => [2,2] => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5,6]] => [2,2,2] => [2,2] => 1
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5,6]] => [2,2,2] => [2,2] => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2,6],[3],[4]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,6],[3],[5]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,6],[4],[5]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,6],[4],[5]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3],[6]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4],[6]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4],[6]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5],[6]] => [2,2,1,1] => [2,1,1] => 1
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => [2,1,1] => 1
[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => [1,1,1,1] => 0
[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => [1,1,1,1] => 0
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => 0
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => 0
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => [1,1,1,1] => 0
[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => [1,1,1,1,1] => 0
[[4,3,2,1],[4,3,2],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,3],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,2],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,3],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,2],[4,2],[4]] => [[1,1,1,1],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,2],[4,2],[3]] => [[1,1,1,2],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,2],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,2],[4,2],[2]] => [[1,1,2,2],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,2],[3,2],[2]] => [[1,1,2,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,2],[4]] => [[1,1,1,1],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,2],[3]] => [[1,1,1,2],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,2],[2]] => [[1,1,2,2],[2,2,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[4,2],[4]] => [[1,1,1,1],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[4,2],[3]] => [[1,1,1,2],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[3,2,1],[3,2],[3]] => [[1,1,1,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[4,2],[2]] => [[1,1,2,2],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[3,2],[2]] => [[1,1,2,3],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[3,2,1],[3,2],[2]] => [[1,1,2,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,1],[4]] => [[1,1,1,1],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,1],[3]] => [[1,1,1,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[3,1],[3]] => [[1,1,1,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,1],[2]] => [[1,1,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[3,1],[2]] => [[1,1,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[4,1],[4]] => [[1,1,1,1],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[4,1],[3]] => [[1,1,1,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[3,1],[3]] => [[1,1,1,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[3,2,1],[3,1],[3]] => [[1,1,1,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[4,1],[2]] => [[1,1,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[3,1],[2]] => [[1,1,2,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[3,2,1],[3,1],[2]] => [[1,1,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[2,1],[2]] => [[1,1,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[3,2,1],[2,1],[2]] => [[1,1,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[4,1],[1]] => [[1,2,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,3,1],[3,1],[1]] => [[1,2,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[4,1],[1]] => [[1,2,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[3,1],[1]] => [[1,2,2,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[3,2,1],[3,1],[1]] => [[1,2,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[4,2,1],[2,1],[1]] => [[1,2,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
[[4,3,2,1],[3,2,1],[2,1],[1]] => [[1,2,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => [3,2,1] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The spin of an integer partition.
The Ferrers shape of an integer partition $\lambda$ can be decomposed into border strips. The spin is then defined to be the total number of crossings of border strips of $\lambda$ with the vertical lines in the Ferrers shape.
The following example is taken from Appendix B in [1]: Let $\lambda = (5,5,4,4,2,1)$. Removing the border strips successively yields the sequence of partitions
$$(5,5,4,4,2,1), (4,3,3,1), (2,2), (1), ().$$
The first strip $(5,5,4,4,2,1) \setminus (4,3,3,1)$ crosses $4$ times, the second strip $(4,3,3,1) \setminus (2,2)$ crosses $3$ times, the strip $(2,2) \setminus (1)$ crosses $1$ time, and the remaining strip $(1) \setminus ()$ does not cross.
This yields the spin of $(5,5,4,4,2,1)$ to be $4+3+1 = 8$.
The Ferrers shape of an integer partition $\lambda$ can be decomposed into border strips. The spin is then defined to be the total number of crossings of border strips of $\lambda$ with the vertical lines in the Ferrers shape.
The following example is taken from Appendix B in [1]: Let $\lambda = (5,5,4,4,2,1)$. Removing the border strips successively yields the sequence of partitions
$$(5,5,4,4,2,1), (4,3,3,1), (2,2), (1), ().$$
The first strip $(5,5,4,4,2,1) \setminus (4,3,3,1)$ crosses $4$ times, the second strip $(4,3,3,1) \setminus (2,2)$ crosses $3$ times, the strip $(2,2) \setminus (1)$ crosses $1$ time, and the remaining strip $(1) \setminus ()$ does not cross.
This yields the spin of $(5,5,4,4,2,1)$ to be $4+3+1 = 8$.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Map
shape
Description
Return the shape of a tableau.
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