Identifier
-
Mp00078:
Gelfand-Tsetlin patterns
—Schuetzenberger involution⟶
Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
St000103: Semistandard tableaux ⟶ ℤ
Values
[[1,0],[0]] => [[1,0],[1]] => [[1]] => 1
[[2,0],[0]] => [[2,0],[2]] => [[1,1]] => 2
[[2,0],[1]] => [[2,0],[1]] => [[1,2]] => 3
[[2,0],[2]] => [[2,0],[0]] => [[2,2]] => 4
[[1,1],[1]] => [[1,1],[1]] => [[1],[2]] => 3
[[1,0,0],[0,0],[0]] => [[1,0,0],[1,0],[1]] => [[1]] => 1
[[3,0],[0]] => [[3,0],[3]] => [[1,1,1]] => 3
[[3,0],[1]] => [[3,0],[2]] => [[1,1,2]] => 4
[[3,0],[2]] => [[3,0],[1]] => [[1,2,2]] => 5
[[3,0],[3]] => [[3,0],[0]] => [[2,2,2]] => 6
[[2,1],[1]] => [[2,1],[2]] => [[1,1],[2]] => 4
[[2,1],[2]] => [[2,1],[1]] => [[1,2],[2]] => 5
[[2,0,0],[0,0],[0]] => [[2,0,0],[2,0],[2]] => [[1,1]] => 2
[[2,0,0],[1,0],[0]] => [[2,0,0],[2,0],[1]] => [[1,2]] => 3
[[2,0,0],[2,0],[0]] => [[2,0,0],[2,0],[0]] => [[2,2]] => 4
[[1,1,0],[1,0],[0]] => [[1,1,0],[1,1],[1]] => [[1],[2]] => 3
[[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => 1
[[4,0],[0]] => [[4,0],[4]] => [[1,1,1,1]] => 4
[[4,0],[1]] => [[4,0],[3]] => [[1,1,1,2]] => 5
[[4,0],[2]] => [[4,0],[2]] => [[1,1,2,2]] => 6
[[4,0],[3]] => [[4,0],[1]] => [[1,2,2,2]] => 7
[[4,0],[4]] => [[4,0],[0]] => [[2,2,2,2]] => 8
[[3,1],[1]] => [[3,1],[3]] => [[1,1,1],[2]] => 5
[[3,1],[2]] => [[3,1],[2]] => [[1,1,2],[2]] => 6
[[3,1],[3]] => [[3,1],[1]] => [[1,2,2],[2]] => 7
[[2,2],[2]] => [[2,2],[2]] => [[1,1],[2,2]] => 6
[[3,0,0],[0,0],[0]] => [[3,0,0],[3,0],[3]] => [[1,1,1]] => 3
[[3,0,0],[1,0],[0]] => [[3,0,0],[3,0],[2]] => [[1,1,2]] => 4
[[3,0,0],[1,0],[1]] => [[3,0,0],[2,0],[2]] => [[1,1,3]] => 5
[[3,0,0],[2,0],[0]] => [[3,0,0],[3,0],[1]] => [[1,2,2]] => 5
[[3,0,0],[2,0],[1]] => [[3,0,0],[2,0],[1]] => [[1,2,3]] => 6
[[3,0,0],[2,0],[2]] => [[3,0,0],[1,0],[1]] => [[1,3,3]] => 7
[[3,0,0],[3,0],[0]] => [[3,0,0],[3,0],[0]] => [[2,2,2]] => 6
[[3,0,0],[3,0],[1]] => [[3,0,0],[2,0],[0]] => [[2,2,3]] => 7
[[3,0,0],[3,0],[2]] => [[3,0,0],[1,0],[0]] => [[2,3,3]] => 8
[[3,0,0],[3,0],[3]] => [[3,0,0],[0,0],[0]] => [[3,3,3]] => 9
[[2,1,0],[1,0],[0]] => [[2,1,0],[2,1],[2]] => [[1,1],[2]] => 4
[[2,1,0],[1,0],[1]] => [[2,1,0],[2,0],[2]] => [[1,1],[3]] => 5
[[2,1,0],[1,1],[1]] => [[2,1,0],[2,0],[1]] => [[1,2],[3]] => 6
[[2,1,0],[2,0],[0]] => [[2,1,0],[2,1],[1]] => [[1,2],[2]] => 5
[[2,1,0],[2,0],[1]] => [[2,1,0],[1,1],[1]] => [[1,3],[2]] => 6
[[2,1,0],[2,0],[2]] => [[2,1,0],[1,0],[1]] => [[1,3],[3]] => 7
[[2,1,0],[2,1],[1]] => [[2,1,0],[2,0],[0]] => [[2,2],[3]] => 7
[[2,1,0],[2,1],[2]] => [[2,1,0],[1,0],[0]] => [[2,3],[3]] => 8
[[1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1]] => [[1],[2],[3]] => 6
[[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => 2
[[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => 3
[[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => 4
[[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => 3
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => 1
[[5,0],[0]] => [[5,0],[5]] => [[1,1,1,1,1]] => 5
[[5,0],[1]] => [[5,0],[4]] => [[1,1,1,1,2]] => 6
[[5,0],[2]] => [[5,0],[3]] => [[1,1,1,2,2]] => 7
[[5,0],[3]] => [[5,0],[2]] => [[1,1,2,2,2]] => 8
[[5,0],[4]] => [[5,0],[1]] => [[1,2,2,2,2]] => 9
[[5,0],[5]] => [[5,0],[0]] => [[2,2,2,2,2]] => 10
[[4,1],[1]] => [[4,1],[4]] => [[1,1,1,1],[2]] => 6
[[4,1],[2]] => [[4,1],[3]] => [[1,1,1,2],[2]] => 7
[[4,1],[3]] => [[4,1],[2]] => [[1,1,2,2],[2]] => 8
[[4,1],[4]] => [[4,1],[1]] => [[1,2,2,2],[2]] => 9
[[3,2],[2]] => [[3,2],[3]] => [[1,1,1],[2,2]] => 7
[[3,2],[3]] => [[3,2],[2]] => [[1,1,2],[2,2]] => 8
[[4,0,0],[0,0],[0]] => [[4,0,0],[4,0],[4]] => [[1,1,1,1]] => 4
[[4,0,0],[1,0],[0]] => [[4,0,0],[4,0],[3]] => [[1,1,1,2]] => 5
[[4,0,0],[1,0],[1]] => [[4,0,0],[3,0],[3]] => [[1,1,1,3]] => 6
[[4,0,0],[2,0],[0]] => [[4,0,0],[4,0],[2]] => [[1,1,2,2]] => 6
[[4,0,0],[2,0],[1]] => [[4,0,0],[3,0],[2]] => [[1,1,2,3]] => 7
[[4,0,0],[2,0],[2]] => [[4,0,0],[2,0],[2]] => [[1,1,3,3]] => 8
[[4,0,0],[3,0],[0]] => [[4,0,0],[4,0],[1]] => [[1,2,2,2]] => 7
[[4,0,0],[3,0],[1]] => [[4,0,0],[3,0],[1]] => [[1,2,2,3]] => 8
[[4,0,0],[3,0],[2]] => [[4,0,0],[2,0],[1]] => [[1,2,3,3]] => 9
[[4,0,0],[3,0],[3]] => [[4,0,0],[1,0],[1]] => [[1,3,3,3]] => 10
[[4,0,0],[4,0],[0]] => [[4,0,0],[4,0],[0]] => [[2,2,2,2]] => 8
[[4,0,0],[4,0],[1]] => [[4,0,0],[3,0],[0]] => [[2,2,2,3]] => 9
[[4,0,0],[4,0],[2]] => [[4,0,0],[2,0],[0]] => [[2,2,3,3]] => 10
[[4,0,0],[4,0],[3]] => [[4,0,0],[1,0],[0]] => [[2,3,3,3]] => 11
[[4,0,0],[4,0],[4]] => [[4,0,0],[0,0],[0]] => [[3,3,3,3]] => 12
[[3,1,0],[1,0],[0]] => [[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => 5
[[3,1,0],[1,0],[1]] => [[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => 6
[[3,1,0],[1,1],[1]] => [[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => 7
[[3,1,0],[2,0],[0]] => [[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => 6
[[3,1,0],[2,0],[1]] => [[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => 7
[[3,1,0],[2,0],[2]] => [[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => 8
[[3,1,0],[2,1],[1]] => [[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => 8
[[3,1,0],[2,1],[2]] => [[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => 9
[[3,1,0],[3,0],[0]] => [[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => 7
[[3,1,0],[3,0],[1]] => [[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => 8
[[3,1,0],[3,0],[2]] => [[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => 9
[[3,1,0],[3,0],[3]] => [[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => 10
[[3,1,0],[3,1],[1]] => [[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => 9
[[3,1,0],[3,1],[2]] => [[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => 10
[[3,1,0],[3,1],[3]] => [[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => 11
[[2,2,0],[2,0],[0]] => [[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => 6
[[2,2,0],[2,0],[1]] => [[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => 7
[[2,2,0],[2,0],[2]] => [[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => 8
[[2,2,0],[2,1],[1]] => [[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => 8
[[2,2,0],[2,1],[2]] => [[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => 9
[[2,2,0],[2,2],[2]] => [[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => 10
[[2,1,1],[1,1],[1]] => [[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => 7
[[2,1,1],[2,1],[1]] => [[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => 8
[[2,1,1],[2,1],[2]] => [[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => 9
>>> Load all 765 entries. <<<[[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => 3
[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => 4
[[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => 5
[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => 5
[[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => 6
[[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => 7
[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => 6
[[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => 7
[[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => 8
[[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => 9
[[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => 4
[[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => 5
[[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => 6
[[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => 5
[[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => 6
[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => 7
[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => 7
[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => 8
[[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => 6
[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => 2
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => 3
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => 4
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => 3
[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[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]] => 1
[[5,0,0],[0,0],[0]] => [[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => 5
[[5,0,0],[1,0],[0]] => [[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => 6
[[5,0,0],[1,0],[1]] => [[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => 7
[[5,0,0],[2,0],[0]] => [[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => 7
[[5,0,0],[2,0],[1]] => [[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => 8
[[5,0,0],[2,0],[2]] => [[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => 9
[[5,0,0],[3,0],[0]] => [[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => 8
[[5,0,0],[3,0],[1]] => [[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => 9
[[5,0,0],[3,0],[2]] => [[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => 10
[[5,0,0],[3,0],[3]] => [[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => 11
[[5,0,0],[4,0],[0]] => [[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => 9
[[5,0,0],[4,0],[1]] => [[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => 10
[[5,0,0],[4,0],[2]] => [[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => 11
[[5,0,0],[4,0],[3]] => [[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => 12
[[5,0,0],[4,0],[4]] => [[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => 13
[[5,0,0],[5,0],[0]] => [[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => 10
[[5,0,0],[5,0],[1]] => [[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => 11
[[5,0,0],[5,0],[2]] => [[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => 12
[[5,0,0],[5,0],[3]] => [[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => 13
[[5,0,0],[5,0],[4]] => [[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => 14
[[5,0,0],[5,0],[5]] => [[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => 15
[[4,1,0],[1,0],[0]] => [[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => 6
[[4,1,0],[1,0],[1]] => [[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => 7
[[4,1,0],[1,1],[1]] => [[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => 8
[[4,1,0],[2,0],[0]] => [[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => 7
[[4,1,0],[2,0],[1]] => [[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => 8
[[4,1,0],[2,0],[2]] => [[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => 9
[[4,1,0],[2,1],[1]] => [[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => 9
[[4,1,0],[2,1],[2]] => [[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => 10
[[4,1,0],[3,0],[0]] => [[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => 8
[[4,1,0],[3,0],[1]] => [[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => 9
[[4,1,0],[3,0],[2]] => [[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => 10
[[4,1,0],[3,0],[3]] => [[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => 11
[[4,1,0],[3,1],[1]] => [[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => 10
[[4,1,0],[3,1],[2]] => [[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => 11
[[4,1,0],[3,1],[3]] => [[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => 12
[[4,1,0],[4,0],[0]] => [[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => 9
[[4,1,0],[4,0],[1]] => [[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => 10
[[4,1,0],[4,0],[2]] => [[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => 11
[[4,1,0],[4,0],[3]] => [[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => 12
[[4,1,0],[4,0],[4]] => [[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => 13
[[4,1,0],[4,1],[1]] => [[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => 11
[[4,1,0],[4,1],[2]] => [[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => 12
[[4,1,0],[4,1],[3]] => [[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => 13
[[4,1,0],[4,1],[4]] => [[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => 14
[[3,2,0],[2,0],[0]] => [[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => 7
[[3,2,0],[2,0],[1]] => [[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => 8
[[3,2,0],[2,0],[2]] => [[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => 9
[[3,2,0],[2,1],[1]] => [[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => 9
[[3,2,0],[2,1],[2]] => [[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => 10
[[3,2,0],[2,2],[2]] => [[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => 11
[[3,2,0],[3,0],[0]] => [[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => 8
[[3,2,0],[3,0],[1]] => [[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => 9
[[3,2,0],[3,0],[2]] => [[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => 10
[[3,2,0],[3,0],[3]] => [[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => 11
[[3,2,0],[3,1],[1]] => [[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => 10
[[3,2,0],[3,1],[2]] => [[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => 11
[[3,2,0],[3,1],[3]] => [[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => 12
[[3,2,0],[3,2],[2]] => [[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => 12
[[3,2,0],[3,2],[3]] => [[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => 13
[[3,1,1],[1,1],[1]] => [[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => 8
[[3,1,1],[2,1],[1]] => [[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => 9
[[3,1,1],[2,1],[2]] => [[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => 10
[[3,1,1],[3,1],[1]] => [[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => 10
[[3,1,1],[3,1],[2]] => [[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => 11
[[3,1,1],[3,1],[3]] => [[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => 12
[[2,2,1],[2,1],[1]] => [[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => 9
[[2,2,1],[2,1],[2]] => [[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => 10
[[2,2,1],[2,2],[2]] => [[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => 11
[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => 4
[[4,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => 5
[[4,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => 6
[[4,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => 7
[[4,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => 6
[[4,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => 7
[[4,0,0,0],[2,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => 8
[[4,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => 8
[[4,0,0,0],[2,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => 9
[[4,0,0,0],[2,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => 10
[[4,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => 7
[[4,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => 8
[[4,0,0,0],[3,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => 9
[[4,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => 9
[[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => 10
[[4,0,0,0],[3,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => 11
[[4,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => 10
[[4,0,0,0],[3,0,0],[3,0],[1]] => [[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => 11
[[4,0,0,0],[3,0,0],[3,0],[2]] => [[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => 12
[[4,0,0,0],[3,0,0],[3,0],[3]] => [[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => 13
[[4,0,0,0],[4,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => 8
[[4,0,0,0],[4,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => 9
[[4,0,0,0],[4,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => 10
[[4,0,0,0],[4,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => 10
[[4,0,0,0],[4,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => 11
[[4,0,0,0],[4,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => 12
[[4,0,0,0],[4,0,0],[3,0],[0]] => [[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => 11
[[4,0,0,0],[4,0,0],[3,0],[1]] => [[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => 12
[[4,0,0,0],[4,0,0],[3,0],[2]] => [[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => 13
[[4,0,0,0],[4,0,0],[3,0],[3]] => [[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => 14
[[4,0,0,0],[4,0,0],[4,0],[0]] => [[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => 12
[[4,0,0,0],[4,0,0],[4,0],[1]] => [[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => 13
[[4,0,0,0],[4,0,0],[4,0],[2]] => [[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => 14
[[4,0,0,0],[4,0,0],[4,0],[3]] => [[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => 15
[[4,0,0,0],[4,0,0],[4,0],[4]] => [[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => 16
[[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => 5
[[3,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => 6
[[3,1,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => 7
[[3,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => 7
[[3,1,0,0],[1,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => 8
[[3,1,0,0],[1,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => 9
[[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => 6
[[3,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => 7
[[3,1,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => 8
[[3,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => 8
[[3,1,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => 9
[[3,1,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => 10
[[3,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => 8
[[3,1,0,0],[2,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => 9
[[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => 10
[[3,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => 9
[[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => 10
[[3,1,0,0],[2,1,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => 11
[[3,1,0,0],[2,1,0],[2,1],[1]] => [[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => 11
[[3,1,0,0],[2,1,0],[2,1],[2]] => [[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => 12
[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => 7
[[3,1,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => 8
[[3,1,0,0],[3,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => 9
[[3,1,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => 9
[[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => 10
[[3,1,0,0],[3,0,0],[2,0],[2]] => [[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => 11
[[3,1,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => 10
[[3,1,0,0],[3,0,0],[3,0],[1]] => [[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => 11
[[3,1,0,0],[3,0,0],[3,0],[2]] => [[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => 12
[[3,1,0,0],[3,0,0],[3,0],[3]] => [[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => 13
[[3,1,0,0],[3,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => 9
[[3,1,0,0],[3,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => 10
[[3,1,0,0],[3,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => 11
[[3,1,0,0],[3,1,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => 10
[[3,1,0,0],[3,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => 11
[[3,1,0,0],[3,1,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => 12
[[3,1,0,0],[3,1,0],[2,1],[1]] => [[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => 12
[[3,1,0,0],[3,1,0],[2,1],[2]] => [[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => 13
[[3,1,0,0],[3,1,0],[3,0],[0]] => [[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => 11
[[3,1,0,0],[3,1,0],[3,0],[1]] => [[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => 12
[[3,1,0,0],[3,1,0],[3,0],[2]] => [[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => 13
[[3,1,0,0],[3,1,0],[3,0],[3]] => [[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => 14
[[3,1,0,0],[3,1,0],[3,1],[1]] => [[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => 13
[[3,1,0,0],[3,1,0],[3,1],[2]] => [[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => 14
[[3,1,0,0],[3,1,0],[3,1],[3]] => [[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => 15
[[2,2,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => 6
[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => 7
[[2,2,0,0],[2,0,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => 8
[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => 8
[[2,2,0,0],[2,0,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => 9
[[2,2,0,0],[2,0,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => 10
[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => 8
[[2,2,0,0],[2,1,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => 9
[[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => 10
[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => 9
[[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => 10
[[2,2,0,0],[2,1,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => 11
[[2,2,0,0],[2,1,0],[2,1],[1]] => [[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => 11
[[2,2,0,0],[2,1,0],[2,1],[2]] => [[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => 12
[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => 10
[[2,2,0,0],[2,2,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => 11
[[2,2,0,0],[2,2,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => 12
[[2,2,0,0],[2,2,0],[2,1],[1]] => [[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => 12
[[2,2,0,0],[2,2,0],[2,1],[2]] => [[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => 13
[[2,2,0,0],[2,2,0],[2,2],[2]] => [[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => 14
[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => 7
[[2,1,1,0],[1,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => 8
[[2,1,1,0],[1,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => 9
[[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => 10
[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => 8
[[2,1,1,0],[2,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => 9
[[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => 10
[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => 9
[[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => 10
[[2,1,1,0],[2,1,0],[2,0],[2]] => [[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => 11
[[2,1,1,0],[2,1,0],[2,1],[1]] => [[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => 11
[[2,1,1,0],[2,1,0],[2,1],[2]] => [[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => 12
[[2,1,1,0],[2,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => 11
[[2,1,1,0],[2,1,1],[2,1],[1]] => [[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => 12
[[2,1,1,0],[2,1,1],[2,1],[2]] => [[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => 13
[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => 10
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => 3
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => 4
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => 5
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => 5
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => 6
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => 7
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => 6
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => 7
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => 8
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => 9
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => 4
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => 5
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => 6
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => 5
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => 6
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => 7
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => 7
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => 8
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => 6
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => 2
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => 3
[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => 4
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[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]] => 3
[[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => 1
[[5,0,0,0],[0,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => 5
[[5,0,0,0],[1,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => 6
[[5,0,0,0],[1,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => 7
[[5,0,0,0],[1,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => 8
[[5,0,0,0],[2,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => 7
[[5,0,0,0],[2,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => 8
[[5,0,0,0],[2,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => 9
[[5,0,0,0],[2,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => 9
[[5,0,0,0],[2,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => 10
[[5,0,0,0],[2,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => 11
[[5,0,0,0],[3,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => 8
[[5,0,0,0],[3,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => 9
[[5,0,0,0],[3,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => 10
[[5,0,0,0],[3,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => 10
[[5,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => 11
[[5,0,0,0],[3,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => 12
[[5,0,0,0],[3,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => 11
[[5,0,0,0],[3,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => 12
[[5,0,0,0],[3,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => 13
[[5,0,0,0],[3,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => 14
[[5,0,0,0],[4,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => 9
[[5,0,0,0],[4,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => 10
[[5,0,0,0],[4,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => 11
[[5,0,0,0],[4,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => 11
[[5,0,0,0],[4,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => 12
[[5,0,0,0],[4,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => 13
[[5,0,0,0],[4,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => 12
[[5,0,0,0],[4,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => 13
[[5,0,0,0],[4,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => 14
[[5,0,0,0],[4,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => 15
[[5,0,0,0],[4,0,0],[4,0],[0]] => [[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => 13
[[5,0,0,0],[4,0,0],[4,0],[1]] => [[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => 14
[[5,0,0,0],[4,0,0],[4,0],[2]] => [[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => 15
[[5,0,0,0],[4,0,0],[4,0],[3]] => [[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => 16
[[5,0,0,0],[4,0,0],[4,0],[4]] => [[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => 17
[[5,0,0,0],[5,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => 10
[[5,0,0,0],[5,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => 11
[[5,0,0,0],[5,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => 12
[[5,0,0,0],[5,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => 12
[[5,0,0,0],[5,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => 13
[[5,0,0,0],[5,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => 14
[[5,0,0,0],[5,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => 13
[[5,0,0,0],[5,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => 14
[[5,0,0,0],[5,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => 15
[[5,0,0,0],[5,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => 16
[[5,0,0,0],[5,0,0],[4,0],[0]] => [[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => 14
[[5,0,0,0],[5,0,0],[4,0],[1]] => [[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => 15
[[5,0,0,0],[5,0,0],[4,0],[2]] => [[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => 16
[[5,0,0,0],[5,0,0],[4,0],[3]] => [[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => 17
[[5,0,0,0],[5,0,0],[4,0],[4]] => [[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => 18
[[5,0,0,0],[5,0,0],[5,0],[0]] => [[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => 15
[[5,0,0,0],[5,0,0],[5,0],[1]] => [[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => 16
[[5,0,0,0],[5,0,0],[5,0],[2]] => [[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => 17
[[5,0,0,0],[5,0,0],[5,0],[3]] => [[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => 18
[[5,0,0,0],[5,0,0],[5,0],[4]] => [[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => 19
[[5,0,0,0],[5,0,0],[5,0],[5]] => [[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => 20
[[4,1,0,0],[1,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => 6
[[4,1,0,0],[1,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => 7
[[4,1,0,0],[1,0,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]] => 8
[[4,1,0,0],[1,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => 8
[[4,1,0,0],[1,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]] => 9
[[4,1,0,0],[1,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]] => 10
[[4,1,0,0],[2,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => 7
[[4,1,0,0],[2,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => 8
[[4,1,0,0],[2,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]] => 9
[[4,1,0,0],[2,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => 9
[[4,1,0,0],[2,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]] => 10
[[4,1,0,0],[2,0,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]] => 11
[[4,1,0,0],[2,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => 9
[[4,1,0,0],[2,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]] => 10
[[4,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]] => 11
[[4,1,0,0],[2,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => 10
[[4,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]] => 11
[[4,1,0,0],[2,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]] => 12
[[4,1,0,0],[2,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]] => 12
[[4,1,0,0],[2,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]] => 13
[[4,1,0,0],[3,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => 8
[[4,1,0,0],[3,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => 9
[[4,1,0,0],[3,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]] => 10
[[4,1,0,0],[3,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => 10
[[4,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]] => 11
[[4,1,0,0],[3,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]] => 12
[[4,1,0,0],[3,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => 11
[[4,1,0,0],[3,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]] => 12
[[4,1,0,0],[3,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]] => 13
[[4,1,0,0],[3,0,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]] => 14
[[4,1,0,0],[3,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => 10
[[4,1,0,0],[3,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]] => 11
[[4,1,0,0],[3,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]] => 12
[[4,1,0,0],[3,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => 11
[[4,1,0,0],[3,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]] => 12
[[4,1,0,0],[3,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]] => 13
[[4,1,0,0],[3,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]] => 13
[[4,1,0,0],[3,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]] => 14
[[4,1,0,0],[3,1,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => 12
[[4,1,0,0],[3,1,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]] => 13
[[4,1,0,0],[3,1,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]] => 14
[[4,1,0,0],[3,1,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]] => 15
[[4,1,0,0],[3,1,0],[3,1],[1]] => [[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]] => 14
[[4,1,0,0],[3,1,0],[3,1],[2]] => [[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]] => 15
[[4,1,0,0],[3,1,0],[3,1],[3]] => [[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]] => 16
[[4,1,0,0],[4,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => 9
[[4,1,0,0],[4,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => 10
[[4,1,0,0],[4,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]] => 11
[[4,1,0,0],[4,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => 11
[[4,1,0,0],[4,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]] => 12
[[4,1,0,0],[4,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]] => 13
[[4,1,0,0],[4,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => 12
[[4,1,0,0],[4,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]] => 13
[[4,1,0,0],[4,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]] => 14
[[4,1,0,0],[4,0,0],[3,0],[3]] => [[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]] => 15
[[4,1,0,0],[4,0,0],[4,0],[0]] => [[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => 13
[[4,1,0,0],[4,0,0],[4,0],[1]] => [[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]] => 14
[[4,1,0,0],[4,0,0],[4,0],[2]] => [[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]] => 15
[[4,1,0,0],[4,0,0],[4,0],[3]] => [[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]] => 16
[[4,1,0,0],[4,0,0],[4,0],[4]] => [[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]] => 17
[[4,1,0,0],[4,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => 11
[[4,1,0,0],[4,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]] => 12
[[4,1,0,0],[4,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]] => 13
[[4,1,0,0],[4,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => 12
[[4,1,0,0],[4,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]] => 13
[[4,1,0,0],[4,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]] => 14
[[4,1,0,0],[4,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]] => 14
[[4,1,0,0],[4,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]] => 15
[[4,1,0,0],[4,1,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => 13
[[4,1,0,0],[4,1,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]] => 14
[[4,1,0,0],[4,1,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]] => 15
[[4,1,0,0],[4,1,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]] => 16
[[4,1,0,0],[4,1,0],[3,1],[1]] => [[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]] => 15
[[4,1,0,0],[4,1,0],[3,1],[2]] => [[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]] => 16
[[4,1,0,0],[4,1,0],[3,1],[3]] => [[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]] => 17
[[4,1,0,0],[4,1,0],[4,0],[0]] => [[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => 14
[[4,1,0,0],[4,1,0],[4,0],[1]] => [[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]] => 15
[[4,1,0,0],[4,1,0],[4,0],[2]] => [[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]] => 16
[[4,1,0,0],[4,1,0],[4,0],[3]] => [[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]] => 17
[[4,1,0,0],[4,1,0],[4,0],[4]] => [[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]] => 18
[[4,1,0,0],[4,1,0],[4,1],[1]] => [[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]] => 16
[[4,1,0,0],[4,1,0],[4,1],[2]] => [[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]] => 17
[[4,1,0,0],[4,1,0],[4,1],[3]] => [[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]] => 18
[[4,1,0,0],[4,1,0],[4,1],[4]] => [[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]] => 19
[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => 7
[[3,2,0,0],[2,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => 8
[[3,2,0,0],[2,0,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]] => 9
[[3,2,0,0],[2,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => 9
[[3,2,0,0],[2,0,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]] => 10
[[3,2,0,0],[2,0,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]] => 11
[[3,2,0,0],[2,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => 9
[[3,2,0,0],[2,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]] => 10
[[3,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]] => 11
[[3,2,0,0],[2,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => 10
[[3,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]] => 11
[[3,2,0,0],[2,1,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]] => 12
[[3,2,0,0],[2,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]] => 12
[[3,2,0,0],[2,1,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]] => 13
[[3,2,0,0],[2,2,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => 11
[[3,2,0,0],[2,2,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]] => 12
[[3,2,0,0],[2,2,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]] => 13
[[3,2,0,0],[2,2,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]] => 13
[[3,2,0,0],[2,2,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]] => 14
[[3,2,0,0],[2,2,0],[2,2],[2]] => [[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]] => 15
[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => 8
[[3,2,0,0],[3,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => 9
[[3,2,0,0],[3,0,0],[1,0],[1]] => [[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]] => 10
[[3,2,0,0],[3,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => 10
[[3,2,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]] => 11
[[3,2,0,0],[3,0,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]] => 12
[[3,2,0,0],[3,0,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => 11
[[3,2,0,0],[3,0,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]] => 12
[[3,2,0,0],[3,0,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]] => 13
[[3,2,0,0],[3,0,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]] => 14
[[3,2,0,0],[3,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => 10
[[3,2,0,0],[3,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]] => 11
[[3,2,0,0],[3,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]] => 12
[[3,2,0,0],[3,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => 11
[[3,2,0,0],[3,1,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]] => 12
[[3,2,0,0],[3,1,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]] => 13
[[3,2,0,0],[3,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]] => 13
[[3,2,0,0],[3,1,0],[2,1],[2]] => [[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]] => 14
[[3,2,0,0],[3,1,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => 12
[[3,2,0,0],[3,1,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]] => 13
[[3,2,0,0],[3,1,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]] => 14
[[3,2,0,0],[3,1,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]] => 15
[[3,2,0,0],[3,1,0],[3,1],[1]] => [[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]] => 14
[[3,2,0,0],[3,1,0],[3,1],[2]] => [[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]] => 15
[[3,2,0,0],[3,1,0],[3,1],[3]] => [[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]] => 16
[[3,2,0,0],[3,2,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => 12
[[3,2,0,0],[3,2,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]] => 13
[[3,2,0,0],[3,2,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]] => 14
[[3,2,0,0],[3,2,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]] => 14
[[3,2,0,0],[3,2,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]] => 15
[[3,2,0,0],[3,2,0],[2,2],[2]] => [[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]] => 16
[[3,2,0,0],[3,2,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => 13
[[3,2,0,0],[3,2,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]] => 14
[[3,2,0,0],[3,2,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]] => 15
[[3,2,0,0],[3,2,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]] => 16
[[3,2,0,0],[3,2,0],[3,1],[1]] => [[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]] => 15
[[3,2,0,0],[3,2,0],[3,1],[2]] => [[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]] => 16
[[3,2,0,0],[3,2,0],[3,1],[3]] => [[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]] => 17
[[3,2,0,0],[3,2,0],[3,2],[2]] => [[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]] => 17
[[3,2,0,0],[3,2,0],[3,2],[3]] => [[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]] => 18
[[3,1,1,0],[1,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => 8
[[3,1,1,0],[1,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => 9
[[3,1,1,0],[1,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => 10
[[3,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => 11
[[3,1,1,0],[2,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => 9
[[3,1,1,0],[2,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => 10
[[3,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => 11
[[3,1,1,0],[2,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => 10
[[3,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => 11
[[3,1,1,0],[2,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => 12
[[3,1,1,0],[2,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => 12
[[3,1,1,0],[2,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => 13
[[3,1,1,0],[2,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => 12
[[3,1,1,0],[2,1,1],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => 13
[[3,1,1,0],[2,1,1],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => 14
[[3,1,1,0],[3,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => 10
[[3,1,1,0],[3,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => 11
[[3,1,1,0],[3,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => 12
[[3,1,1,0],[3,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => 11
[[3,1,1,0],[3,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => 12
[[3,1,1,0],[3,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => 13
[[3,1,1,0],[3,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => 13
[[3,1,1,0],[3,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => 14
[[3,1,1,0],[3,1,0],[3,0],[0]] => [[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => 12
[[3,1,1,0],[3,1,0],[3,0],[1]] => [[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => 13
[[3,1,1,0],[3,1,0],[3,0],[2]] => [[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => 14
[[3,1,1,0],[3,1,0],[3,0],[3]] => [[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => 15
[[3,1,1,0],[3,1,0],[3,1],[1]] => [[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => 14
[[3,1,1,0],[3,1,0],[3,1],[2]] => [[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => 15
[[3,1,1,0],[3,1,0],[3,1],[3]] => [[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => 16
[[3,1,1,0],[3,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => 13
[[3,1,1,0],[3,1,1],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => 14
[[3,1,1,0],[3,1,1],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => 15
[[3,1,1,0],[3,1,1],[3,1],[1]] => [[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => 15
[[3,1,1,0],[3,1,1],[3,1],[2]] => [[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => 16
[[3,1,1,0],[3,1,1],[3,1],[3]] => [[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => 17
[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => 9
[[2,2,1,0],[2,1,0],[1,0],[1]] => [[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]] => 10
[[2,2,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]] => 11
[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => 10
[[2,2,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]] => 11
[[2,2,1,0],[2,1,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]] => 12
[[2,2,1,0],[2,1,0],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]] => 12
[[2,2,1,0],[2,1,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]] => 13
[[2,2,1,0],[2,1,1],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]] => 12
[[2,2,1,0],[2,1,1],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]] => 13
[[2,2,1,0],[2,1,1],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]] => 14
[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => 11
[[2,2,1,0],[2,2,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]] => 12
[[2,2,1,0],[2,2,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]] => 13
[[2,2,1,0],[2,2,0],[2,1],[1]] => [[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]] => 13
[[2,2,1,0],[2,2,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]] => 14
[[2,2,1,0],[2,2,0],[2,2],[2]] => [[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]] => 15
[[2,2,1,0],[2,2,1],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]] => 14
[[2,2,1,0],[2,2,1],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]] => 15
[[2,2,1,0],[2,2,1],[2,2],[2]] => [[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]] => 16
[[2,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]] => 11
[[2,1,1,1],[2,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]] => 12
[[2,1,1,1],[2,1,1],[2,1],[1]] => [[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]] => 13
[[2,1,1,1],[2,1,1],[2,1],[2]] => [[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]] => 14
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => 4
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => 5
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => 6
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => 7
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => 6
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => 7
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => 8
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => 8
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => 9
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => 10
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => 7
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => 8
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => 9
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => 9
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => 10
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => 11
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => 10
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => 11
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => 12
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => 13
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => 8
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => 9
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => 10
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => 10
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => 11
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => 12
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => 11
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => 12
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => 13
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => 14
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => 12
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => 13
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => 14
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => 15
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => 16
[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => 5
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => 6
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => 7
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => 7
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => 8
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => 9
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => 6
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => 7
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => 8
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => 8
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => 9
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => 10
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => 8
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => 9
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => 10
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => 9
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => 10
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => 11
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => 11
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => 12
[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => 7
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => 8
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => 9
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => 9
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => 10
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => 11
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => 10
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => 11
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => 12
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => 13
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => 9
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => 10
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => 11
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => 10
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => 11
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => 12
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => 12
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => 13
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => 11
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => 12
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => 13
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => 14
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => 13
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => 14
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => 15
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => 6
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => 7
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => 8
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => 8
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => 9
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => 10
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => 8
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => 9
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => 10
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => 9
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => 10
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => 11
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => 11
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => 12
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => 10
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => 11
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => 12
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => 12
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => 13
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => 14
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => 7
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => 8
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => 9
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => 10
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => 8
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => 9
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => 10
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => 9
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => 10
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => 11
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => 11
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => 12
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => 11
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => 12
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => 13
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => 10
[[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => 3
[[3,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => 4
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => 5
[[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => 5
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => 6
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => 7
[[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => 7
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => 8
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => 9
[[2,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[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]] => 4
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[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]] => 5
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[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]] => 6
[[2,1,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[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]] => 5
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[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]] => 6
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[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]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[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]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[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]] => 8
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[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]] => 6
[[2,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => 3
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => 4
[[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]] => [[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]] => 3
[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => 1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5]] => 15
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2]] => 15
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3]] => 15
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4]] => 15
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5]] => 15
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4]] => 15
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4]] => 15
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5]] => 15
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5]] => 15
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5]] => 15
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3]] => 15
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4]] => 15
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4]] => 15
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5]] => 15
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5]] => 15
[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5]] => 15
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4]] => 15
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4]] => 15
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3]] => 15
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5]] => 15
[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5]] => 15
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4]] => 15
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5]] => 15
[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5]] => 15
[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5]] => 15
[[1,1,1,1,1],[1,1,1,1],[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]] => 15
[[1]] => [[1]] => [[1]] => 1
[[2]] => [[2]] => [[1,1]] => 2
[[3]] => [[3]] => [[1,1,1]] => 3
[[4]] => [[4]] => [[1,1,1,1]] => 4
[[5]] => [[5]] => [[1,1,1,1,1]] => 5
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Generating function
$F_{(2, 2)} = q^{2} + 2\ q^{3} + q^{4}$
$F_{(2, 3)} = q^{3} + 2\ q^{4} + 2\ q^{5} + q^{6}$
$F_{(2, 4)} = q^{4} + 2\ q^{5} + 3\ q^{6} + 2\ q^{7} + q^{8}$
$F_{(3, 3)} = q^{3} + 2\ q^{4} + 4\ q^{5} + 5\ q^{6} + 4\ q^{7} + 2\ q^{8} + q^{9}$
$F_{(2, 5)} = q^{5} + 2\ q^{6} + 3\ q^{7} + 3\ q^{8} + 2\ q^{9} + q^{10}$
$F_{(3, 4)} = q^{4} + 2\ q^{5} + 5\ q^{6} + 7\ q^{7} + 9\ q^{8} + 7\ q^{9} + 5\ q^{10} + 2\ q^{11} + q^{12}$
$F_{(3, 5)} = q^{5} + 2\ q^{6} + 5\ q^{7} + 8\ q^{8} + 12\ q^{9} + 13\ q^{10} + 12\ q^{11} + 8\ q^{12} + 5\ q^{13} + 2\ q^{14} + q^{15}$
$F_{(4, 4)} = q^{4} + 2\ q^{5} + 5\ q^{6} + 9\ q^{7} + 14\ q^{8} + 17\ q^{9} + 20\ q^{10} + 17\ q^{11} + 14\ q^{12} + 9\ q^{13} + 5\ q^{14} + 2\ q^{15} + q^{16}$
$F_{(4, 5)} = q^{5} + 2\ q^{6} + 5\ q^{7} + 10\ q^{8} + 17\ q^{9} + 25\ q^{10} + 33\ q^{11} + 37\ q^{12} + 37\ q^{13} + 33\ q^{14} + 25\ q^{15} + 17\ q^{16} + 10\ q^{17} + 5\ q^{18} + 2\ q^{19} + q^{20}$
Description
The sum of the entries of a semistandard tableau.
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
Schuetzenberger involution
Description
Applies the Schuetzenberger involution to a Gelfand-Tsetlin pattern.
The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries. It is also known as evacuation, and in the context of crystal graphs of type $A$ it realizes Lusztig's involution.
In the language of tableaux it is defined as follows. Consider a semistandard tableau with no entry larger than $n$. Use Schuetzenberger's jeu de taquin to slide all entries equal to $1$ to the outer border of the tableau. Do the same for all entries equal to $2$, restricting the tableau to the entries larger than $2$, and so on, until the tableau is a reverse semistandard tableau. Finally, replace each entry with its complement with respect to $n$, that is, replace $e$ with $n+1-e$.
The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries. It is also known as evacuation, and in the context of crystal graphs of type $A$ it realizes Lusztig's involution.
In the language of tableaux it is defined as follows. Consider a semistandard tableau with no entry larger than $n$. Use Schuetzenberger's jeu de taquin to slide all entries equal to $1$ to the outer border of the tableau. Do the same for all entries equal to $2$, restricting the tableau to the entries larger than $2$, and so on, until the tableau is a reverse semistandard tableau. Finally, replace each entry with its complement with respect to $n$, that is, replace $e$ with $n+1-e$.
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