- FindStat

Identifier

Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
St000459: Integer partitions ⟶ ℤ

Values

[[1,0],[0]] => [[2]] => [1] => [1] => 1

[[1,0],[1]] => [[1]] => [1] => [1] => 1

[[2,0],[0]] => [[2,2]] => [1,2] => [1,1] => 2

[[2,0],[1]] => [[1,2]] => [1,2] => [1,1] => 2

[[2,0],[2]] => [[1,1]] => [1,2] => [1,1] => 2

[[1,1],[1]] => [[1],[2]] => [2,1] => [2] => 2

[[1,0,0],[0,0],[0]] => [[3]] => [1] => [1] => 1

[[1,0,0],[1,0],[0]] => [[2]] => [1] => [1] => 1

[[1,0,0],[1,0],[1]] => [[1]] => [1] => [1] => 1

[[3,0],[0]] => [[2,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0],[1]] => [[1,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0],[2]] => [[1,1,2]] => [1,2,3] => [1,1,1] => 3

[[3,0],[3]] => [[1,1,1]] => [1,2,3] => [1,1,1] => 3

[[2,1],[1]] => [[1,2],[2]] => [2,1,3] => [2,1] => 3

[[2,1],[2]] => [[1,1],[2]] => [3,1,2] => [2,1] => 3

[[2,0,0],[0,0],[0]] => [[3,3]] => [1,2] => [1,1] => 2

[[2,0,0],[1,0],[0]] => [[2,3]] => [1,2] => [1,1] => 2

[[2,0,0],[1,0],[1]] => [[1,3]] => [1,2] => [1,1] => 2

[[2,0,0],[2,0],[0]] => [[2,2]] => [1,2] => [1,1] => 2

[[2,0,0],[2,0],[1]] => [[1,2]] => [1,2] => [1,1] => 2

[[2,0,0],[2,0],[2]] => [[1,1]] => [1,2] => [1,1] => 2

[[1,1,0],[1,0],[0]] => [[2],[3]] => [2,1] => [2] => 2

[[1,1,0],[1,0],[1]] => [[1],[3]] => [2,1] => [2] => 2

[[1,1,0],[1,1],[1]] => [[1],[2]] => [2,1] => [2] => 2

[[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1] => 1

[[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1] => 1

[[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1] => 1

[[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1] => 1

[[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => [1,1,1,1] => 4

[[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => [2,1,1] => 4

[[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => [2,1,1] => 4

[[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => [1,1,1] => 3

[[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0],[2,0],[0]] => [[2,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0],[2,0],[1]] => [[1,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0],[2,0],[2]] => [[1,1],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0],[2,1],[2]] => [[1,1],[2]] => [3,1,2] => [2,1] => 3

[[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [3,2,1] => [3] => 3

[[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [1,2] => [1,1] => 2

[[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,2] => [1,1] => 2

[[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,2] => [1,1] => 2

[[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,2] => [1,1] => 2

[[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [1,2] => [1,1] => 2

[[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,2] => [1,1] => 2

[[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,2] => [1,1] => 2

[[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [1,2] => [1,1] => 2

[[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,2] => [1,1] => 2

[[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [1,2] => [1,1] => 2

[[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [2,1] => [2] => 2

[[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [2,1] => [2] => 2

[[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [2,1] => [2] => 2

[[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [2,1] => [2] => 2

[[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [2,1] => [2] => 2

[[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [2,1] => [2] => 2

[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1] => 1

[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1] => 1

[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1] => 1

[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1] => 1

[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1] => 1

[[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[4,1],[1]] => [[1,2,2,2],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1],[2]] => [[1,1,2,2],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1],[3]] => [[1,1,1,2],[2]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1],[4]] => [[1,1,1,1],[2]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[3,2],[2]] => [[1,1,2],[2,2]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2],[3]] => [[1,1,1],[2,2]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

>>> Load all 1552 entries. <<<

[[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => [1,1,1,1] => 4

[[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => [2,1,1] => 4

[[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => [2,1,1] => 4

[[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [3,2,1,4] => [3,1] => 4

[[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [4,2,1,3] => [3,1] => 4

[[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [4,3,1,2] => [3,1] => 4

[[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => [1,1,1] => 3

[[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [3,1,2] => [2,1] => 3

[[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [3,2,1] => [3] => 3

[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,2] => [1,1] => 2

[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [1,2] => [1,1] => 2

[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [2,1] => [2] => 2

[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [2,1] => [2] => 2

[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => [1] => 1

[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1] => 1

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1] => 1

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => [1] => 1

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => [1] => 1

[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => [1] => 1

[[6,0],[0]] => [[2,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0],[1]] => [[1,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0],[2]] => [[1,1,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0],[3]] => [[1,1,1,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0],[4]] => [[1,1,1,1,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0],[5]] => [[1,1,1,1,1,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0],[6]] => [[1,1,1,1,1,1]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[5,1],[1]] => [[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1],[2]] => [[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1],[3]] => [[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1],[5]] => [[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[4,2],[2]] => [[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2],[4]] => [[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[3,3],[3]] => [[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,2,1,4,5] => [3,1,1] => 5

[[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [5,4,1,2,3] => [3,1,1] => 5

[[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [5,3,4,1,2] => [3,1,1] => 5

[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => [1,1,1,1] => 4

[[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => [2,1,1] => 4

[[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => [2,1,1] => 4

[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [4,3,1,2] => [3,1] => 4

[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [4,3,2,1] => [4] => 4

[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => [1,1,1] => 3

[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [3,1,2] => [2,1] => 3

[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [3,2,1] => [3] => 3

[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [1,2] => [1,1] => 2

[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [2,1] => [2] => 2

[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [2,1] => [2] => 2

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => [1] => 1

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1] => 1

[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1] => 1

[[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],[0,0],[0]] => [[3]] => [1] => [1] => 1

[[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],[0]] => [[2]] => [1] => [1] => 1

[[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] => [1] => 1

[[7,0],[0]] => [[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7

[[7,0],[1]] => [[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7

[[7,0],[2]] => [[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7

[[7,0],[3]] => [[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7

[[7,0],[4]] => [[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7

[[7,0],[5]] => [[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7

[[7,0],[6]] => [[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => [1,1,1,1,1,1,1] => 7

[[6,1],[1]] => [[1,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7] => [2,1,1,1,1,1] => 7

[[6,1],[2]] => [[1,1,2,2,2,2],[2]] => [3,1,2,4,5,6,7] => [2,1,1,1,1,1] => 7

[[6,1],[3]] => [[1,1,1,2,2,2],[2]] => [4,1,2,3,5,6,7] => [2,1,1,1,1,1] => 7

[[6,1],[4]] => [[1,1,1,1,2,2],[2]] => [5,1,2,3,4,6,7] => [2,1,1,1,1,1] => 7

[[6,1],[5]] => [[1,1,1,1,1,2],[2]] => [6,1,2,3,4,5,7] => [2,1,1,1,1,1] => 7

[[6,1],[6]] => [[1,1,1,1,1,1],[2]] => [7,1,2,3,4,5,6] => [2,1,1,1,1,1] => 7

[[5,2],[2]] => [[1,1,2,2,2],[2,2]] => [3,4,1,2,5,6,7] => [2,1,1,1,1,1] => 7

[[5,2],[3]] => [[1,1,1,2,2],[2,2]] => [4,5,1,2,3,6,7] => [2,1,1,1,1,1] => 7

[[5,2],[4]] => [[1,1,1,1,2],[2,2]] => [5,6,1,2,3,4,7] => [2,1,1,1,1,1] => 7

[[5,2],[5]] => [[1,1,1,1,1],[2,2]] => [6,7,1,2,3,4,5] => [2,1,1,1,1,1] => 7

[[4,3],[3]] => [[1,1,1,2],[2,2,2]] => [4,5,6,1,2,3,7] => [2,1,1,1,1,1] => 7

[[4,3],[4]] => [[1,1,1,1],[2,2,2]] => [5,6,7,1,2,3,4] => [2,1,1,1,1,1] => 7

[[6,0,0],[0,0],[0]] => [[3,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[1,0],[0]] => [[2,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[1,0],[1]] => [[1,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[2,0],[0]] => [[2,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[2,0],[1]] => [[1,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[2,0],[2]] => [[1,1,3,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[3,0],[0]] => [[2,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[3,0],[1]] => [[1,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[3,0],[2]] => [[1,1,2,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[3,0],[3]] => [[1,1,1,3,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[4,0],[0]] => [[2,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[4,0],[1]] => [[1,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[4,0],[2]] => [[1,1,2,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[4,0],[3]] => [[1,1,1,2,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[4,0],[4]] => [[1,1,1,1,3,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[5,0],[0]] => [[2,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[5,0],[1]] => [[1,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[5,0],[2]] => [[1,1,2,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[5,0],[3]] => [[1,1,1,2,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[5,0],[4]] => [[1,1,1,1,2,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[5,0],[5]] => [[1,1,1,1,1,3]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[6,0],[0]] => [[2,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[6,0],[1]] => [[1,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[6,0],[2]] => [[1,1,2,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[6,0],[3]] => [[1,1,1,2,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[6,0],[4]] => [[1,1,1,1,2,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[6,0],[5]] => [[1,1,1,1,1,2]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[6,0,0],[6,0],[6]] => [[1,1,1,1,1,1]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[5,1,0],[1,0],[0]] => [[2,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[1,0],[1]] => [[1,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[1,1],[1]] => [[1,3,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[2,0],[0]] => [[2,2,3,3,3],[3]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[2,0],[1]] => [[1,2,3,3,3],[3]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[2,0],[2]] => [[1,1,3,3,3],[3]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[2,1],[1]] => [[1,2,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[2,1],[2]] => [[1,1,3,3,3],[2]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[3,0],[0]] => [[2,2,2,3,3],[3]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[3,0],[1]] => [[1,2,2,3,3],[3]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[3,0],[2]] => [[1,1,2,3,3],[3]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[3,0],[3]] => [[1,1,1,3,3],[3]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[3,1],[1]] => [[1,2,2,3,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[3,1],[2]] => [[1,1,2,3,3],[2]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[3,1],[3]] => [[1,1,1,3,3],[2]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,0],[0]] => [[2,2,2,2,3],[3]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,0],[1]] => [[1,2,2,2,3],[3]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,0],[2]] => [[1,1,2,2,3],[3]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,0],[3]] => [[1,1,1,2,3],[3]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,0],[4]] => [[1,1,1,1,3],[3]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,1],[1]] => [[1,2,2,2,3],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,1],[2]] => [[1,1,2,2,3],[2]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,1],[3]] => [[1,1,1,2,3],[2]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[4,1],[4]] => [[1,1,1,1,3],[2]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1,0],[5,0],[0]] => [[2,2,2,2,2],[3]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[5,1,0],[5,0],[1]] => [[1,2,2,2,2],[3]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[5,1,0],[5,0],[2]] => [[1,1,2,2,2],[3]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[5,1,0],[5,0],[3]] => [[1,1,1,2,2],[3]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[5,1,0],[5,0],[4]] => [[1,1,1,1,2],[3]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[5,1,0],[5,0],[5]] => [[1,1,1,1,1],[3]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[5,1,0],[5,1],[1]] => [[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[5,1],[2]] => [[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[5,1],[3]] => [[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[5,1,0],[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[5,1,0],[5,1],[5]] => [[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[4,2,0],[2,0],[0]] => [[2,2,3,3],[3,3]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[2,0],[1]] => [[1,2,3,3],[3,3]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[2,0],[2]] => [[1,1,3,3],[3,3]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[2,1],[1]] => [[1,2,3,3],[2,3]] => [2,4,1,3,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[2,1],[2]] => [[1,1,3,3],[2,3]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[2,2],[2]] => [[1,1,3,3],[2,2]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,0],[0]] => [[2,2,2,3],[3,3]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,0],[1]] => [[1,2,2,3],[3,3]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,0],[2]] => [[1,1,2,3],[3,3]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,0],[3]] => [[1,1,1,3],[3,3]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,1],[1]] => [[1,2,2,3],[2,3]] => [2,5,1,3,4,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,1],[2]] => [[1,1,2,3],[2,3]] => [3,5,1,2,4,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,1],[3]] => [[1,1,1,3],[2,3]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,2],[2]] => [[1,1,2,3],[2,2]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[3,2],[3]] => [[1,1,1,3],[2,2]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2,0],[4,0],[0]] => [[2,2,2,2],[3,3]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[4,2,0],[4,0],[1]] => [[1,2,2,2],[3,3]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[4,2,0],[4,0],[2]] => [[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[4,2,0],[4,0],[3]] => [[1,1,1,2],[3,3]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[4,2,0],[4,0],[4]] => [[1,1,1,1],[3,3]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[4,2,0],[4,1],[1]] => [[1,2,2,2],[2,3]] => [2,6,1,3,4,5] => [2,1,1,1,1] => 6

[[4,2,0],[4,1],[2]] => [[1,1,2,2],[2,3]] => [3,6,1,2,4,5] => [2,1,1,1,1] => 6

[[4,2,0],[4,1],[3]] => [[1,1,1,2],[2,3]] => [4,6,1,2,3,5] => [2,1,1,1,1] => 6

[[4,2,0],[4,1],[4]] => [[1,1,1,1],[2,3]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[4,2,0],[4,2],[2]] => [[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[4,2,0],[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[4,2,0],[4,2],[4]] => [[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[4,1,1],[1,1],[1]] => [[1,3,3,3],[2],[3]] => [3,2,1,4,5,6] => [3,1,1,1] => 6

[[4,1,1],[2,1],[1]] => [[1,2,3,3],[2],[3]] => [4,2,1,3,5,6] => [3,1,1,1] => 6

[[4,1,1],[2,1],[2]] => [[1,1,3,3],[2],[3]] => [4,3,1,2,5,6] => [3,1,1,1] => 6

[[4,1,1],[3,1],[1]] => [[1,2,2,3],[2],[3]] => [5,2,1,3,4,6] => [3,1,1,1] => 6

[[4,1,1],[3,1],[2]] => [[1,1,2,3],[2],[3]] => [5,3,1,2,4,6] => [3,1,1,1] => 6

[[4,1,1],[3,1],[3]] => [[1,1,1,3],[2],[3]] => [5,4,1,2,3,6] => [3,1,1,1] => 6

[[4,1,1],[4,1],[1]] => [[1,2,2,2],[2],[3]] => [6,2,1,3,4,5] => [3,1,1,1] => 6

[[4,1,1],[4,1],[2]] => [[1,1,2,2],[2],[3]] => [6,3,1,2,4,5] => [3,1,1,1] => 6

[[4,1,1],[4,1],[3]] => [[1,1,1,2],[2],[3]] => [6,4,1,2,3,5] => [3,1,1,1] => 6

[[4,1,1],[4,1],[4]] => [[1,1,1,1],[2],[3]] => [6,5,1,2,3,4] => [3,1,1,1] => 6

[[3,3,0],[3,0],[0]] => [[2,2,2],[3,3,3]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[3,3,0],[3,0],[1]] => [[1,2,2],[3,3,3]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[3,3,0],[3,0],[2]] => [[1,1,2],[3,3,3]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[3,3,0],[3,0],[3]] => [[1,1,1],[3,3,3]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[3,3,0],[3,1],[1]] => [[1,2,2],[2,3,3]] => [2,5,6,1,3,4] => [2,1,1,1,1] => 6

[[3,3,0],[3,1],[2]] => [[1,1,2],[2,3,3]] => [3,5,6,1,2,4] => [2,1,1,1,1] => 6

[[3,3,0],[3,1],[3]] => [[1,1,1],[2,3,3]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[3,3,0],[3,2],[2]] => [[1,1,2],[2,2,3]] => [3,4,6,1,2,5] => [2,1,1,1,1] => 6

[[3,3,0],[3,2],[3]] => [[1,1,1],[2,2,3]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[3,3,0],[3,3],[3]] => [[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[3,2,1],[2,1],[1]] => [[1,2,3],[2,3],[3]] => [4,2,5,1,3,6] => [3,1,1,1] => 6

[[3,2,1],[2,1],[2]] => [[1,1,3],[2,3],[3]] => [4,3,5,1,2,6] => [3,1,1,1] => 6

[[3,2,1],[2,2],[2]] => [[1,1,3],[2,2],[3]] => [5,3,4,1,2,6] => [3,1,1,1] => 6

[[3,2,1],[3,1],[1]] => [[1,2,2],[2,3],[3]] => [5,2,6,1,3,4] => [3,1,1,1] => 6

[[3,2,1],[3,1],[2]] => [[1,1,2],[2,3],[3]] => [5,3,6,1,2,4] => [3,1,1,1] => 6

[[3,2,1],[3,1],[3]] => [[1,1,1],[2,3],[3]] => [5,4,6,1,2,3] => [3,1,1,1] => 6

[[3,2,1],[3,2],[2]] => [[1,1,2],[2,2],[3]] => [6,3,4,1,2,5] => [3,1,1,1] => 6

[[3,2,1],[3,2],[3]] => [[1,1,1],[2,2],[3]] => [6,4,5,1,2,3] => [3,1,1,1] => 6

[[2,2,2],[2,2],[2]] => [[1,1],[2,2],[3,3]] => [5,6,3,4,1,2] => [3,1,1,1] => 6

[[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0],[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => [3,2,1,4,5] => [3,1,1] => 5

[[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => [3,2,1,4,5] => [3,1,1] => 5

[[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => [3,2,1,4,5] => [3,1,1] => 5

[[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => [3,2,1,4,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => [3,2,1,4,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => [5,4,1,2,3] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => [5,4,1,2,3] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => [5,4,1,2,3] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => [5,4,1,2,3] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => [5,4,1,2,3] => [3,1,1] => 5

[[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,2,1,4,5] => [3,1,1] => 5

[[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [5,4,1,2,3] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]] => [3,2,5,1,4] => [3,1,1] => 5

[[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]] => [5,3,4,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]] => [5,3,4,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]] => [5,3,4,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]] => [5,2,4,1,3] => [3,1,1] => 5

[[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]] => [5,3,4,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]] => [5,3,4,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [5,3,4,1,2] => [3,1,1] => 5

[[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]] => [4,3,2,1,5] => [4,1] => 5

[[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]] => [5,3,2,1,4] => [4,1] => 5

[[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]] => [5,4,2,1,3] => [4,1] => 5

[[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]] => [5,4,3,1,2] => [4,1] => 5

[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,5]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => [1,1,1,1] => 4

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => [1,1,1,1] => 4

[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5],[5]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[5]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[5]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[5]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5,5],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5,5],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5,5],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[5]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,5],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,5],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,5],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,5],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,5],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,5],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,5],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,5],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,5],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[5]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [4,1,2,3] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => [2,1,1] => 4

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,5]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,5]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,4,1,3] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [3,4,1,2] => [2,1,1] => 4

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => [2,1,1] => 4

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4],[5]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4],[5]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4],[5]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[5]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[5]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[5]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,5],[2],[3]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[5]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[5]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [4,3,1,2] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [3,2,1,4] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [4,2,1,3] => [3,1] => 4

[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [4,3,1,2] => [3,1] => 4

[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4],[5]] => [4,3,2,1] => [4] => 4

[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4],[5]] => [4,3,2,1] => [4] => 4

[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4],[5]] => [4,3,2,1] => [4] => 4

[[1,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3],[5]] => [4,3,2,1] => [4] => 4

[[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [4,3,2,1] => [4] => 4

[[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6,6]] => [1,2,3] => [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]] => [[5,6,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,6]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => [1,1,1] => 3

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => [1,1,1] => 3

[[2,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6],[6]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[6]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[6]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[6]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[6]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,6],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,6],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,6],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,6],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,6],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,6],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[6]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [3,1,2] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1,3] => [2,1] => 3

[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [3,1,2] => [2,1] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[6]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [3,2,1] => [3] => 3

[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [3,2,1] => [3] => 3

[[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]] => [[7,7]] => [1,2] => [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]] => [[6,7]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,7]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,7]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,7]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,7]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,7]] => [1,2] => [1,1] => 2

[[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]] => [[6,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,2] => [1,1] => 2

[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,2] => [1,1] => 2

[[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],[0,0],[0]] => [[3,3]] => [1,2] => [1,1] => 2

[[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],[1,0],[0]] => [[2,3]] => [1,2] => [1,1] => 2

[[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],[1,0],[1]] => [[1,3]] => [1,2] => [1,1] => 2

[[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]] => [1,2] => [1,1] => 2

[[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]] => [1,2] => [1,1] => 2

[[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]] => [1,2] => [1,1] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[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]] => [2,1] => [2] => 2

[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => [1] => 1

[[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],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => [1] => 1

[[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],[0,0,0],[0,0],[0]] => [[4]] => [1] => [1] => 1

[[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],[0,0],[0]] => [[3]] => [1] => [1] => 1

[[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],[0]] => [[2]] => [1] => [1] => 1

[[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] => [1] => 1

[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5]] => [5,1,2,3,4] => [2,1,1,1] => 5

[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4]] => [4,1,2,3,5] => [2,1,1,1] => 5

[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3]] => [3,1,2,4,5] => [2,1,1,1] => 5

[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,1,1] => 5

[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5]] => [4,5,1,2,3] => [2,1,1,1] => 5

[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5]] => [3,5,1,2,4] => [2,1,1,1] => 5

[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4]] => [3,4,1,2,5] => [2,1,1,1] => 5

[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5]] => [2,5,1,3,4] => [2,1,1,1] => 5

[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4]] => [2,4,1,3,5] => [2,1,1,1] => 5

[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => [3,1,1] => 5

[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => [3,1,1] => 5

[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => [3,1,1] => 5

[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5]] => [5,2,1,3,4] => [3,1,1] => 5

[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4]] => [4,2,1,3,5] => [3,1,1] => 5

[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3]] => [3,2,1,4,5] => [3,1,1] => 5

[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => [3,1,1] => 5

[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4]] => [4,3,5,1,2] => [3,1,1] => 5

[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5]] => [5,2,4,1,3] => [3,1,1] => 5

[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4]] => [4,2,5,1,3] => [3,1,1] => 5

[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3]] => [3,2,5,1,4] => [3,1,1] => 5

[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => [4,1] => 5

[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5]] => [5,4,2,1,3] => [4,1] => 5

[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5]] => [5,3,2,1,4] => [4,1] => 5

[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4]] => [4,3,2,1,5] => [4,1] => 5

[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5] => 5

[[1]] => [[1]] => [1] => [1] => 1

[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,1,1,1,1,1] => 6

[[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]] => [2,1,3,4,5,6] => [2,1,1,1,1] => 6

[[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]] => [3,1,2,4,5,6] => [2,1,1,1,1] => 6

[[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]] => [4,1,2,3,5,6] => [2,1,1,1,1] => 6

[[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]] => [5,1,2,3,4,6] => [2,1,1,1,1] => 6

[[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]] => [6,1,2,3,4,5] => [2,1,1,1,1] => 6

[[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]] => [2,4,1,3,5,6] => [2,1,1,1,1] => 6

[[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]] => [3,4,1,2,5,6] => [2,1,1,1,1] => 6

[[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]] => [2,5,1,3,4,6] => [2,1,1,1,1] => 6

[[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]] => [3,5,1,2,4,6] => [2,1,1,1,1] => 6

[[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]] => [4,5,1,2,3,6] => [2,1,1,1,1] => 6

[[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]] => [2,6,1,3,4,5] => [2,1,1,1,1] => 6

[[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]] => [3,6,1,2,4,5] => [2,1,1,1,1] => 6

[[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]] => [4,6,1,2,3,5] => [2,1,1,1,1] => 6

[[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]] => [5,6,1,2,3,4] => [2,1,1,1,1] => 6

[[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]] => [3,2,1,4,5,6] => [3,1,1,1] => 6

[[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]] => [4,2,1,3,5,6] => [3,1,1,1] => 6

[[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]] => [4,3,1,2,5,6] => [3,1,1,1] => 6

[[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]] => [5,2,1,3,4,6] => [3,1,1,1] => 6

[[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]] => [5,3,1,2,4,6] => [3,1,1,1] => 6

[[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]] => [5,4,1,2,3,6] => [3,1,1,1] => 6

[[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]] => [6,2,1,3,4,5] => [3,1,1,1] => 6

[[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]] => [6,3,1,2,4,5] => [3,1,1,1] => 6

[[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]] => [6,4,1,2,3,5] => [3,1,1,1] => 6

[[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]] => [6,5,1,2,3,4] => [3,1,1,1] => 6

[[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]] => [2,4,6,1,3,5] => [2,1,1,1,1] => 6

[[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]] => [3,4,6,1,2,5] => [2,1,1,1,1] => 6

[[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]] => [2,5,6,1,3,4] => [2,1,1,1,1] => 6

[[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]] => [3,5,6,1,2,4] => [2,1,1,1,1] => 6

[[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]] => [4,5,6,1,2,3] => [2,1,1,1,1] => 6

[[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]] => [3,2,5,1,4,6] => [3,1,1,1] => 6

[[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]] => [4,2,5,1,3,6] => [3,1,1,1] => 6

[[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]] => [4,3,5,1,2,6] => [3,1,1,1] => 6

[[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]] => [5,2,4,1,3,6] => [3,1,1,1] => 6

[[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]] => [5,3,4,1,2,6] => [3,1,1,1] => 6

[[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]] => [3,2,6,1,4,5] => [3,1,1,1] => 6

[[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]] => [4,2,6,1,3,5] => [3,1,1,1] => 6

[[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]] => [4,3,6,1,2,5] => [3,1,1,1] => 6

[[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]] => [5,2,6,1,3,4] => [3,1,1,1] => 6

[[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]] => [5,3,6,1,2,4] => [3,1,1,1] => 6

[[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]] => [5,4,6,1,2,3] => [3,1,1,1] => 6

[[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]] => [6,2,4,1,3,5] => [3,1,1,1] => 6

[[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]] => [6,3,4,1,2,5] => [3,1,1,1] => 6

[[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]] => [6,2,5,1,3,4] => [3,1,1,1] => 6

[[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]] => [6,3,5,1,2,4] => [3,1,1,1] => 6

[[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]] => [6,4,5,1,2,3] => [3,1,1,1] => 6

[[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]] => [4,3,2,1,5,6] => [4,1,1] => 6

[[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]] => [5,3,2,1,4,6] => [4,1,1] => 6

[[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]] => [5,4,2,1,3,6] => [4,1,1] => 6

[[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]] => [5,4,3,1,2,6] => [4,1,1] => 6

[[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]] => [6,3,2,1,4,5] => [4,1,1] => 6

[[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]] => [6,4,2,1,3,5] => [4,1,1] => 6

[[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]] => [6,4,3,1,2,5] => [4,1,1] => 6

[[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]] => [6,5,2,1,3,4] => [4,1,1] => 6

[[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]] => [6,5,3,1,2,4] => [4,1,1] => 6

[[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]] => [6,5,4,1,2,3] => [4,1,1] => 6

[[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]] => [3,6,2,5,1,4] => [3,1,1,1] => 6

[[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]] => [4,6,2,5,1,3] => [3,1,1,1] => 6

[[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]] => [4,6,3,5,1,2] => [3,1,1,1] => 6

[[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]] => [5,6,2,4,1,3] => [3,1,1,1] => 6

[[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]] => [5,6,3,4,1,2] => [3,1,1,1] => 6

[[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]] => [4,3,2,6,1,5] => [4,1,1] => 6

[[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]] => [5,3,2,6,1,4] => [4,1,1] => 6

[[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]] => [5,4,2,6,1,3] => [4,1,1] => 6

[[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]] => [5,4,3,6,1,2] => [4,1,1] => 6

[[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]] => [6,3,2,5,1,4] => [4,1,1] => 6

[[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]] => [6,4,2,5,1,3] => [4,1,1] => 6

[[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]] => [6,4,3,5,1,2] => [4,1,1] => 6

[[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]] => [6,5,2,4,1,3] => [4,1,1] => 6

[[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]] => [6,5,3,4,1,2] => [4,1,1] => 6

[[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]] => [5,4,3,2,1,6] => [5,1] => 6

[[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]] => [6,4,3,2,1,5] => [5,1] => 6

[[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]] => [6,5,3,2,1,4] => [5,1] => 6

[[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]] => [6,5,4,2,1,3] => [5,1] => 6

[[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]] => [6,5,4,3,1,2] => [5,1] => 6

[[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]] => [6,5,4,3,2,1] => [6] => 6

[[2]] => [[1,1]] => [1,2] => [1,1] => 2

[[3]] => [[1,1,1]] => [1,2,3] => [1,1,1] => 3

[[4]] => [[1,1,1,1]] => [1,2,3,4] => [1,1,1,1] => 4

[[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => [1,1,1,1,1] => 5

[[4,3,2,1],[4,3,2],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,3],[4]] => [10,8,9,5,6,7,1,2,3,4] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,2],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,3],[4]] => [10,8,9,4,5,6,1,2,3,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,2],[4,2],[4]] => [[1,1,1,1],[2,2,3],[3,3],[4]] => [10,7,8,5,6,9,1,2,3,4] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,2],[4,2],[3]] => [[1,1,1,2],[2,2,3],[3,3],[4]] => [10,7,8,4,5,9,1,2,3,6] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,2],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,3],[4]] => [10,6,7,4,5,8,1,2,3,9] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,2],[4,2],[2]] => [[1,1,2,2],[2,2,3],[3,3],[4]] => [10,7,8,3,4,9,1,2,5,6] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,2],[3,2],[2]] => [[1,1,2,3],[2,2,3],[3,3],[4]] => [10,6,7,3,4,8,1,2,5,9] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,4],[4]] => [9,8,10,5,6,7,1,2,3,4] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,4],[4]] => [9,8,10,4,5,6,1,2,3,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,2],[4]] => [[1,1,1,1],[2,2,3],[3,4],[4]] => [9,7,10,5,6,8,1,2,3,4] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,2],[3]] => [[1,1,1,2],[2,2,3],[3,4],[4]] => [9,7,10,4,5,8,1,2,3,6] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,4],[4]] => [9,6,10,4,5,7,1,2,3,8] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,2],[2]] => [[1,1,2,2],[2,2,3],[3,4],[4]] => [9,7,10,3,4,8,1,2,5,6] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[4,2],[4]] => [[1,1,1,1],[2,2,4],[3,4],[4]] => [8,7,9,5,6,10,1,2,3,4] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[4,2],[3]] => [[1,1,1,2],[2,2,4],[3,4],[4]] => [8,7,9,4,5,10,1,2,3,6] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[3,2,1],[3,2],[3]] => [[1,1,1,4],[2,2,4],[3,4],[4]] => [7,6,8,4,5,9,1,2,3,10] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[4,2],[2]] => [[1,1,2,2],[2,2,4],[3,4],[4]] => [8,7,9,3,4,10,1,2,5,6] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[3,2],[2]] => [[1,1,2,3],[2,2,4],[3,4],[4]] => [8,6,9,3,4,10,1,2,5,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[3,2,1],[3,2],[2]] => [[1,1,2,4],[2,2,4],[3,4],[4]] => [7,6,8,3,4,9,1,2,5,10] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,1],[4]] => [[1,1,1,1],[2,3,3],[3,4],[4]] => [9,6,10,5,7,8,1,2,3,4] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,1],[3]] => [[1,1,1,2],[2,3,3],[3,4],[4]] => [9,6,10,4,7,8,1,2,3,5] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[3,1],[3]] => [[1,1,1,3],[2,3,3],[3,4],[4]] => [9,5,10,4,6,7,1,2,3,8] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,1],[2]] => [[1,1,2,2],[2,3,3],[3,4],[4]] => [9,6,10,3,7,8,1,2,4,5] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[3,1],[2]] => [[1,1,2,3],[2,3,3],[3,4],[4]] => [9,5,10,3,6,7,1,2,4,8] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[4,1],[4]] => [[1,1,1,1],[2,3,4],[3,4],[4]] => [8,6,9,5,7,10,1,2,3,4] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[4,1],[3]] => [[1,1,1,2],[2,3,4],[3,4],[4]] => [8,6,9,4,7,10,1,2,3,5] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[3,1],[3]] => [[1,1,1,3],[2,3,4],[3,4],[4]] => [8,5,9,4,6,10,1,2,3,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[3,2,1],[3,1],[3]] => [[1,1,1,4],[2,3,4],[3,4],[4]] => [7,5,8,4,6,9,1,2,3,10] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[4,1],[2]] => [[1,1,2,2],[2,3,4],[3,4],[4]] => [8,6,9,3,7,10,1,2,4,5] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[3,1],[2]] => [[1,1,2,3],[2,3,4],[3,4],[4]] => [8,5,9,3,6,10,1,2,4,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[3,2,1],[3,1],[2]] => [[1,1,2,4],[2,3,4],[3,4],[4]] => [7,5,8,3,6,9,1,2,4,10] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[2,1],[2]] => [[1,1,3,3],[2,3,4],[3,4],[4]] => [8,4,9,3,5,10,1,2,6,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[3,2,1],[2,1],[2]] => [[1,1,3,4],[2,3,4],[3,4],[4]] => [7,4,8,3,5,9,1,2,6,10] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[4,1],[1]] => [[1,2,2,2],[2,3,3],[3,4],[4]] => [9,6,10,2,7,8,1,3,4,5] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,3,1],[3,1],[1]] => [[1,2,2,3],[2,3,3],[3,4],[4]] => [9,5,10,2,6,7,1,3,4,8] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[4,1],[1]] => [[1,2,2,2],[2,3,4],[3,4],[4]] => [8,6,9,2,7,10,1,3,4,5] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[3,1],[1]] => [[1,2,2,3],[2,3,4],[3,4],[4]] => [8,5,9,2,6,10,1,3,4,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[3,2,1],[3,1],[1]] => [[1,2,2,4],[2,3,4],[3,4],[4]] => [7,5,8,2,6,9,1,3,4,10] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[4,2,1],[2,1],[1]] => [[1,2,3,3],[2,3,4],[3,4],[4]] => [8,4,9,2,5,10,1,3,6,7] => [4,1,1,1,1,1,1] => 10

[[4,3,2,1],[3,2,1],[2,1],[1]] => [[1,2,3,4],[2,3,4],[3,4],[4]] => [7,4,8,2,5,9,1,3,6,10] => [4,1,1,1,1,1,1] => 10

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Description

The hook length of the base cell of a partition.
This is also known as the perimeter of a partition. In particular, the perimeter of the empty partition is zero.

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 $k=1,\dots,n$.

Map

LLPS

Description

The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).