- FindStat

Identifier

Mp00078: Gelfand-Tsetlin patterns —Schuetzenberger involution⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
St000103: Semistandard tableaux ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[4,0],[4]] => [[4,0],[0]] => [[2,2,2,2]] => 8

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

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

[[3,1],[3]] => [[3,1],[1]] => [[1,2,2],[2]] => 7

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

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

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

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

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

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

[[3,0,0],[2,0],[2]] => [[3,0,0],[1,0],[1]] => [[1,3,3]] => 7

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

[[3,0,0],[3,0],[1]] => [[3,0,0],[2,0],[0]] => [[2,2,3]] => 7

[[3,0,0],[3,0],[2]] => [[3,0,0],[1,0],[0]] => [[2,3,3]] => 8

[[3,0,0],[3,0],[3]] => [[3,0,0],[0,0],[0]] => [[3,3,3]] => 9

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

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

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

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

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

[[2,1,0],[2,0],[2]] => [[2,1,0],[1,0],[1]] => [[1,3],[3]] => 7

[[2,1,0],[2,1],[1]] => [[2,1,0],[2,0],[0]] => [[2,2],[3]] => 7

[[2,1,0],[2,1],[2]] => [[2,1,0],[1,0],[0]] => [[2,3],[3]] => 8

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

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

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

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

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

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

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

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

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

[[5,0],[3]] => [[5,0],[2]] => [[1,1,2,2,2]] => 8

[[5,0],[4]] => [[5,0],[1]] => [[1,2,2,2,2]] => 9

[[5,0],[5]] => [[5,0],[0]] => [[2,2,2,2,2]] => 10

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

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

[[4,1],[3]] => [[4,1],[2]] => [[1,1,2,2],[2]] => 8

[[4,1],[4]] => [[4,1],[1]] => [[1,2,2,2],[2]] => 9

[[3,2],[2]] => [[3,2],[3]] => [[1,1,1],[2,2]] => 7

[[3,2],[3]] => [[3,2],[2]] => [[1,1,2],[2,2]] => 8

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

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

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

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

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

[[4,0,0],[2,0],[2]] => [[4,0,0],[2,0],[2]] => [[1,1,3,3]] => 8

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

[[4,0,0],[3,0],[1]] => [[4,0,0],[3,0],[1]] => [[1,2,2,3]] => 8

[[4,0,0],[3,0],[2]] => [[4,0,0],[2,0],[1]] => [[1,2,3,3]] => 9

[[4,0,0],[3,0],[3]] => [[4,0,0],[1,0],[1]] => [[1,3,3,3]] => 10

[[4,0,0],[4,0],[0]] => [[4,0,0],[4,0],[0]] => [[2,2,2,2]] => 8

[[4,0,0],[4,0],[1]] => [[4,0,0],[3,0],[0]] => [[2,2,2,3]] => 9

[[4,0,0],[4,0],[2]] => [[4,0,0],[2,0],[0]] => [[2,2,3,3]] => 10

[[4,0,0],[4,0],[3]] => [[4,0,0],[1,0],[0]] => [[2,3,3,3]] => 11

[[4,0,0],[4,0],[4]] => [[4,0,0],[0,0],[0]] => [[3,3,3,3]] => 12

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

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

[[3,1,0],[1,1],[1]] => [[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => 7

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

[[3,1,0],[2,0],[1]] => [[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => 7

[[3,1,0],[2,0],[2]] => [[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => 8

[[3,1,0],[2,1],[1]] => [[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => 8

[[3,1,0],[2,1],[2]] => [[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => 9

[[3,1,0],[3,0],[0]] => [[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => 7

[[3,1,0],[3,0],[1]] => [[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => 8

[[3,1,0],[3,0],[2]] => [[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => 9

[[3,1,0],[3,0],[3]] => [[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => 10

[[3,1,0],[3,1],[1]] => [[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => 9

[[3,1,0],[3,1],[2]] => [[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => 10

[[3,1,0],[3,1],[3]] => [[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => 11

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

[[2,2,0],[2,0],[1]] => [[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => 7

[[2,2,0],[2,0],[2]] => [[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => 8

[[2,2,0],[2,1],[1]] => [[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => 8

[[2,2,0],[2,1],[2]] => [[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => 9

[[2,2,0],[2,2],[2]] => [[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => 10

[[2,1,1],[1,1],[1]] => [[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => 7

[[2,1,1],[2,1],[1]] => [[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => 8

[[2,1,1],[2,1],[2]] => [[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => 9

>>> Load all 765 entries. <<<

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

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

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

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

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

[[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => 7

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

[[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => 7

[[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => 8

[[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => 9

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

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

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

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

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

[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => 7

[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => 7

[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => 8

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

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

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

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

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

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

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

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

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

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

[[5,0,0],[2,0],[1]] => [[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => 8

[[5,0,0],[2,0],[2]] => [[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => 9

[[5,0,0],[3,0],[0]] => [[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => 8

[[5,0,0],[3,0],[1]] => [[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => 9

[[5,0,0],[3,0],[2]] => [[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => 10

[[5,0,0],[3,0],[3]] => [[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => 11

[[5,0,0],[4,0],[0]] => [[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => 9

[[5,0,0],[4,0],[1]] => [[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => 10

[[5,0,0],[4,0],[2]] => [[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => 11

[[5,0,0],[4,0],[3]] => [[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => 12

[[5,0,0],[4,0],[4]] => [[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => 13

[[5,0,0],[5,0],[0]] => [[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => 10

[[5,0,0],[5,0],[1]] => [[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => 11

[[5,0,0],[5,0],[2]] => [[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => 12

[[5,0,0],[5,0],[3]] => [[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => 13

[[5,0,0],[5,0],[4]] => [[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => 14

[[5,0,0],[5,0],[5]] => [[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => 15

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

[[4,1,0],[1,0],[1]] => [[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => 7

[[4,1,0],[1,1],[1]] => [[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => 8

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

[[4,1,0],[2,0],[1]] => [[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => 8

[[4,1,0],[2,0],[2]] => [[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => 9

[[4,1,0],[2,1],[1]] => [[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => 9

[[4,1,0],[2,1],[2]] => [[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => 10

[[4,1,0],[3,0],[0]] => [[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => 8

[[4,1,0],[3,0],[1]] => [[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => 9

[[4,1,0],[3,0],[2]] => [[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => 10

[[4,1,0],[3,0],[3]] => [[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => 11

[[4,1,0],[3,1],[1]] => [[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => 10

[[4,1,0],[3,1],[2]] => [[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => 11

[[4,1,0],[3,1],[3]] => [[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => 12

[[4,1,0],[4,0],[0]] => [[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => 9

[[4,1,0],[4,0],[1]] => [[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => 10

[[4,1,0],[4,0],[2]] => [[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => 11

[[4,1,0],[4,0],[3]] => [[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => 12

[[4,1,0],[4,0],[4]] => [[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => 13

[[4,1,0],[4,1],[1]] => [[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => 11

[[4,1,0],[4,1],[2]] => [[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => 12

[[4,1,0],[4,1],[3]] => [[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => 13

[[4,1,0],[4,1],[4]] => [[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => 14

[[3,2,0],[2,0],[0]] => [[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => 7

[[3,2,0],[2,0],[1]] => [[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => 8

[[3,2,0],[2,0],[2]] => [[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => 9

[[3,2,0],[2,1],[1]] => [[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => 9

[[3,2,0],[2,1],[2]] => [[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => 10

[[3,2,0],[2,2],[2]] => [[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => 11

[[3,2,0],[3,0],[0]] => [[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => 8

[[3,2,0],[3,0],[1]] => [[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => 9

[[3,2,0],[3,0],[2]] => [[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => 10

[[3,2,0],[3,0],[3]] => [[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => 11

[[3,2,0],[3,1],[1]] => [[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => 10

[[3,2,0],[3,1],[2]] => [[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => 11

[[3,2,0],[3,1],[3]] => [[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => 12

[[3,2,0],[3,2],[2]] => [[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => 12

[[3,2,0],[3,2],[3]] => [[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => 13

[[3,1,1],[1,1],[1]] => [[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => 8

[[3,1,1],[2,1],[1]] => [[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => 9

[[3,1,1],[2,1],[2]] => [[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => 10

[[3,1,1],[3,1],[1]] => [[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => 10

[[3,1,1],[3,1],[2]] => [[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => 11

[[3,1,1],[3,1],[3]] => [[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => 12

[[2,2,1],[2,1],[1]] => [[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => 9

[[2,2,1],[2,1],[2]] => [[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => 10

[[2,2,1],[2,2],[2]] => [[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => 11

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

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

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

[[4,0,0,0],[1,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => 7

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

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

[[4,0,0,0],[2,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => 8

[[4,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => 8

[[4,0,0,0],[2,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => 9

[[4,0,0,0],[2,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => 10

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

[[4,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => 8

[[4,0,0,0],[3,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => 9

[[4,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => 9

[[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => 10

[[4,0,0,0],[3,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => 11

[[4,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => 10

[[4,0,0,0],[3,0,0],[3,0],[1]] => [[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => 11

[[4,0,0,0],[3,0,0],[3,0],[2]] => [[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => 12

[[4,0,0,0],[3,0,0],[3,0],[3]] => [[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => 13

[[4,0,0,0],[4,0,0],[0,0],[0]] => [[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => 8

[[4,0,0,0],[4,0,0],[1,0],[0]] => [[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => 9

[[4,0,0,0],[4,0,0],[1,0],[1]] => [[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => 10

[[4,0,0,0],[4,0,0],[2,0],[0]] => [[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => 10

[[4,0,0,0],[4,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => 11

[[4,0,0,0],[4,0,0],[2,0],[2]] => [[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => 12

[[4,0,0,0],[4,0,0],[3,0],[0]] => [[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => 11

[[4,0,0,0],[4,0,0],[3,0],[1]] => [[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => 12

[[4,0,0,0],[4,0,0],[3,0],[2]] => [[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => 13

[[4,0,0,0],[4,0,0],[3,0],[3]] => [[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => 14

[[4,0,0,0],[4,0,0],[4,0],[0]] => [[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => 12

[[4,0,0,0],[4,0,0],[4,0],[1]] => [[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => 13

[[4,0,0,0],[4,0,0],[4,0],[2]] => [[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => 14

[[4,0,0,0],[4,0,0],[4,0],[3]] => [[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => 15

[[4,0,0,0],[4,0,0],[4,0],[4]] => [[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => 16

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

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

[[3,1,0,0],[1,0,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => 7

[[3,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => 7

[[3,1,0,0],[1,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => 8

[[3,1,0,0],[1,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => 9

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

[[3,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => 7

[[3,1,0,0],[2,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => 8

[[3,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => 8

[[3,1,0,0],[2,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => 9

[[3,1,0,0],[2,0,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => 10

[[3,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => 8

[[3,1,0,0],[2,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => 9

[[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => 10

[[3,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => 9

[[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => 10

[[3,1,0,0],[2,1,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => 11

[[3,1,0,0],[2,1,0],[2,1],[1]] => [[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => 11

[[3,1,0,0],[2,1,0],[2,1],[2]] => [[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => 12

[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => 7

[[3,1,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => 8

[[3,1,0,0],[3,0,0],[1,0],[1]] => [[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => 9

[[3,1,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => 9

[[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => 10

[[3,1,0,0],[3,0,0],[2,0],[2]] => [[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => 11

[[3,1,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => 10

[[3,1,0,0],[3,0,0],[3,0],[1]] => [[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => 11

[[3,1,0,0],[3,0,0],[3,0],[2]] => [[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => 12

[[3,1,0,0],[3,0,0],[3,0],[3]] => [[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => 13

[[3,1,0,0],[3,1,0],[1,0],[0]] => [[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => 9

[[3,1,0,0],[3,1,0],[1,0],[1]] => [[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => 10

[[3,1,0,0],[3,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => 11

[[3,1,0,0],[3,1,0],[2,0],[0]] => [[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => 10

[[3,1,0,0],[3,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => 11

[[3,1,0,0],[3,1,0],[2,0],[2]] => [[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => 12

[[3,1,0,0],[3,1,0],[2,1],[1]] => [[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => 12

[[3,1,0,0],[3,1,0],[2,1],[2]] => [[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => 13

[[3,1,0,0],[3,1,0],[3,0],[0]] => [[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => 11

[[3,1,0,0],[3,1,0],[3,0],[1]] => [[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => 12

[[3,1,0,0],[3,1,0],[3,0],[2]] => [[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => 13

[[3,1,0,0],[3,1,0],[3,0],[3]] => [[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => 14

[[3,1,0,0],[3,1,0],[3,1],[1]] => [[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => 13

[[3,1,0,0],[3,1,0],[3,1],[2]] => [[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => 14

[[3,1,0,0],[3,1,0],[3,1],[3]] => [[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => 15

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

[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => 7

[[2,2,0,0],[2,0,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => 8

[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => 8

[[2,2,0,0],[2,0,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => 9

[[2,2,0,0],[2,0,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => 10

[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => 8

[[2,2,0,0],[2,1,0],[1,0],[1]] => [[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => 9

[[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => 10

[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => 9

[[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => 10

[[2,2,0,0],[2,1,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => 11

[[2,2,0,0],[2,1,0],[2,1],[1]] => [[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => 11

[[2,2,0,0],[2,1,0],[2,1],[2]] => [[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => 12

[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => 10

[[2,2,0,0],[2,2,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => 11

[[2,2,0,0],[2,2,0],[2,0],[2]] => [[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => 12

[[2,2,0,0],[2,2,0],[2,1],[1]] => [[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => 12

[[2,2,0,0],[2,2,0],[2,1],[2]] => [[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => 13

[[2,2,0,0],[2,2,0],[2,2],[2]] => [[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => 14

[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => 7

[[2,1,1,0],[1,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => 8

[[2,1,1,0],[1,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => 9

[[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => 10

[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => 8

[[2,1,1,0],[2,1,0],[1,0],[1]] => [[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => 9

[[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => 10

[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => 9

[[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => 10

[[2,1,1,0],[2,1,0],[2,0],[2]] => [[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => 11

[[2,1,1,0],[2,1,0],[2,1],[1]] => [[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => 11

[[2,1,1,0],[2,1,0],[2,1],[2]] => [[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => 12

[[2,1,1,0],[2,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => 11

[[2,1,1,0],[2,1,1],[2,1],[1]] => [[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => 12

[[2,1,1,0],[2,1,1],[2,1],[2]] => [[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => 13

[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => 10

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

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

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

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

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

[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => 7

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

[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => 7

[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => 8

[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => 9

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

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

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

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

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

[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => 7

[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => 7

[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => 8

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

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

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

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

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

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

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

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

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

[[5,0,0,0],[1,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => 8

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

[[5,0,0,0],[2,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => 8

[[5,0,0,0],[2,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => 9

[[5,0,0,0],[2,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => 9

[[5,0,0,0],[2,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => 10

[[5,0,0,0],[2,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => 11

[[5,0,0,0],[3,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => 8

[[5,0,0,0],[3,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => 9

[[5,0,0,0],[3,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => 10

[[5,0,0,0],[3,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => 10

[[5,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => 11

[[5,0,0,0],[3,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => 12

[[5,0,0,0],[3,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => 11

[[5,0,0,0],[3,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => 12

[[5,0,0,0],[3,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => 13

[[5,0,0,0],[3,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => 14

[[5,0,0,0],[4,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => 9

[[5,0,0,0],[4,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => 10

[[5,0,0,0],[4,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => 11

[[5,0,0,0],[4,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => 11

[[5,0,0,0],[4,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => 12

[[5,0,0,0],[4,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => 13

[[5,0,0,0],[4,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => 12

[[5,0,0,0],[4,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => 13

[[5,0,0,0],[4,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => 14

[[5,0,0,0],[4,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => 15

[[5,0,0,0],[4,0,0],[4,0],[0]] => [[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => 13

[[5,0,0,0],[4,0,0],[4,0],[1]] => [[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => 14

[[5,0,0,0],[4,0,0],[4,0],[2]] => [[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => 15

[[5,0,0,0],[4,0,0],[4,0],[3]] => [[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => 16

[[5,0,0,0],[4,0,0],[4,0],[4]] => [[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => 17

[[5,0,0,0],[5,0,0],[0,0],[0]] => [[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => 10

[[5,0,0,0],[5,0,0],[1,0],[0]] => [[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => 11

[[5,0,0,0],[5,0,0],[1,0],[1]] => [[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => 12

[[5,0,0,0],[5,0,0],[2,0],[0]] => [[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => 12

[[5,0,0,0],[5,0,0],[2,0],[1]] => [[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => 13

[[5,0,0,0],[5,0,0],[2,0],[2]] => [[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => 14

[[5,0,0,0],[5,0,0],[3,0],[0]] => [[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => 13

[[5,0,0,0],[5,0,0],[3,0],[1]] => [[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => 14

[[5,0,0,0],[5,0,0],[3,0],[2]] => [[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => 15

[[5,0,0,0],[5,0,0],[3,0],[3]] => [[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => 16

[[5,0,0,0],[5,0,0],[4,0],[0]] => [[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => 14

[[5,0,0,0],[5,0,0],[4,0],[1]] => [[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => 15

[[5,0,0,0],[5,0,0],[4,0],[2]] => [[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => 16

[[5,0,0,0],[5,0,0],[4,0],[3]] => [[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => 17

[[5,0,0,0],[5,0,0],[4,0],[4]] => [[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => 18

[[5,0,0,0],[5,0,0],[5,0],[0]] => [[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => 15

[[5,0,0,0],[5,0,0],[5,0],[1]] => [[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => 16

[[5,0,0,0],[5,0,0],[5,0],[2]] => [[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => 17

[[5,0,0,0],[5,0,0],[5,0],[3]] => [[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => 18

[[5,0,0,0],[5,0,0],[5,0],[4]] => [[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => 19

[[5,0,0,0],[5,0,0],[5,0],[5]] => [[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => 20

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

[[4,1,0,0],[1,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => 7

[[4,1,0,0],[1,0,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]] => 8

[[4,1,0,0],[1,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => 8

[[4,1,0,0],[1,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]] => 9

[[4,1,0,0],[1,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]] => 10

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

[[4,1,0,0],[2,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => 8

[[4,1,0,0],[2,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]] => 9

[[4,1,0,0],[2,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => 9

[[4,1,0,0],[2,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]] => 10

[[4,1,0,0],[2,0,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]] => 11

[[4,1,0,0],[2,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => 9

[[4,1,0,0],[2,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]] => 10

[[4,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]] => 11

[[4,1,0,0],[2,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => 10

[[4,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]] => 11

[[4,1,0,0],[2,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]] => 12

[[4,1,0,0],[2,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]] => 12

[[4,1,0,0],[2,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]] => 13

[[4,1,0,0],[3,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => 8

[[4,1,0,0],[3,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => 9

[[4,1,0,0],[3,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]] => 10

[[4,1,0,0],[3,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => 10

[[4,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]] => 11

[[4,1,0,0],[3,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]] => 12

[[4,1,0,0],[3,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => 11

[[4,1,0,0],[3,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]] => 12

[[4,1,0,0],[3,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]] => 13

[[4,1,0,0],[3,0,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]] => 14

[[4,1,0,0],[3,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => 10

[[4,1,0,0],[3,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]] => 11

[[4,1,0,0],[3,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]] => 12

[[4,1,0,0],[3,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => 11

[[4,1,0,0],[3,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]] => 12

[[4,1,0,0],[3,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]] => 13

[[4,1,0,0],[3,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]] => 13

[[4,1,0,0],[3,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]] => 14

[[4,1,0,0],[3,1,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => 12

[[4,1,0,0],[3,1,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]] => 13

[[4,1,0,0],[3,1,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]] => 14

[[4,1,0,0],[3,1,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]] => 15

[[4,1,0,0],[3,1,0],[3,1],[1]] => [[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]] => 14

[[4,1,0,0],[3,1,0],[3,1],[2]] => [[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]] => 15

[[4,1,0,0],[3,1,0],[3,1],[3]] => [[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]] => 16

[[4,1,0,0],[4,0,0],[0,0],[0]] => [[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => 9

[[4,1,0,0],[4,0,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => 10

[[4,1,0,0],[4,0,0],[1,0],[1]] => [[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]] => 11

[[4,1,0,0],[4,0,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => 11

[[4,1,0,0],[4,0,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]] => 12

[[4,1,0,0],[4,0,0],[2,0],[2]] => [[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]] => 13

[[4,1,0,0],[4,0,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => 12

[[4,1,0,0],[4,0,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]] => 13

[[4,1,0,0],[4,0,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]] => 14

[[4,1,0,0],[4,0,0],[3,0],[3]] => [[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]] => 15

[[4,1,0,0],[4,0,0],[4,0],[0]] => [[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => 13

[[4,1,0,0],[4,0,0],[4,0],[1]] => [[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]] => 14

[[4,1,0,0],[4,0,0],[4,0],[2]] => [[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]] => 15

[[4,1,0,0],[4,0,0],[4,0],[3]] => [[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]] => 16

[[4,1,0,0],[4,0,0],[4,0],[4]] => [[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]] => 17

[[4,1,0,0],[4,1,0],[1,0],[0]] => [[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => 11

[[4,1,0,0],[4,1,0],[1,0],[1]] => [[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]] => 12

[[4,1,0,0],[4,1,0],[1,1],[1]] => [[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]] => 13

[[4,1,0,0],[4,1,0],[2,0],[0]] => [[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => 12

[[4,1,0,0],[4,1,0],[2,0],[1]] => [[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]] => 13

[[4,1,0,0],[4,1,0],[2,0],[2]] => [[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]] => 14

[[4,1,0,0],[4,1,0],[2,1],[1]] => [[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]] => 14

[[4,1,0,0],[4,1,0],[2,1],[2]] => [[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]] => 15

[[4,1,0,0],[4,1,0],[3,0],[0]] => [[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => 13

[[4,1,0,0],[4,1,0],[3,0],[1]] => [[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]] => 14

[[4,1,0,0],[4,1,0],[3,0],[2]] => [[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]] => 15

[[4,1,0,0],[4,1,0],[3,0],[3]] => [[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]] => 16

[[4,1,0,0],[4,1,0],[3,1],[1]] => [[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]] => 15

[[4,1,0,0],[4,1,0],[3,1],[2]] => [[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]] => 16

[[4,1,0,0],[4,1,0],[3,1],[3]] => [[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]] => 17

[[4,1,0,0],[4,1,0],[4,0],[0]] => [[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => 14

[[4,1,0,0],[4,1,0],[4,0],[1]] => [[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]] => 15

[[4,1,0,0],[4,1,0],[4,0],[2]] => [[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]] => 16

[[4,1,0,0],[4,1,0],[4,0],[3]] => [[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]] => 17

[[4,1,0,0],[4,1,0],[4,0],[4]] => [[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]] => 18

[[4,1,0,0],[4,1,0],[4,1],[1]] => [[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]] => 16

[[4,1,0,0],[4,1,0],[4,1],[2]] => [[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]] => 17

[[4,1,0,0],[4,1,0],[4,1],[3]] => [[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]] => 18

[[4,1,0,0],[4,1,0],[4,1],[4]] => [[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]] => 19

[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => 7

[[3,2,0,0],[2,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => 8

[[3,2,0,0],[2,0,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]] => 9

[[3,2,0,0],[2,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => 9

[[3,2,0,0],[2,0,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]] => 10

[[3,2,0,0],[2,0,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]] => 11

[[3,2,0,0],[2,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => 9

[[3,2,0,0],[2,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]] => 10

[[3,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]] => 11

[[3,2,0,0],[2,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => 10

[[3,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]] => 11

[[3,2,0,0],[2,1,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]] => 12

[[3,2,0,0],[2,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]] => 12

[[3,2,0,0],[2,1,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]] => 13

[[3,2,0,0],[2,2,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => 11

[[3,2,0,0],[2,2,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]] => 12

[[3,2,0,0],[2,2,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]] => 13

[[3,2,0,0],[2,2,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]] => 13

[[3,2,0,0],[2,2,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]] => 14

[[3,2,0,0],[2,2,0],[2,2],[2]] => [[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]] => 15

[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => 8

[[3,2,0,0],[3,0,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => 9

[[3,2,0,0],[3,0,0],[1,0],[1]] => [[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]] => 10

[[3,2,0,0],[3,0,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => 10

[[3,2,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]] => 11

[[3,2,0,0],[3,0,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]] => 12

[[3,2,0,0],[3,0,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => 11

[[3,2,0,0],[3,0,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]] => 12

[[3,2,0,0],[3,0,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]] => 13

[[3,2,0,0],[3,0,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]] => 14

[[3,2,0,0],[3,1,0],[1,0],[0]] => [[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => 10

[[3,2,0,0],[3,1,0],[1,0],[1]] => [[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]] => 11

[[3,2,0,0],[3,1,0],[1,1],[1]] => [[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]] => 12

[[3,2,0,0],[3,1,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => 11

[[3,2,0,0],[3,1,0],[2,0],[1]] => [[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]] => 12

[[3,2,0,0],[3,1,0],[2,0],[2]] => [[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]] => 13

[[3,2,0,0],[3,1,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]] => 13

[[3,2,0,0],[3,1,0],[2,1],[2]] => [[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]] => 14

[[3,2,0,0],[3,1,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => 12

[[3,2,0,0],[3,1,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]] => 13

[[3,2,0,0],[3,1,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]] => 14

[[3,2,0,0],[3,1,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]] => 15

[[3,2,0,0],[3,1,0],[3,1],[1]] => [[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]] => 14

[[3,2,0,0],[3,1,0],[3,1],[2]] => [[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]] => 15

[[3,2,0,0],[3,1,0],[3,1],[3]] => [[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]] => 16

[[3,2,0,0],[3,2,0],[2,0],[0]] => [[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => 12

[[3,2,0,0],[3,2,0],[2,0],[1]] => [[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]] => 13

[[3,2,0,0],[3,2,0],[2,0],[2]] => [[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]] => 14

[[3,2,0,0],[3,2,0],[2,1],[1]] => [[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]] => 14

[[3,2,0,0],[3,2,0],[2,1],[2]] => [[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]] => 15

[[3,2,0,0],[3,2,0],[2,2],[2]] => [[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]] => 16

[[3,2,0,0],[3,2,0],[3,0],[0]] => [[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => 13

[[3,2,0,0],[3,2,0],[3,0],[1]] => [[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]] => 14

[[3,2,0,0],[3,2,0],[3,0],[2]] => [[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]] => 15

[[3,2,0,0],[3,2,0],[3,0],[3]] => [[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]] => 16

[[3,2,0,0],[3,2,0],[3,1],[1]] => [[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]] => 15

[[3,2,0,0],[3,2,0],[3,1],[2]] => [[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]] => 16

[[3,2,0,0],[3,2,0],[3,1],[3]] => [[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]] => 17

[[3,2,0,0],[3,2,0],[3,2],[2]] => [[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]] => 17

[[3,2,0,0],[3,2,0],[3,2],[3]] => [[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]] => 18

[[3,1,1,0],[1,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => 8

[[3,1,1,0],[1,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => 9

[[3,1,1,0],[1,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => 10

[[3,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => 11

[[3,1,1,0],[2,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => 9

[[3,1,1,0],[2,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => 10

[[3,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => 11

[[3,1,1,0],[2,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => 10

[[3,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => 11

[[3,1,1,0],[2,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => 12

[[3,1,1,0],[2,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => 12

[[3,1,1,0],[2,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => 13

[[3,1,1,0],[2,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => 12

[[3,1,1,0],[2,1,1],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => 13

[[3,1,1,0],[2,1,1],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => 14

[[3,1,1,0],[3,1,0],[1,0],[0]] => [[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => 10

[[3,1,1,0],[3,1,0],[1,0],[1]] => [[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => 11

[[3,1,1,0],[3,1,0],[1,1],[1]] => [[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => 12

[[3,1,1,0],[3,1,0],[2,0],[0]] => [[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => 11

[[3,1,1,0],[3,1,0],[2,0],[1]] => [[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => 12

[[3,1,1,0],[3,1,0],[2,0],[2]] => [[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => 13

[[3,1,1,0],[3,1,0],[2,1],[1]] => [[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => 13

[[3,1,1,0],[3,1,0],[2,1],[2]] => [[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => 14

[[3,1,1,0],[3,1,0],[3,0],[0]] => [[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => 12

[[3,1,1,0],[3,1,0],[3,0],[1]] => [[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => 13

[[3,1,1,0],[3,1,0],[3,0],[2]] => [[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => 14

[[3,1,1,0],[3,1,0],[3,0],[3]] => [[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => 15

[[3,1,1,0],[3,1,0],[3,1],[1]] => [[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => 14

[[3,1,1,0],[3,1,0],[3,1],[2]] => [[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => 15

[[3,1,1,0],[3,1,0],[3,1],[3]] => [[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => 16

[[3,1,1,0],[3,1,1],[1,1],[1]] => [[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => 13

[[3,1,1,0],[3,1,1],[2,1],[1]] => [[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => 14

[[3,1,1,0],[3,1,1],[2,1],[2]] => [[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => 15

[[3,1,1,0],[3,1,1],[3,1],[1]] => [[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => 15

[[3,1,1,0],[3,1,1],[3,1],[2]] => [[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => 16

[[3,1,1,0],[3,1,1],[3,1],[3]] => [[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => 17

[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => 9

[[2,2,1,0],[2,1,0],[1,0],[1]] => [[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]] => 10

[[2,2,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]] => 11

[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => 10

[[2,2,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]] => 11

[[2,2,1,0],[2,1,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]] => 12

[[2,2,1,0],[2,1,0],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]] => 12

[[2,2,1,0],[2,1,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]] => 13

[[2,2,1,0],[2,1,1],[1,1],[1]] => [[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]] => 12

[[2,2,1,0],[2,1,1],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]] => 13

[[2,2,1,0],[2,1,1],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]] => 14

[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => 11

[[2,2,1,0],[2,2,0],[2,0],[1]] => [[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]] => 12

[[2,2,1,0],[2,2,0],[2,0],[2]] => [[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]] => 13

[[2,2,1,0],[2,2,0],[2,1],[1]] => [[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]] => 13

[[2,2,1,0],[2,2,0],[2,1],[2]] => [[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]] => 14

[[2,2,1,0],[2,2,0],[2,2],[2]] => [[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]] => 15

[[2,2,1,0],[2,2,1],[2,1],[1]] => [[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]] => 14

[[2,2,1,0],[2,2,1],[2,1],[2]] => [[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]] => 15

[[2,2,1,0],[2,2,1],[2,2],[2]] => [[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]] => 16

[[2,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]] => 11

[[2,1,1,1],[2,1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]] => 12

[[2,1,1,1],[2,1,1],[2,1],[1]] => [[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]] => 13

[[2,1,1,1],[2,1,1],[2,1],[2]] => [[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]] => 14

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

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

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

[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => 7

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

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

[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => 8

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => 8

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => 9

[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => 10

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

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => 8

[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => 9

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => 9

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => 10

[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => 11

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => 10

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => 11

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => 12

[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => 13

[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => 8

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => 9

[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => 10

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => 10

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => 11

[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => 12

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => 11

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => 12

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => 13

[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => 14

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => 12

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => 13

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => 14

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => 15

[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => 16

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

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

[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => 7

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => 7

[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => 8

[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => 9

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

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => 7

[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => 8

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => 8

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => 9

[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => 10

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => 8

[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => 9

[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => 10

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => 9

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => 10

[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => 11

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => 11

[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => 12

[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => 7

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => 8

[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => 9

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => 9

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => 10

[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => 11

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => 10

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => 11

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => 12

[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => 13

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => 9

[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => 10

[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => 11

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => 10

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => 11

[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => 12

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => 12

[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => 13

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => 11

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => 12

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => 13

[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => 14

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => 13

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => 14

[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => 15

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

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => 7

[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => 8

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => 8

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => 9

[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => 10

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => 8

[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => 9

[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => 10

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => 9

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => 10

[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => 11

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => 11

[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => 12

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => 10

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => 11

[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => 12

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => 12

[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => 13

[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => 14

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => 7

[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => 8

[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => 9

[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => 10

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => 8

[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => 9

[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => 10

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => 9

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => 10

[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => 11

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => 11

[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => 12

[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => 11

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => 12

[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => 13

[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => 10

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

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

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

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

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

[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => 7

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

[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => 7

[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => 8

[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => 9

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

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

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

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

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

[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => 7

[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => 7

[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => 8

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

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

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

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

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

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

[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5]] => 15

[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2]] => 15

[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3]] => 15

[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4]] => 15

[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5]] => 15

[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4]] => 15

[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4]] => 15

[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5]] => 15

[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5]] => 15

[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5]] => 15

[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3]] => 15

[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4]] => 15

[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4]] => 15

[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5]] => 15

[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5]] => 15

[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5]] => 15

[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4]] => 15

[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4]] => 15

[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3]] => 15

[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5]] => 15

[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5]] => 15

[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4]] => 15

[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5]] => 15

[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5]] => 15

[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5]] => 15

[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5]] => 15

[[1]] => [[1]] => [[1]] => 1

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

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

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

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{(2, 2)} = q^{2} + 2\ q^{3} + q^{4}$

$F_{(2, 3)} = q^{3} + 2\ q^{4} + 2\ q^{5} + q^{6}$

$F_{(2, 4)} = q^{4} + 2\ q^{5} + 3\ q^{6} + 2\ q^{7} + q^{8}$

$F_{(3, 3)} = q^{3} + 2\ q^{4} + 4\ q^{5} + 5\ q^{6} + 4\ q^{7} + 2\ q^{8} + q^{9}$

$F_{(2, 5)} = q^{5} + 2\ q^{6} + 3\ q^{7} + 3\ q^{8} + 2\ q^{9} + q^{10}$

$F_{(3, 4)} = q^{4} + 2\ q^{5} + 5\ q^{6} + 7\ q^{7} + 9\ q^{8} + 7\ q^{9} + 5\ q^{10} + 2\ q^{11} + q^{12}$

$F_{(3, 5)} = q^{5} + 2\ q^{6} + 5\ q^{7} + 8\ q^{8} + 12\ q^{9} + 13\ q^{10} + 12\ q^{11} + 8\ q^{12} + 5\ q^{13} + 2\ q^{14} + q^{15}$

$F_{(4, 4)} = q^{4} + 2\ q^{5} + 5\ q^{6} + 9\ q^{7} + 14\ q^{8} + 17\ q^{9} + 20\ q^{10} + 17\ q^{11} + 14\ q^{12} + 9\ q^{13} + 5\ q^{14} + 2\ q^{15} + q^{16}$

$F_{(4, 5)} = q^{5} + 2\ q^{6} + 5\ q^{7} + 10\ q^{8} + 17\ q^{9} + 25\ q^{10} + 33\ q^{11} + 37\ q^{12} + 37\ q^{13} + 33\ q^{14} + 25\ q^{15} + 17\ q^{16} + 10\ q^{17} + 5\ q^{18} + 2\ q^{19} + q^{20}$

Description

The sum of the entries of a semistandard tableau.

Map

to semistandard tableau

Description

Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let

$G$ be a Gelfand-Tsetlin pattern and let

$\lambda^{(k)}$ be its

$(n-k+1)$ -st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,

$\lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)},$
where

$\lambda^{(0)}$ is the empty partition.
Each skew shape

$\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau

$T(G)$ by inserting

$k$ into the cells of the skew shape

$\lambda^{(k)} / \lambda^{(k-1)}$ , for

$k=1,\dots,n$ .

Map

Schuetzenberger involution

Description

Applies the Schuetzenberger involution to a Gelfand-Tsetlin pattern.
The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries. It is also known as evacuation, and in the context of crystal graphs of type

$A$ it realizes Lusztig's involution.
In the language of tableaux it is defined as follows. Consider a semistandard tableau with no entry larger than

$n$ . Use Schuetzenberger's jeu de taquin to slide all entries equal to

$1$ to the outer border of the tableau. Do the same for all entries equal to

$2$ , restricting the tableau to the entries larger than

$2$ , and so on, until the tableau is a reverse semistandard tableau. Finally, replace each entry with its complement with respect to

$n$ , that is, replace

$e$ with

$n+1-e$ .