Identifier
-
Mp00036:
Gelfand-Tsetlin patterns
—to semistandard tableau⟶
Semistandard tableaux
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000189: Posets ⟶ ℤ
Values
[[1,0],[0]] => [[2]] => [1] => ([],1) => 1
[[1,0],[1]] => [[1]] => [1] => ([],1) => 1
[[2,0],[0]] => [[2,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0],[1]] => [[1,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0],[2]] => [[1,1]] => [1,2] => ([(0,1)],2) => 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] => ([(0,2),(2,1)],3) => 3
[[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[2,1],[1]] => [[1,2],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1],[2]] => [[1,1],[2]] => [3,1,2] => ([(1,2)],3) => 3
[[2,0,0],[0,0],[0]] => [[3,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0],[1,0],[0]] => [[2,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0],[1,0],[1]] => [[1,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0],[2,0],[0]] => [[2,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0],[2,0],[1]] => [[1,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0],[2,0],[2]] => [[1,1]] => [1,2] => ([(0,1)],2) => 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] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0],[2,0],[0]] => [[2,2],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0],[2,0],[1]] => [[1,2],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0],[2,0],[2]] => [[1,1],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0],[2,1],[2]] => [[1,1],[2]] => [3,1,2] => ([(1,2)],3) => 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] => ([(0,1)],2) => 2
[[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [1,2] => ([(0,1)],2) => 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] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[4,1],[1]] => [[1,2,2,2],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1],[2]] => [[1,1,2,2],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1],[3]] => [[1,1,1,2],[2]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1],[4]] => [[1,1,1,1],[2]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[3,2],[2]] => [[1,1,2],[2,2]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2],[3]] => [[1,1,1],[2,2]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
>>> Load all 1493 entries. <<<[[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [4,3,1,2] => ([(2,3)],4) => 4
[[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [3,1,2] => ([(1,2)],3) => 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] => ([(0,1)],2) => 2
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,2] => ([(0,1)],2) => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [1,2] => ([(0,1)],2) => 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] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0],[1]] => [[1,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0],[2]] => [[1,1,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0],[3]] => [[1,1,1,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0],[4]] => [[1,1,1,1,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0],[5]] => [[1,1,1,1,1,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0],[6]] => [[1,1,1,1,1,1]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[5,1],[1]] => [[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1],[2]] => [[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1],[3]] => [[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1],[5]] => [[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[4,2],[2]] => [[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2],[4]] => [[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[3,3],[3]] => [[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
[[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => 5
[[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => 5
[[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 5
[[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 5
[[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 5
[[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 5
[[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 5
[[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 5
[[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
[[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 5
[[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 5
[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [4,3,1,2] => ([(2,3)],4) => 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] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [3,1,2] => ([(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1,3] => ([(0,2),(1,2)],3) => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [3,1,2] => ([(1,2)],3) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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
[[6,0,0],[0,0],[0]] => [[3,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[1,0],[0]] => [[2,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[1,0],[1]] => [[1,3,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[2,0],[0]] => [[2,2,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[2,0],[1]] => [[1,2,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[2,0],[2]] => [[1,1,3,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[3,0],[0]] => [[2,2,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[3,0],[1]] => [[1,2,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[3,0],[2]] => [[1,1,2,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[3,0],[3]] => [[1,1,1,3,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[4,0],[0]] => [[2,2,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[4,0],[1]] => [[1,2,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[4,0],[2]] => [[1,1,2,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[4,0],[3]] => [[1,1,1,2,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[4,0],[4]] => [[1,1,1,1,3,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[5,0],[0]] => [[2,2,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[5,0],[1]] => [[1,2,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[5,0],[2]] => [[1,1,2,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[5,0],[3]] => [[1,1,1,2,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[5,0],[4]] => [[1,1,1,1,2,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[5,0],[5]] => [[1,1,1,1,1,3]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[6,0],[0]] => [[2,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[6,0],[1]] => [[1,2,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[6,0],[2]] => [[1,1,2,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[6,0],[3]] => [[1,1,1,2,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[6,0],[4]] => [[1,1,1,1,2,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[6,0],[5]] => [[1,1,1,1,1,2]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[6,0,0],[6,0],[6]] => [[1,1,1,1,1,1]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 6
[[5,1,0],[1,0],[0]] => [[2,3,3,3,3],[3]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1,0],[1,0],[1]] => [[1,3,3,3,3],[3]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1,0],[1,1],[1]] => [[1,3,3,3,3],[2]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1,0],[2,0],[0]] => [[2,2,3,3,3],[3]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1,0],[2,0],[1]] => [[1,2,3,3,3],[3]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1,0],[2,0],[2]] => [[1,1,3,3,3],[3]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1,0],[2,1],[1]] => [[1,2,3,3,3],[2]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1,0],[2,1],[2]] => [[1,1,3,3,3],[2]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1,0],[3,0],[0]] => [[2,2,2,3,3],[3]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1,0],[3,0],[1]] => [[1,2,2,3,3],[3]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1,0],[3,0],[2]] => [[1,1,2,3,3],[3]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1,0],[3,0],[3]] => [[1,1,1,3,3],[3]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1,0],[3,1],[1]] => [[1,2,2,3,3],[2]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1,0],[3,1],[2]] => [[1,1,2,3,3],[2]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1,0],[3,1],[3]] => [[1,1,1,3,3],[2]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1,0],[4,0],[0]] => [[2,2,2,2,3],[3]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1,0],[4,0],[1]] => [[1,2,2,2,3],[3]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1,0],[4,0],[2]] => [[1,1,2,2,3],[3]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1,0],[4,0],[3]] => [[1,1,1,2,3],[3]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1,0],[4,0],[4]] => [[1,1,1,1,3],[3]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1,0],[4,1],[1]] => [[1,2,2,2,3],[2]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1,0],[4,1],[2]] => [[1,1,2,2,3],[2]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1,0],[4,1],[3]] => [[1,1,1,2,3],[2]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1,0],[4,1],[4]] => [[1,1,1,1,3],[2]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1,0],[5,0],[0]] => [[2,2,2,2,2],[3]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[5,1,0],[5,0],[1]] => [[1,2,2,2,2],[3]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[5,1,0],[5,0],[2]] => [[1,1,2,2,2],[3]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[5,1,0],[5,0],[3]] => [[1,1,1,2,2],[3]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[5,1,0],[5,0],[4]] => [[1,1,1,1,2],[3]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[5,1,0],[5,0],[5]] => [[1,1,1,1,1],[3]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[5,1,0],[5,1],[1]] => [[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 6
[[5,1,0],[5,1],[2]] => [[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 6
[[5,1,0],[5,1],[3]] => [[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 6
[[5,1,0],[5,1],[4]] => [[1,1,1,1,2],[2]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 6
[[5,1,0],[5,1],[5]] => [[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 6
[[4,2,0],[2,0],[0]] => [[2,2,3,3],[3,3]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2,0],[2,0],[1]] => [[1,2,3,3],[3,3]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2,0],[2,0],[2]] => [[1,1,3,3],[3,3]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2,0],[2,1],[1]] => [[1,2,3,3],[2,3]] => [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 6
[[4,2,0],[2,1],[2]] => [[1,1,3,3],[2,3]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2,0],[2,2],[2]] => [[1,1,3,3],[2,2]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2,0],[3,0],[0]] => [[2,2,2,3],[3,3]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2,0],[3,0],[1]] => [[1,2,2,3],[3,3]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2,0],[3,0],[2]] => [[1,1,2,3],[3,3]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2,0],[3,0],[3]] => [[1,1,1,3],[3,3]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2,0],[3,1],[1]] => [[1,2,2,3],[2,3]] => [2,5,1,3,4,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 6
[[4,2,0],[3,1],[2]] => [[1,1,2,3],[2,3]] => [3,5,1,2,4,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 6
[[4,2,0],[3,1],[3]] => [[1,1,1,3],[2,3]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2,0],[3,2],[2]] => [[1,1,2,3],[2,2]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2,0],[3,2],[3]] => [[1,1,1,3],[2,2]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2,0],[4,0],[0]] => [[2,2,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[4,2,0],[4,0],[1]] => [[1,2,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[4,2,0],[4,0],[2]] => [[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[4,2,0],[4,0],[3]] => [[1,1,1,2],[3,3]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[4,2,0],[4,0],[4]] => [[1,1,1,1],[3,3]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[4,2,0],[4,1],[1]] => [[1,2,2,2],[2,3]] => [2,6,1,3,4,5] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 6
[[4,2,0],[4,1],[2]] => [[1,1,2,2],[2,3]] => [3,6,1,2,4,5] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 6
[[4,2,0],[4,1],[3]] => [[1,1,1,2],[2,3]] => [4,6,1,2,3,5] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 6
[[4,2,0],[4,1],[4]] => [[1,1,1,1],[2,3]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[4,2,0],[4,2],[2]] => [[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 6
[[4,2,0],[4,2],[3]] => [[1,1,1,2],[2,2]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 6
[[4,2,0],[4,2],[4]] => [[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 6
[[4,1,1],[1,1],[1]] => [[1,3,3,3],[2],[3]] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 6
[[4,1,1],[2,1],[1]] => [[1,2,3,3],[2],[3]] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 6
[[4,1,1],[2,1],[2]] => [[1,1,3,3],[2],[3]] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 6
[[4,1,1],[3,1],[1]] => [[1,2,2,3],[2],[3]] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 6
[[4,1,1],[3,1],[2]] => [[1,1,2,3],[2],[3]] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 6
[[4,1,1],[3,1],[3]] => [[1,1,1,3],[2],[3]] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 6
[[4,1,1],[4,1],[1]] => [[1,2,2,2],[2],[3]] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 6
[[4,1,1],[4,1],[2]] => [[1,1,2,2],[2],[3]] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 6
[[4,1,1],[4,1],[3]] => [[1,1,1,2],[2],[3]] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 6
[[4,1,1],[4,1],[4]] => [[1,1,1,1],[2],[3]] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 6
[[3,3,0],[3,0],[0]] => [[2,2,2],[3,3,3]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[3,3,0],[3,0],[1]] => [[1,2,2],[3,3,3]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[3,3,0],[3,0],[2]] => [[1,1,2],[3,3,3]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[3,3,0],[3,0],[3]] => [[1,1,1],[3,3,3]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[3,3,0],[3,1],[1]] => [[1,2,2],[2,3,3]] => [2,5,6,1,3,4] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 6
[[3,3,0],[3,1],[2]] => [[1,1,2],[2,3,3]] => [3,5,6,1,2,4] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 6
[[3,3,0],[3,1],[3]] => [[1,1,1],[2,3,3]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[3,3,0],[3,2],[2]] => [[1,1,2],[2,2,3]] => [3,4,6,1,2,5] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 6
[[3,3,0],[3,2],[3]] => [[1,1,1],[2,2,3]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[3,3,0],[3,3],[3]] => [[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 6
[[3,2,1],[2,1],[1]] => [[1,2,3],[2,3],[3]] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 6
[[3,2,1],[2,1],[2]] => [[1,1,3],[2,3],[3]] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 6
[[3,2,1],[2,2],[2]] => [[1,1,3],[2,2],[3]] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 6
[[3,2,1],[3,1],[1]] => [[1,2,2],[2,3],[3]] => [5,2,6,1,3,4] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 6
[[3,2,1],[3,1],[2]] => [[1,1,2],[2,3],[3]] => [5,3,6,1,2,4] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 6
[[3,2,1],[3,1],[3]] => [[1,1,1],[2,3],[3]] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 6
[[3,2,1],[3,2],[2]] => [[1,1,2],[2,2],[3]] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 6
[[3,2,1],[3,2],[3]] => [[1,1,1],[2,2],[3]] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 6
[[2,2,2],[2,2],[2]] => [[1,1],[2,2],[3,3]] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 6
[[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 5
[[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 5
[[4,1,0,0],[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 5
[[4,1,0,0],[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 5
[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => 5
[[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => 5
[[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => 5
[[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => 5
[[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => 5
[[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => 5
[[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => 5
[[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => 5
[[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => 5
[[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => 5
[[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => 5
[[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 5
[[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 5
[[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 5
[[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 5
[[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 5
[[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 5
[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]] => [3,2,5,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 5
[[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 5
[[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 5
[[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 5
[[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 5
[[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 5
[[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]] => [5,4,3,1,2] => ([(3,4)],5) => 5
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,5]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[5]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[5]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,5],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,5],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,5],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,5],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,5],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[5]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,5]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,5]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 4
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4],[5]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4],[5]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4],[5]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[5]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[5]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[5]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,5],[2],[3]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[5]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[5]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [4,3,1,2] => ([(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [4,3,1,2] => ([(2,3)],4) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(2,1)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(0,2),(1,2)],3) => 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] => ([(1,2)],3) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,1)],2) => 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] => ([(0,4),(2,3),(3,1),(4,2)],5) => 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] => ([(1,4),(3,2),(4,3)],5) => 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] => ([(0,4),(1,2),(2,3),(3,4)],5) => 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] => ([(0,4),(1,2),(2,4),(4,3)],5) => 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] => ([(0,4),(1,4),(2,3),(4,2)],5) => 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] => ([(0,3),(1,4),(4,2)],5) => 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] => ([(0,3),(1,2),(1,4),(3,4)],5) => 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] => ([(0,3),(1,2),(2,4),(3,4)],5) => 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] => ([(0,4),(1,2),(1,4),(4,3)],5) => 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] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 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] => ([(2,3),(3,4)],5) => 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] => ([(1,4),(2,3),(3,4)],5) => 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] => ([(0,4),(1,4),(2,3),(3,4)],5) => 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] => ([(1,4),(2,4),(4,3)],5) => 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] => ([(0,4),(1,3),(2,3),(3,4)],5) => 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] => ([(0,4),(1,4),(2,4),(4,3)],5) => 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] => ([(1,4),(2,3)],5) => 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] => ([(0,4),(1,4),(2,3)],5) => 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] => ([(1,4),(2,3),(2,4)],5) => 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] => ([(0,4),(1,3),(2,3),(2,4)],5) => 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] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 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] => ([(3,4)],5) => 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] => ([(2,4),(3,4)],5) => 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] => ([(1,4),(2,4),(3,4)],5) => 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] => ([(0,4),(1,4),(2,4),(3,4)],5) => 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] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 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] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 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] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 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] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 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] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 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] => ([(1,5),(3,4),(4,2),(5,3)],6) => 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] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 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] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 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] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => 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] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => 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] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 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] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => 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] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => 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] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => 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] => ([(0,5),(1,3),(4,2),(5,4)],6) => 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] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 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] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 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] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 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] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 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] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 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] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 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] => ([(1,5),(2,5),(3,4),(5,3)],6) => 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] => ([(1,5),(2,3),(3,5),(5,4)],6) => 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] => ([(1,5),(2,3),(3,4),(4,5)],6) => 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] => ([(2,3),(3,5),(5,4)],6) => 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] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => 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] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => 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] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => 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] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => 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] => ([(0,5),(1,4),(4,2),(5,3)],6) => 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] => ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 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] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 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] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 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] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 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] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 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] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 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] => ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) => 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] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) => 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] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6) => 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] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => 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] => ([(0,5),(1,5),(2,3),(3,4)],6) => 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] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 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] => ([(1,4),(2,3),(3,5),(4,5)],6) => 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] => ([(1,5),(2,3),(2,5),(5,4)],6) => 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] => ([(1,4),(2,3),(2,5),(4,5)],6) => 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] => ([(1,3),(2,4),(4,5)],6) => 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] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 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] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 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] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 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] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 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] => ([(1,5),(2,5),(3,5),(5,4)],6) => 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] => ([(1,5),(2,4),(3,4),(4,5)],6) => 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] => ([(1,5),(2,5),(3,4),(4,5)],6) => 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] => ([(2,5),(3,5),(5,4)],6) => 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] => ([(2,5),(3,4),(4,5)],6) => 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] => ([(3,4),(4,5)],6) => 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] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 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] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => 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] => ([(0,5),(1,3),(2,4),(2,5)],6) => 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] => ([(0,5),(1,3),(2,4),(2,5)],6) => 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] => ([(0,5),(1,4),(2,3)],6) => 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] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 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] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 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] => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6) => 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] => ([(0,5),(1,5),(2,5),(3,4)],6) => 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] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 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] => ([(1,5),(2,4),(3,4),(3,5)],6) => 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] => ([(1,5),(2,5),(3,4)],6) => 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] => ([(2,5),(3,4),(3,5)],6) => 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] => ([(2,5),(3,4)],6) => 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] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 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] => ([(1,5),(2,5),(3,5),(4,5)],6) => 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] => ([(2,5),(3,5),(4,5)],6) => 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] => ([(3,5),(4,5)],6) => 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] => ([(4,5)],6) => 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] => ([(0,1)],2) => 2
[[3]] => [[1,1,1]] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[[4]] => [[1,1,1,1]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[[5]] => [[1,1,1,1,1]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
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Generating function
F(2,1)=2 q
F(2,2)=4 q2
F(3,1)=3 q
F(2,3)=6 q3
F(3,2)=9 q2
F(4,1)=4 q
F(2,4)=9 q4
F(3,3)=19 q3
F(4,2)=16 q2
F(5,1)=5 q
F(2,5)=12 q5
F(3,4)=39 q4
F(4,3)=44 q3
F(5,2)=25 q2
F(6,1)=6 q
F(2,6)=16 q6
F(3,5)=69 q5
F(4,4)=116 q4
F(5,3)=85 q3
F(6,2)=36 q2
F(3,6)=119 q6
F(4,5)=260 q5
F(5,4)=275 q4
F(6,3)=146 q3
F(7,2)=49 q2
Description
The number of elements in the poset.
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let G be a Gelfand-Tsetlin pattern and let λ(k) be its (n−k+1)-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
λ(0)⊆λ(1)⊆⋯⊆λ(n),
where λ(0) is the empty partition.
Each skew shape λ(k)/λ(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 λ(k)/λ(k−1), for k=1,…,n.
Let G be a Gelfand-Tsetlin pattern and let λ(k) be its (n−k+1)-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
λ(0)⊆λ(1)⊆⋯⊆λ(n),
where λ(0) is the empty partition.
Each skew shape λ(k)/λ(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 λ(k)/λ(k−1), for k=1,…,n.
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).
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation π of length n, this poset has vertices
{(i,π(i)) : 1≤i≤n}
and the cover relation is given by (w,x)≤(y,z) if w≤y and x≤z.
For example, the permutation [3,1,5,4,2] is mapped to the poset with cover relations
{(2,1)≺(5,2), (2,1)≺(4,4), (2,1)≺(3,5), (1,3)≺(4,4), (1,3)≺(3,5)}.
For a permutation π of length n, this poset has vertices
{(i,π(i)) : 1≤i≤n}
and the cover relation is given by (w,x)≤(y,z) if w≤y and x≤z.
For example, the permutation [3,1,5,4,2] is mapped to the poset with cover relations
{(2,1)≺(5,2), (2,1)≺(4,4), (2,1)≺(3,5), (1,3)≺(4,4), (1,3)≺(3,5)}.
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