Identifier
-
Mp00185:
Skew partitions
—cell poset⟶
Posets
Mp00074: Posets —to graph⟶ Graphs
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
St000383: Integer compositions ⟶ ℤ
Values
[[1],[]] => ([],1) => ([],1) => [1] => 1
[[2],[]] => ([(0,1)],2) => ([(0,1)],2) => [1,1] => 1
[[1,1],[]] => ([(0,1)],2) => ([(0,1)],2) => [1,1] => 1
[[2,1],[1]] => ([],2) => ([],2) => [2] => 2
[[3],[]] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => [1,1,1] => 1
[[2,1],[]] => ([(0,1),(0,2)],3) => ([(0,2),(1,2)],3) => [1,1,1] => 1
[[3,1],[1]] => ([(1,2)],3) => ([(1,2)],3) => [1,2] => 2
[[2,2],[1]] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => [1,1,1] => 1
[[3,2],[2]] => ([(1,2)],3) => ([(1,2)],3) => [1,2] => 2
[[1,1,1],[]] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => [1,1,1] => 1
[[2,2,1],[1,1]] => ([(1,2)],3) => ([(1,2)],3) => [1,2] => 2
[[2,1,1],[1]] => ([(1,2)],3) => ([(1,2)],3) => [1,2] => 2
[[3,2,1],[2,1]] => ([],3) => ([],3) => [3] => 3
[[4],[]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[3,1],[]] => ([(0,2),(0,3),(3,1)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[4,1],[1]] => ([(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[2,2],[]] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => [1,2,1] => 1
[[3,2],[1]] => ([(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[4,2],[2]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => [2,2] => 2
[[2,1,1],[]] => ([(0,2),(0,3),(3,1)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[3,2,1],[1,1]] => ([(1,2),(1,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[3,1,1],[1]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => [2,2] => 2
[[4,2,1],[2,1]] => ([(2,3)],4) => ([(2,3)],4) => [1,3] => 3
[[3,3],[2]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[4,3],[3]] => ([(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[2,2,1],[1]] => ([(0,3),(1,2),(1,3)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[3,3,1],[2,1]] => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[3,2,1],[2]] => ([(1,2),(1,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[4,3,1],[3,1]] => ([(2,3)],4) => ([(2,3)],4) => [1,3] => 3
[[2,2,2],[1,1]] => ([(0,3),(1,2),(2,3)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[3,3,2],[2,2]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => [2,2] => 2
[[3,2,2],[2,1]] => ([(1,3),(2,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[4,3,2],[3,2]] => ([(2,3)],4) => ([(2,3)],4) => [1,3] => 3
[[1,1,1,1],[]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => [1,1,1,1] => 1
[[2,2,2,1],[1,1,1]] => ([(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[2,2,1,1],[1,1]] => ([(0,3),(1,2)],4) => ([(0,3),(1,2)],4) => [2,2] => 2
[[3,3,2,1],[2,2,1]] => ([(2,3)],4) => ([(2,3)],4) => [1,3] => 3
[[2,1,1,1],[1]] => ([(1,2),(2,3)],4) => ([(1,3),(2,3)],4) => [1,1,2] => 2
[[3,2,2,1],[2,1,1]] => ([(2,3)],4) => ([(2,3)],4) => [1,3] => 3
[[3,2,1,1],[2,1]] => ([(2,3)],4) => ([(2,3)],4) => [1,3] => 3
[[4,3,2,1],[3,2,1]] => ([],4) => ([],4) => [4] => 4
[[5],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[4,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[5,1],[1]] => ([(1,4),(3,2),(4,3)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[3,2],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [1,1,1,1,1] => 1
[[4,2],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[5,2],[2]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[3,1,1],[]] => ([(0,3),(0,4),(3,2),(4,1)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[4,2,1],[1,1]] => ([(1,3),(1,4),(4,2)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[4,1,1],[1]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[5,2,1],[2,1]] => ([(2,3),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[3,3],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [1,1,1,1,1] => 1
[[4,3],[2]] => ([(0,3),(1,2),(1,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[5,3],[3]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[2,2,1],[]] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [1,1,1,1,1] => 1
[[3,3,1],[1,1]] => ([(1,2),(1,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => [1,2,2] => 2
[[3,2,1],[1]] => ([(0,3),(0,4),(1,2),(1,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[4,3,1],[2,1]] => ([(1,4),(2,3),(2,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[4,2,1],[2]] => ([(0,4),(1,2),(1,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[5,3,1],[3,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[3,2,2],[1,1]] => ([(0,4),(1,2),(1,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[4,3,2],[2,2]] => ([(0,4),(1,2),(1,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[4,2,2],[2,1]] => ([(0,4),(1,4),(2,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[5,3,2],[3,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[2,1,1,1],[]] => ([(0,2),(0,4),(3,1),(4,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[3,2,2,1],[1,1,1]] => ([(1,3),(1,4),(4,2)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[3,2,1,1],[1,1]] => ([(0,4),(1,2),(1,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[4,3,2,1],[2,2,1]] => ([(2,3),(2,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[3,1,1,1],[1]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[4,2,2,1],[2,1,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[4,2,1,1],[2,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[5,3,2,1],[3,2,1]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[4,4],[3]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[5,4],[4]] => ([(1,4),(3,2),(4,3)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[3,3,1],[2]] => ([(0,4),(1,2),(1,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[4,4,1],[3,1]] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[4,3,1],[3]] => ([(1,3),(1,4),(4,2)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[5,4,1],[4,1]] => ([(2,3),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[2,2,2],[1]] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [1,1,1,1,1] => 1
[[3,3,2],[2,1]] => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[4,4,2],[3,2]] => ([(0,4),(1,4),(2,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[3,2,2],[2]] => ([(1,2),(1,3),(2,4),(3,4)],5) => ([(1,3),(1,4),(2,3),(2,4)],5) => [1,2,2] => 2
[[4,3,2],[3,1]] => ([(1,4),(2,3),(2,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[5,4,2],[4,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[2,2,1,1],[1]] => ([(0,4),(1,2),(1,4),(2,3)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[3,3,2,1],[2,1,1]] => ([(1,4),(2,3),(2,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[3,3,1,1],[2,1]] => ([(0,4),(1,4),(2,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[4,4,2,1],[3,2,1]] => ([(2,4),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[3,2,1,1],[2]] => ([(1,3),(1,4),(4,2)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[4,3,2,1],[3,1,1]] => ([(2,3),(2,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[4,3,1,1],[3,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[5,4,2,1],[4,2,1]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[3,3,3],[2,2]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[4,4,3],[3,3]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[4,3,3],[3,2]] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[5,4,3],[4,3]] => ([(2,3),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[2,2,2,1],[1,1]] => ([(0,3),(1,2),(1,4),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[3,3,3,1],[2,2,1]] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[3,3,2,1],[2,2]] => ([(0,4),(1,2),(1,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[4,4,3,1],[3,3,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[3,2,2,1],[2,1]] => ([(1,4),(2,3),(2,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
>>> Load all 1304 entries. <<<[[4,3,3,1],[3,2,1]] => ([(2,4),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[4,3,2,1],[3,2]] => ([(2,3),(2,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[5,4,3,1],[4,3,1]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[2,2,2,2],[1,1,1]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[3,3,3,2],[2,2,2]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[3,3,2,2],[2,2,1]] => ([(0,4),(1,4),(2,3)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[4,4,3,2],[3,3,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[3,2,2,2],[2,1,1]] => ([(1,4),(2,3),(3,4)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[4,3,3,2],[3,2,2]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[4,3,2,2],[3,2,1]] => ([(2,4),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[5,4,3,2],[4,3,2]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[1,1,1,1,1],[]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => [1,1,1,1,1] => 1
[[2,2,2,2,1],[1,1,1,1]] => ([(1,4),(3,2),(4,3)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[2,2,2,1,1],[1,1,1]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[3,3,3,2,1],[2,2,2,1]] => ([(2,3),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[2,2,1,1,1],[1,1]] => ([(0,3),(1,4),(4,2)],5) => ([(0,1),(2,4),(3,4)],5) => [1,1,1,2] => 2
[[3,3,2,2,1],[2,2,1,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[3,3,2,1,1],[2,2,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[4,4,3,2,1],[3,3,2,1]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[2,1,1,1,1],[1]] => ([(1,4),(3,2),(4,3)],5) => ([(1,4),(2,3),(3,4)],5) => [1,1,1,2] => 2
[[3,2,2,2,1],[2,1,1,1]] => ([(2,3),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[3,2,2,1,1],[2,1,1]] => ([(1,4),(2,3)],5) => ([(1,4),(2,3)],5) => [2,3] => 3
[[4,3,3,2,1],[3,2,2,1]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[3,2,1,1,1],[2,1]] => ([(2,3),(3,4)],5) => ([(2,4),(3,4)],5) => [1,1,3] => 3
[[4,3,2,2,1],[3,2,1,1]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[4,3,2,1,1],[3,2,1]] => ([(3,4)],5) => ([(3,4)],5) => [1,4] => 4
[[5,4,3,2,1],[4,3,2,1]] => ([],5) => ([],5) => [5] => 5
[[6],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[6,1],[1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,2],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[5,2],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[6,2],[2]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,2,1],[1,1]] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,1,1],[1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[6,2,1],[2,1]] => ([(2,3),(3,5),(5,4)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[3,3],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => [1,2,1,1,1] => 1
[[4,3],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,3],[2]] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[6,3],[3]] => ([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[3,2,1],[]] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,3,1],[1,1]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[4,2,1],[1]] => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,3,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,2,1],[2]] => ([(0,5),(1,3),(1,4),(5,2)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[6,3,1],[3,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,2,2],[1,1]] => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,3,2],[2,2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,2,2],[2,1]] => ([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[6,3,2],[3,2]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,1,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,2,2,1],[1,1,1]] => ([(1,4),(1,5),(4,3),(5,2)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,2,1,1],[1,1]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,3,2,1],[2,2,1]] => ([(2,3),(2,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[4,1,1,1],[1]] => ([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[5,2,2,1],[2,1,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,2,1,1],[2,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[6,3,2,1],[3,2,1]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[4,4],[2]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[5,4],[3]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[6,4],[4]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[3,3,1],[1]] => ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[4,4,1],[2,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[4,3,1],[2]] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,4,1],[3,1]] => ([(1,4),(2,3),(2,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,3,1],[3]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[6,4,1],[4,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[2,2,2],[]] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => [1,2,1,1,1] => 1
[[3,3,2],[1,1]] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[4,4,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [1,3,2] => 2
[[3,2,2],[1]] => ([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[4,3,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,4,2],[3,2]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,2,2],[2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [1,3,2] => 2
[[5,3,2],[3,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[6,4,2],[4,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[2,2,1,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[3,3,2,1],[1,1,1]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[3,3,1,1],[1,1]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [1,3,2] => 2
[[4,4,2,1],[2,2,1]] => ([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => [1,2,3] => 3
[[3,2,1,1],[1]] => ([(0,3),(0,5),(1,4),(1,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,3,2,1],[2,1,1]] => ([(1,4),(1,5),(2,3),(2,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,3,1,1],[2,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,4,2,1],[3,2,1]] => ([(2,5),(3,4),(3,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[4,2,1,1],[2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,3,2,1],[3,1,1]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,3,1,1],[3,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[6,4,2,1],[4,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[4,3,3],[2,2]] => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,4,3],[3,3]] => ([(0,5),(1,3),(1,4),(5,2)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[5,3,3],[3,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[6,4,3],[4,3]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,2,2,1],[1,1]] => ([(0,4),(0,5),(1,2),(1,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,3,3,1],[2,2,1]] => ([(1,5),(2,3),(2,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,3,2,1],[2,2]] => ([(0,4),(0,5),(1,2),(1,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[5,4,3,1],[3,3,1]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,2,2,1],[2,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,3,3,1],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,3,2,1],[3,2]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[6,4,3,1],[4,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[3,2,2,2],[1,1,1]] => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,3,3,2],[2,2,2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,3,2,2],[2,2,1]] => ([(0,5),(1,5),(2,3),(2,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[5,4,3,2],[3,3,2]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,2,2,2],[2,1,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,3,3,2],[3,2,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[5,3,2,2],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[6,4,3,2],[4,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[2,1,1,1,1],[]] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[3,2,2,2,1],[1,1,1,1]] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[3,2,2,1,1],[1,1,1]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,3,3,2,1],[2,2,2,1]] => ([(2,3),(2,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[3,2,1,1,1],[1,1]] => ([(0,5),(1,3),(1,4),(5,2)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[4,3,2,2,1],[2,2,1,1]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,2,1,1],[2,2,1]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,3,2,1],[3,3,2,1]] => ([(3,4),(3,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[3,1,1,1,1],[1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,2,2,2,1],[2,1,1,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,2,2,1,1],[2,1,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[5,3,3,2,1],[3,2,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[4,2,1,1,1],[2,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,3,2,2,1],[3,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[5,3,2,1,1],[3,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[6,4,3,2,1],[4,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[5,5],[4]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[6,5],[5]] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,4,1],[3]] => ([(0,5),(1,2),(1,4),(3,5),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,5,1],[4,1]] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,4,1],[4]] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[6,5,1],[5,1]] => ([(2,3),(3,5),(5,4)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[3,3,2],[2]] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[4,4,2],[3,1]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,5,2],[4,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,3,2],[3]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[5,4,2],[4,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[6,5,2],[5,2]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,3,1,1],[2]] => ([(0,5),(1,3),(1,4),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,4,2,1],[3,1,1]] => ([(1,5),(2,3),(2,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,4,1,1],[3,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,5,2,1],[4,2,1]] => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[4,3,1,1],[3]] => ([(1,4),(1,5),(4,3),(5,2)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,4,2,1],[4,1,1]] => ([(2,3),(2,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[5,4,1,1],[4,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[6,5,2,1],[5,2,1]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[3,3,3],[2,1]] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,4,3],[3,2]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,5,3],[4,3]] => ([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[4,3,3],[3,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[5,4,3],[4,2]] => ([(1,4),(2,3),(2,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[6,5,3],[5,3]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[2,2,2,1],[1]] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[3,3,3,1],[2,1,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[3,3,2,1],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,4,3,1],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,4,2,1],[3,2]] => ([(0,5),(1,5),(2,3),(2,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[5,5,3,1],[4,3,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,2,2,1],[2]] => ([(1,3),(1,4),(3,5),(4,2),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[4,3,3,1],[3,1,1]] => ([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => [1,2,3] => 3
[[4,3,2,1],[3,1]] => ([(1,4),(1,5),(2,3),(2,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,4,3,1],[4,2,1]] => ([(2,5),(3,4),(3,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[5,4,2,1],[4,2]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[6,5,3,1],[5,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[3,3,2,2],[2,1,1]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,4,3,2],[3,2,2]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,4,2,2],[3,2,1]] => ([(0,5),(1,5),(2,4),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[5,5,3,2],[4,3,2]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,2,2],[3,1,1]] => ([(1,5),(2,3),(2,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,4,3,2],[4,2,2]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,2,2],[4,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[6,5,3,2],[5,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[2,2,1,1,1],[1]] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[3,3,2,2,1],[2,1,1,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[3,3,2,1,1],[2,1,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,4,3,2,1],[3,2,2,1]] => ([(2,5),(3,4),(3,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[3,3,1,1,1],[2,1]] => ([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[4,4,2,2,1],[3,2,1,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,4,2,1,1],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,5,3,2,1],[4,3,2,1]] => ([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[3,2,1,1,1],[2]] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,3,2,2,1],[3,1,1,1]] => ([(2,3),(2,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[4,3,2,1,1],[3,1,1]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,3,2,1],[4,2,2,1]] => ([(3,4),(3,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[4,3,1,1,1],[3,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,2,2,1],[4,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[5,4,2,1,1],[4,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[6,5,3,2,1],[5,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[4,4,4],[3,3]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[5,5,4],[4,4]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,4,4],[4,3]] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[6,5,4],[5,4]] => ([(2,3),(3,5),(5,4)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[3,3,3,1],[2,2]] => ([(0,4),(1,2),(1,3),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,4,4,1],[3,3,1]] => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,4,3,1],[3,3]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,5,4,1],[4,4,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,3,1],[3,2]] => ([(1,5),(2,3),(2,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,4,4,1],[4,3,1]] => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[5,4,3,1],[4,3]] => ([(2,3),(2,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[6,5,4,1],[5,4,1]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[2,2,2,2],[1,1]] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [1,1,2,1,1] => 1
[[3,3,3,2],[2,2,1]] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,4,4,2],[3,3,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[3,3,2,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6) => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [1,3,2] => 2
[[4,4,3,2],[3,3,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,5,4,2],[4,4,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[3,2,2,2],[2,1]] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [1,1,1,1,2] => 2
[[4,3,3,2],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,4,4,2],[4,3,2]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,2,2],[3,2]] => ([(2,3),(2,4),(3,5),(4,5)],6) => ([(2,4),(2,5),(3,4),(3,5)],6) => [1,2,3] => 3
[[5,4,3,2],[4,3,1]] => ([(2,5),(3,4),(3,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[6,5,4,2],[5,4,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[2,2,2,1,1],[1,1]] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[3,3,3,2,1],[2,2,1,1]] => ([(1,4),(2,3),(2,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[3,3,3,1,1],[2,2,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,4,4,2,1],[3,3,2,1]] => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[3,3,2,1,1],[2,2]] => ([(0,4),(1,3),(1,5),(5,2)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,4,3,2,1],[3,3,1,1]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,4,3,1,1],[3,3,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[5,5,4,2,1],[4,4,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[3,2,2,1,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,3,3,2,1],[3,2,1,1]] => ([(2,5),(3,4),(3,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[4,3,3,1,1],[3,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,4,2,1],[4,3,2,1]] => ([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[4,3,2,1,1],[3,2]] => ([(2,3),(2,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[5,4,3,2,1],[4,3,1,1]] => ([(3,4),(3,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[5,4,3,1,1],[4,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[6,5,4,2,1],[5,4,2,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[3,3,3,3],[2,2,2]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[4,4,4,3],[3,3,3]] => ([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[4,4,3,3],[3,3,2]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[5,5,4,3],[4,4,3]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,3,3],[3,2,2]] => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[5,4,4,3],[4,3,3]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,3,3],[4,3,2]] => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[6,5,4,3],[5,4,3]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[2,2,2,2,1],[1,1,1]] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[3,3,3,3,1],[2,2,2,1]] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[3,3,3,2,1],[2,2,2]] => ([(0,5),(1,3),(1,4),(5,2)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[4,4,4,3,1],[3,3,3,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,3,2,2,1],[2,2,1]] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,4,3,3,1],[3,3,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,4,3,2,1],[3,3,2]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,5,4,3,1],[4,4,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[3,2,2,2,1],[2,1,1]] => ([(1,4),(2,3),(2,5),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,3,3,3,1],[3,2,2,1]] => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[4,3,3,2,1],[3,2,2]] => ([(1,5),(2,3),(2,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,4,3,1],[4,3,3,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[4,3,2,2,1],[3,2,1]] => ([(2,5),(3,4),(3,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[5,4,3,3,1],[4,3,2,1]] => ([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[5,4,3,2,1],[4,3,2]] => ([(3,4),(3,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[6,5,4,3,1],[5,4,3,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[2,2,2,2,2],[1,1,1,1]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[3,3,3,3,2],[2,2,2,2]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[3,3,3,2,2],[2,2,2,1]] => ([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[4,4,4,3,2],[3,3,3,2]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,3,2,2,2],[2,2,1,1]] => ([(0,5),(1,3),(2,4),(4,5)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[4,4,3,3,2],[3,3,2,2]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[4,4,3,2,2],[3,3,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,5,4,3,2],[4,4,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[3,2,2,2,2],[2,1,1,1]] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[4,3,3,3,2],[3,2,2,2]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,3,2,2],[3,2,2,1]] => ([(1,5),(2,5),(3,4)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[5,4,4,3,2],[4,3,3,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[4,3,2,2,2],[3,2,1,1]] => ([(2,5),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[5,4,3,3,2],[4,3,2,2]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[5,4,3,2,2],[4,3,2,1]] => ([(3,5),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[6,5,4,3,2],[5,4,3,2]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[1,1,1,1,1,1],[]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [1,1,1,1,1,1] => 1
[[2,2,2,2,2,1],[1,1,1,1,1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[2,2,2,2,1,1],[1,1,1,1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[3,3,3,3,2,1],[2,2,2,2,1]] => ([(2,3),(3,5),(5,4)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[2,2,2,1,1,1],[1,1,1]] => ([(0,5),(1,4),(4,2),(5,3)],6) => ([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2] => 2
[[3,3,3,2,2,1],[2,2,2,1,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,3,3,2,1,1],[2,2,2,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,4,4,3,2,1],[3,3,3,2,1]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[2,2,1,1,1,1],[1,1]] => ([(0,5),(1,3),(4,2),(5,4)],6) => ([(0,1),(2,5),(3,4),(4,5)],6) => [1,2,1,2] => 2
[[3,3,2,2,2,1],[2,2,1,1,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[3,3,2,2,1,1],[2,2,1,1]] => ([(0,5),(1,4),(2,3)],6) => ([(0,5),(1,4),(2,3)],6) => [3,3] => 3
[[4,4,3,3,2,1],[3,3,2,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[3,3,2,1,1,1],[2,2,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,4,3,2,2,1],[3,3,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[4,4,3,2,1,1],[3,3,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[5,5,4,3,2,1],[4,4,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[2,1,1,1,1,1],[1]] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(1,5),(2,4),(3,4),(3,5)],6) => [1,1,1,1,2] => 2
[[3,2,2,2,2,1],[2,1,1,1,1]] => ([(2,3),(3,5),(5,4)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[3,2,2,2,1,1],[2,1,1,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,3,3,2,1],[3,2,2,2,1]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[3,2,2,1,1,1],[2,1,1]] => ([(1,3),(2,4),(4,5)],6) => ([(1,2),(3,5),(4,5)],6) => [1,1,1,3] => 3
[[4,3,3,2,2,1],[3,2,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[4,3,3,2,1,1],[3,2,2,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[5,4,4,3,2,1],[4,3,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[3,2,1,1,1,1],[2,1]] => ([(2,3),(3,5),(5,4)],6) => ([(2,5),(3,4),(4,5)],6) => [1,1,1,3] => 3
[[4,3,2,2,2,1],[3,2,1,1,1]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[4,3,2,2,1,1],[3,2,1,1]] => ([(2,5),(3,4)],6) => ([(2,5),(3,4)],6) => [2,4] => 4
[[5,4,3,3,2,1],[4,3,2,2,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[4,3,2,1,1,1],[3,2,1]] => ([(3,4),(4,5)],6) => ([(3,5),(4,5)],6) => [1,1,4] => 4
[[5,4,3,2,2,1],[4,3,2,1,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[5,4,3,2,1,1],[4,3,2,1]] => ([(4,5)],6) => ([(4,5)],6) => [1,5] => 5
[[6,5,4,3,2,1],[5,4,3,2,1]] => ([],6) => ([],6) => [6] => 6
[[7],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[7,1],[1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,2],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,2],[1]] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[7,2],[2]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,2,1],[1,1]] => ([(1,3),(1,6),(4,5),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,1,1],[1]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,2,1],[2,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,3],[1]] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[6,3],[2]] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[7,3],[3]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,2,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[5,3,1],[1,1]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[5,2,1],[1]] => ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,3,1],[2,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,2,1],[2]] => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,3,1],[3,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,2,2],[1,1]] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,3,2],[2,2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,2,2],[2,1]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,3,2],[3,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,1,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,2,2,1],[1,1,1]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,2,1,1],[1,1]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,3,2,1],[2,2,1]] => ([(2,4),(2,6),(5,3),(6,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,1,1,1],[1]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,2,2,1],[2,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,2,1,1],[2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,3,2,1],[3,2,1]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,4],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4],[2]] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[6,4],[3]] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[7,4],[4]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,1],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,1],[1,1]] => ([(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [1,2,1,1,2] => 2
[[4,3,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,1],[2]] => ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,4,1],[3,1]] => ([(1,4),(2,3),(2,6),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,3,1],[3]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,4,1],[4,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[3,2,2],[]] => ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,2],[1,1]] => ([(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,2],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[4,2,2],[1]] => ([(0,3),(0,6),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,3,2],[2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,4,2],[3,2]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,2,2],[2]] => ([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[6,3,2],[3,1]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,4,2],[4,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[3,2,1,1],[]] => ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,2,1],[1,1,1]] => ([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,1,1],[1,1]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[5,4,2,1],[2,2,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[4,2,1,1],[1]] => ([(0,5),(0,6),(1,4),(1,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,3,2,1],[2,1,1]] => ([(1,3),(1,6),(2,4),(2,6),(4,5)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,1,1],[2,1]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,2,1],[3,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,2,1,1],[2]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,3,2,1],[3,1,1]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,3,1,1],[3,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[7,4,2,1],[4,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,3,3],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,4,3],[3,3]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,3,3],[3,2]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,4,3],[4,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,2,2,1],[1,1]] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,3,3,1],[2,2,1]] => ([(1,6),(2,3),(2,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,2,1],[2,2]] => ([(0,3),(0,4),(1,5),(1,6),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,3,1],[3,3,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,2,2,1],[2,1]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,3,3,1],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,3,2,1],[3,2]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[7,4,3,1],[4,3,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,2,2,2],[1,1,1]] => ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,3,3,2],[2,2,2]] => ([(0,4),(1,5),(1,6),(5,3),(6,2)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,2,2],[2,2,1]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,3,2],[3,3,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,2,2,2],[2,1,1]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,3,3,2],[3,2,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,3,2,2],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[7,4,3,2],[4,3,2]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,1,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,2,2,2,1],[1,1,1,1]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,2,2,1,1],[1,1,1]] => ([(0,4),(1,5),(1,6),(5,3),(6,2)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,3,2,1],[2,2,2,1]] => ([(2,5),(2,6),(5,4),(6,3)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,2,1,1,1],[1,1]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,2,2,1],[2,2,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,3,2,1,1],[2,2,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,4,3,2,1],[3,3,2,1]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,1,1,1,1],[1]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,2,2,2,1],[2,1,1,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,2,2,1,1],[2,1,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,3,3,2,1],[3,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,2,1,1,1],[2,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,3,2,2,1],[3,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,3,2,1,1],[3,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,4,3,2,1],[4,3,2,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[5,5],[3]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,5],[4]] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[7,5],[5]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,1],[2]] => ([(0,4),(0,6),(1,2),(1,3),(3,6),(4,5),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,1],[3,1]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[5,4,1],[3]] => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,5,1],[4,1]] => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,1],[4]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,5,1],[5,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[3,3,2],[1]] => ([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(6,4),(6,5)],7) => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => [1,1,1,2,1,1] => 1
[[4,4,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,2],[3,2]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[4,3,2],[2]] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(3,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,2],[3,1]] => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,5,2],[4,2]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,2],[3]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[6,4,2],[4,1]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,5,2],[5,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[3,3,1,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,2,1],[2,1,1]] => ([(1,3),(1,5),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[4,4,1,1],[2,1]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[5,5,2,1],[3,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[4,3,1,1],[2]] => ([(0,4),(0,6),(1,3),(1,5),(3,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,2,1],[3,1,1]] => ([(1,4),(1,6),(2,3),(2,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,1,1],[3,1]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,2,1],[4,2,1]] => ([(2,5),(3,4),(3,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,3,1,1],[3]] => ([(0,4),(1,5),(1,6),(5,3),(6,2)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,2,1],[4,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,4,1,1],[4,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[7,5,2,1],[5,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,3],[1,1]] => ([(0,2),(0,3),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,3],[3,3]] => ([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[4,3,3],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,3],[3,2]] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,5,3],[4,3]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,3],[3,1]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[6,4,3],[4,2]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,5,3],[5,3]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[2,2,2,1],[]] => ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,1],[1,1,1]] => ([(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [1,2,1,1,2] => 2
[[3,3,2,1],[1,1]] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(3,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3,1],[2,2,1]] => ([(1,5),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[4,4,2,1],[2,2]] => ([(0,2),(0,3),(1,4),(1,5),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[5,5,3,1],[3,3,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[3,2,2,1],[1]] => ([(0,3),(0,6),(1,4),(1,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,3,1],[2,1,1]] => ([(1,3),(1,5),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[4,3,2,1],[2,1]] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,3,1],[3,2,1]] => ([(1,5),(2,5),(2,6),(3,4),(3,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,2,1],[3,2]] => ([(0,6),(1,5),(1,6),(2,3),(2,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,3,1],[4,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,2,2,1],[2]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[5,3,3,1],[3,1,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[5,3,2,1],[3,1]] => ([(0,5),(1,4),(1,6),(2,3),(2,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,3,1],[4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,4,2,1],[4,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[7,5,3,1],[5,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[3,3,2,2],[1,1,1]] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3,2],[2,2,2]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[4,4,2,2],[2,2,1]] => ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[5,5,3,2],[3,3,2]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[4,3,2,2],[2,1,1]] => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,3,2],[3,2,2]] => ([(0,5),(1,4),(1,6),(2,3),(2,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,2,2],[3,2,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,3,2],[4,3,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,3,2,2],[3,1,1]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,3,2],[4,2,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,4,2,2],[4,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[7,5,3,2],[5,3,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[2,2,1,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,2,2,1],[1,1,1,1]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[3,3,2,1,1],[1,1,1]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[4,4,3,2,1],[2,2,2,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[3,3,1,1,1],[1,1]] => ([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[4,4,2,2,1],[2,2,1,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[4,4,2,1,1],[2,2,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[5,5,3,2,1],[3,3,2,1]] => ([(3,4),(3,5),(4,6),(5,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => [1,2,4] => 4
[[3,2,1,1,1],[1]] => ([(0,5),(0,6),(1,3),(1,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,2,2,1],[2,1,1,1]] => ([(1,3),(1,6),(2,4),(2,6),(4,5)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,2,1,1],[2,1,1]] => ([(0,5),(1,4),(1,6),(2,3),(2,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,2,1],[3,2,2,1]] => ([(2,5),(2,6),(3,4),(3,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3,1,1,1],[2,1]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,2,2,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,2,1,1],[3,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,3,2,1],[4,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,2,1,1,1],[2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,2,2,1],[3,1,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,3,2,1,1],[3,1,1]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,4,3,2,1],[4,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,3,1,1,1],[3,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,4,2,2,1],[4,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,4,2,1,1],[4,2,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[7,5,3,2,1],[5,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,4,4],[3,3]] => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,5,4],[4,4]] => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,4],[4,3]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[7,5,4],[5,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,1],[2,2]] => ([(0,3),(0,5),(1,2),(1,4),(4,6),(5,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,4,1],[3,3,1]] => ([(1,5),(2,3),(2,4),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,1],[3,3]] => ([(0,3),(0,4),(1,5),(1,6),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,4,1],[4,4,1]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,3,3,1],[3,2]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,4,1],[4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,4,3,1],[4,3]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,5,4,1],[5,4,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,2,2,2],[1,1]] => ([(0,4),(0,6),(1,2),(1,3),(3,6),(4,5),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,3,2],[2,2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,4,2],[3,3,2]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,2,2],[2,2]] => ([(0,2),(0,3),(1,4),(1,5),(4,6),(5,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[5,4,3,2],[3,3,1]] => ([(0,6),(1,5),(1,6),(2,3),(2,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,4,2],[4,4,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,2,2,2],[2,1]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[5,3,3,2],[3,2,1]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,4,2],[4,3,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,3,2,2],[3,2]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[6,4,3,2],[4,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,5,4,2],[5,4,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[3,2,2,1,1],[1,1]] => ([(0,5),(0,6),(1,3),(1,4),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,3,2,1],[2,2,1,1]] => ([(1,4),(1,6),(2,3),(2,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,1,1],[2,2,1]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,2,1],[3,3,2,1]] => ([(2,6),(3,4),(3,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3,2,1,1],[2,2]] => ([(0,3),(0,4),(1,5),(1,6),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,2,1],[3,3,1,1]] => ([(1,5),(1,6),(2,3),(2,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,3,1,1],[3,3,1]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,5,4,2,1],[4,4,2,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,2,2,1,1],[2,1]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,3,2,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,3,3,1,1],[3,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,4,4,2,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,3,2,1,1],[3,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,4,3,2,1],[4,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,4,3,1,1],[4,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[7,5,4,2,1],[5,4,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,3,3,3],[2,2,2]] => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,4,4,3],[3,3,3]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,3],[3,3,2]] => ([(0,6),(1,5),(2,3),(2,4),(5,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,4,3],[4,4,3]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,3,3,3],[3,2,2]] => ([(0,5),(1,4),(2,3),(4,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,4,4,3],[4,3,3]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,4,3,3],[4,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,5,4,3],[5,4,3]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,2,2,2,1],[1,1,1]] => ([(0,4),(0,6),(1,2),(1,5),(3,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,3,3,1],[2,2,2,1]] => ([(1,6),(2,3),(2,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,2,1],[2,2,2]] => ([(0,3),(0,4),(1,5),(1,6),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,3,1],[3,3,3,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,2,2,1],[2,2,1]] => ([(0,6),(1,5),(1,6),(2,3),(2,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,3,1],[3,3,2,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,3,2,1],[3,3,2]] => ([(1,5),(1,6),(2,3),(2,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,4,3,1],[4,4,3,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,2,2,2,1],[2,1,1]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,3,3,1],[3,2,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,3,3,2,1],[3,2,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,4,4,3,1],[4,3,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,3,2,2,1],[3,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,4,3,3,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,4,3,2,1],[4,3,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,5,4,3,1],[5,4,3,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,2,2,2,2],[1,1,1,1]] => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,3,3,3,2],[2,2,2,2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,2,2],[2,2,2,1]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,3,2],[3,3,3,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,2,2,2],[2,2,1,1]] => ([(0,6),(1,5),(2,3),(2,4),(5,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,3,2],[3,3,2,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,4,3,2,2],[3,3,2,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,4,3,2],[4,4,3,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,2,2,2,2],[2,1,1,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,3,3,3,2],[3,2,2,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,3,3,2,2],[3,2,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,4,4,3,2],[4,3,3,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,3,2,2,2],[3,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,4,3,3,2],[4,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,4,3,2,2],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,5,4,3,2],[5,4,3,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[2,1,1,1,1,1],[]] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,2,2,2,2,1],[1,1,1,1,1]] => ([(1,3),(1,6),(4,5),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[3,2,2,2,1,1],[1,1,1,1]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,3,2,1],[2,2,2,2,1]] => ([(2,4),(2,6),(5,3),(6,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[3,2,2,1,1,1],[1,1,1]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,2,2,1],[2,2,2,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,2,1,1],[2,2,2,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,3,2,1],[3,3,3,2,1]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[3,2,1,1,1,1],[1,1]] => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,2,2,2,1],[2,2,1,1,1]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,3,2,2,1,1],[2,2,1,1]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,4,3,3,2,1],[3,3,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,2,1,1,1],[2,2,1]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,3,2,2,1],[3,3,2,1,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,2,1,1],[3,3,2,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,2,1],[4,4,3,2,1]] => ([(4,5),(4,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[3,1,1,1,1,1],[1]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,2,2,2,2,1],[2,1,1,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,2,2,2,1,1],[2,1,1,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,3,3,3,2,1],[3,2,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,2,2,1,1,1],[2,1,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,3,3,2,2,1],[3,2,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,3,3,2,1,1],[3,2,2,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,4,4,3,2,1],[4,3,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,2,1,1,1,1],[2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,3,2,2,2,1],[3,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,3,2,2,1,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,4,3,3,2,1],[4,3,2,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,3,2,1,1,1],[3,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,4,3,2,2,1],[4,3,2,1,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,4,3,2,1,1],[4,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[7,5,4,3,2,1],[5,4,3,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[6,6],[5]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[7,6],[6]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,1],[4]] => ([(0,6),(1,2),(1,5),(3,6),(4,3),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,6,1],[5,1]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,1],[5]] => ([(1,3),(1,6),(4,5),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[7,6,1],[6,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,4,2],[3]] => ([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,2],[4,1]] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,6,2],[5,2]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,2],[4]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[6,5,2],[5,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[7,6,2],[6,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,1,1],[3]] => ([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,2,1],[4,1,1]] => ([(1,6),(2,3),(2,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,1,1],[4,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,2,1],[5,2,1]] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,1,1],[4]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,2,1],[5,1,1]] => ([(2,4),(2,6),(5,3),(6,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,1,1],[5,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,6,2,1],[6,2,1]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[3,3,3],[2]] => ([(0,2),(0,3),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3],[3,1]] => ([(0,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,3],[4,2]] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,6,3],[5,3]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3],[3]] => ([(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [1,2,1,1,2] => 2
[[5,4,3],[4,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,3],[5,2]] => ([(1,4),(2,3),(2,6),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[7,6,3],[6,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[3,3,2,1],[2]] => ([(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3,1],[3,1,1]] => ([(1,5),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[4,4,2,1],[3,1]] => ([(0,6),(1,3),(1,5),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,3,1],[4,2,1]] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,2,1],[4,2]] => ([(0,6),(1,5),(2,3),(2,4),(5,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,3,1],[5,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,2,1],[3]] => ([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,1],[4,1,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[5,4,2,1],[4,1]] => ([(1,3),(1,6),(2,4),(2,6),(4,5)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,3,1],[5,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,2,1],[5,2]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[7,6,3,1],[6,3,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,4,2,2],[3,1,1]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,3,2],[4,2,2]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,2,2],[4,2,1]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,3,2],[5,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,2,2],[4,1,1]] => ([(1,6),(2,3),(2,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,3,2],[5,2,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,2,2],[5,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[7,6,3,2],[6,3,2]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,1,1,1],[2]] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,2,2,1],[3,1,1,1]] => ([(1,6),(2,3),(2,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,2,1,1],[3,1,1]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,3,2,1],[4,2,2,1]] => ([(2,6),(3,4),(3,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,4,1,1,1],[3,1]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,2,2,1],[4,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,2,1,1],[4,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,6,3,2,1],[5,3,2,1]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,3,1,1,1],[3]] => ([(1,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,2,2,1],[4,1,1,1]] => ([(2,5),(2,6),(5,4),(6,3)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,2,1,1],[4,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,3,2,1],[5,2,2,1]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[5,4,1,1,1],[4,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,2,2,1],[5,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,2,1,1],[5,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,6,3,2,1],[6,3,2,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[4,4,4],[3,2]] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,4],[4,3]] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,6,4],[5,4]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4],[4,2]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[6,5,4],[5,3]] => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[7,6,4],[6,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[3,3,3,1],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(4,6),(5,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,1],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,1],[3,2]] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,4,1],[4,3,1]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,3,1],[4,3]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,4,1],[5,4,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,3,3,1],[3,1]] => ([(1,3),(1,5),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[5,4,4,1],[4,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,1],[4,2]] => ([(1,4),(1,6),(2,3),(2,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,4,1],[5,3,1]] => ([(2,5),(3,4),(3,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,3,1],[5,3]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,6,4,1],[6,4,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[2,2,2,2],[1]] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,2],[2,1,1]] => ([(0,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,2],[3,2,2]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[3,3,2,2],[2,1]] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3,2],[3,2,1]] => ([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,4,2],[4,3,2]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,2,2],[3,2]] => ([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[5,5,3,2],[4,3,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,4,2],[5,4,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[3,2,2,2],[2]] => ([(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [1,2,1,1,2] => 2
[[4,3,3,2],[3,1,1]] => ([(1,5),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[5,4,4,2],[4,2,2]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[4,3,2,2],[3,1]] => ([(1,3),(1,5),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[5,4,3,2],[4,2,1]] => ([(1,5),(2,5),(2,6),(3,4),(3,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,4,2],[5,3,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,2,2],[4,2]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[6,5,3,2],[5,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,6,4,2],[6,4,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[2,2,2,1,1],[1]] => ([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,2,1],[2,1,1,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,1,1],[2,1,1]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[4,4,4,2,1],[3,2,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[3,3,2,1,1],[2,1]] => ([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3,2,1],[3,2,1,1]] => ([(1,5),(2,5),(2,6),(3,4),(3,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,1,1],[3,2,1]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,2,1],[4,3,2,1]] => ([(2,6),(3,5),(4,5),(4,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,4,2,1,1],[3,2]] => ([(0,6),(1,6),(2,3),(2,4),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,3,2,1],[4,3,1,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,5,3,1,1],[4,3,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,6,4,2,1],[5,4,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,2,2,1,1],[2]] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[4,3,3,2,1],[3,1,1,1]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[4,3,3,1,1],[3,1,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[5,4,4,2,1],[4,2,2,1]] => ([(3,4),(3,5),(4,6),(5,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => [1,2,4] => 4
[[4,3,2,1,1],[3,1]] => ([(1,3),(1,6),(2,4),(2,6),(4,5)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,2,1],[4,2,1,1]] => ([(2,5),(2,6),(3,4),(3,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,1,1],[4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,4,2,1],[5,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[5,4,2,1,1],[4,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,3,2,1],[5,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,3,1,1],[5,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[7,6,4,2,1],[6,4,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,4,3,3],[3,2,2]] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,4,3],[4,3,3]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,3,3],[4,3,2]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,4,3],[5,4,3]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,3,3],[4,2,2]] => ([(1,5),(2,3),(2,4),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,4,3],[5,3,3]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,3,3],[5,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[7,6,4,3],[6,4,3]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,2,2,1],[2,1,1]] => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3,3,1],[3,2,2,1]] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,2,1],[3,2,2]] => ([(0,6),(1,5),(1,6),(2,3),(2,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,3,1],[4,3,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,2,2,1],[3,2,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,3,3,1],[4,3,2,1]] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,5,3,2,1],[4,3,2]] => ([(1,6),(2,6),(3,4),(3,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,6,4,3,1],[5,4,3,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,2,2,1],[3,1,1]] => ([(1,4),(1,6),(2,3),(2,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,3,1],[4,2,2,1]] => ([(2,6),(3,4),(3,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,2,1],[4,2,2]] => ([(1,5),(1,6),(2,3),(2,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,4,3,1],[5,3,3,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,2,2,1],[4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,3,3,1],[5,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,3,2,1],[5,3,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,6,4,3,1],[6,4,3,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,3,2,2,2],[2,1,1,1]] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,3,3,2],[3,2,2,2]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,2,2],[3,2,2,1]] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,3,2],[4,3,3,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,2,2,2],[3,2,1,1]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,3,3,2],[4,3,2,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,3,2,2],[4,3,2,1]] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,6,4,3,2],[5,4,3,2]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,2,2,2],[3,1,1,1]] => ([(1,6),(2,3),(2,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,3,3,2],[4,2,2,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,3,2,2],[4,2,2,1]] => ([(1,6),(2,6),(3,4),(3,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,4,3,2],[5,3,3,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,2,2,2],[4,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,3,3,2],[5,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,5,3,2,2],[5,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,6,4,3,2],[6,4,3,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[2,2,1,1,1,1],[1]] => ([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,2,2,2,1],[2,1,1,1,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,2,2,1,1],[2,1,1,1]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,3,2,1],[3,2,2,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[3,3,2,1,1,1],[2,1,1]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,2,2,1],[3,2,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,2,1,1],[3,2,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,3,2,1],[4,3,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[3,3,1,1,1,1],[2,1]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,2,2,2,1],[3,2,1,1,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,4,2,2,1,1],[3,2,1,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,3,3,2,1],[4,3,2,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,4,2,1,1,1],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,5,3,2,2,1],[4,3,2,1,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,5,3,2,1,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,6,4,3,2,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[3,2,1,1,1,1],[2]] => ([(1,3),(1,6),(4,5),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,2,2,2,1],[3,1,1,1,1]] => ([(2,4),(2,6),(5,3),(6,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3,2,2,1,1],[3,1,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,3,3,2,1],[4,2,2,2,1]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,3,2,1,1,1],[3,1,1]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,3,2,2,1],[4,2,2,1,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,2,1,1],[4,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,2,1],[5,3,3,2,1]] => ([(4,5),(4,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[4,3,1,1,1,1],[3,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,2,2,2,1],[4,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,2,2,1,1],[4,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,5,3,3,2,1],[5,3,2,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,4,2,1,1,1],[4,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,3,2,2,1],[5,3,2,1,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,5,3,2,1,1],[5,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[7,6,4,3,2,1],[6,4,3,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[5,5,5],[4,4]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[6,6,5],[5,5]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,5],[5,4]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[7,6,5],[6,5]] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,4,4,1],[3,3]] => ([(0,4),(1,2),(1,5),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,5,1],[4,4,1]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,1],[4,4]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,5,1],[5,5,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,1],[4,3]] => ([(1,6),(2,3),(2,4),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,5,1],[5,4,1]] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,1],[5,4]] => ([(2,4),(2,6),(5,3),(6,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[7,6,5,1],[6,5,1]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[3,3,3,2],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,2],[3,3,1]] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,5,2],[4,4,2]] => ([(0,5),(1,4),(2,3),(4,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,2],[3,3]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[5,5,4,2],[4,4,1]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,5,2],[5,5,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,2],[3,2]] => ([(1,5),(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[5,4,4,2],[4,3,1]] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,5,2],[5,4,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,3,2],[4,3]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,2],[5,4,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[7,6,5,2],[6,5,2]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,3,1,1],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,2,1],[3,3,1,1]] => ([(1,5),(2,3),(2,4),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,1,1],[3,3,1]] => ([(0,5),(1,4),(2,3),(4,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,5,2,1],[4,4,2,1]] => ([(2,5),(3,4),(4,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,4,3,1,1],[3,3]] => ([(0,4),(1,5),(1,6),(5,3),(6,2)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,2,1],[4,4,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,1,1],[4,4,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,6,5,2,1],[5,5,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,1,1],[3,2]] => ([(1,6),(2,3),(2,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,2,1],[4,3,1,1]] => ([(2,6),(3,4),(3,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,4,1,1],[4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,5,2,1],[5,4,2,1]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,1,1],[4,3]] => ([(2,5),(2,6),(5,4),(6,3)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,2,1],[5,4,1,1]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,1,1],[5,4,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,6,5,2,1],[6,5,2,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[3,3,3,3],[2,2,1]] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,3],[3,3,2]] => ([(0,5),(0,6),(1,4),(2,3),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,5,3],[4,4,3]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,3],[3,3,1]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[5,5,4,3],[4,4,2]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,5,3],[5,5,3]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,3],[3,2,1]] => ([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,3],[4,3,2]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,5,3],[5,4,3]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,3,3],[4,3,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,3],[5,4,2]] => ([(2,5),(3,4),(3,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[7,6,5,3],[6,5,3]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[2,2,2,2,1],[1,1]] => ([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,3,1],[2,2,1,1]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[3,3,3,2,1],[2,2,1]] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,3,1],[3,3,2,1]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,2,1],[3,3,2]] => ([(0,6),(1,5),(2,3),(2,4),(5,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,5,3,1],[4,4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[3,3,2,2,1],[2,2]] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[4,4,3,3,1],[3,3,1,1]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[4,4,3,2,1],[3,3,1]] => ([(0,5),(1,4),(1,6),(2,3),(2,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,3,1],[4,4,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,2,1],[4,4,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,6,5,3,1],[5,5,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[3,2,2,2,1],[2,1]] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,3,1],[3,2,1,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[4,3,3,2,1],[3,2,1]] => ([(1,5),(2,5),(2,6),(3,4),(3,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,3,1],[4,3,2,1]] => ([(2,6),(3,5),(4,5),(4,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,4,2,1],[4,3,2]] => ([(1,6),(2,6),(3,4),(3,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,5,3,1],[5,4,3,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,2,2,1],[3,2]] => ([(2,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,3,1],[4,3,1,1]] => ([(3,4),(3,5),(4,6),(5,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => [1,2,4] => 4
[[5,4,3,2,1],[4,3,1]] => ([(2,5),(2,6),(3,4),(3,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,3,1],[5,4,2,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,2,1],[5,4,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,6,5,3,1],[6,5,3,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,3,3,2,2],[2,2,1,1]] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,3,2],[3,3,2,2]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,2,2],[3,3,2,1]] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,5,3,2],[4,4,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,2,2],[3,3,1,1]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,3,2],[4,4,2,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,2,2],[4,4,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[6,6,5,3,2],[5,5,3,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[4,3,3,2,2],[3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,3,2],[4,3,2,2]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,2,2],[4,3,2,1]] => ([(1,6),(2,6),(3,5),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[6,5,5,3,2],[5,4,3,2]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,2,2],[4,3,1,1]] => ([(2,6),(3,4),(3,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,3,2],[5,4,2,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,2,2],[5,4,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[7,6,5,3,2],[6,5,3,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[2,2,2,1,1,1],[1,1]] => ([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,2,2,1],[2,2,1,1,1]] => ([(1,4),(2,3),(2,6),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,2,1,1],[2,2,1,1]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,3,2,1],[3,3,2,2,1]] => ([(2,5),(3,4),(3,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[3,3,3,1,1,1],[2,2,1]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,2,2,1],[3,3,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,4,2,1,1],[3,3,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,5,3,2,1],[4,4,3,2,1]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[3,3,2,1,1,1],[2,2]] => ([(0,4),(1,3),(1,6),(5,2),(6,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,2,2,1],[3,3,1,1,1]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,2,1,1],[3,3,1,1]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,3,2,1],[4,4,2,2,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,4,3,1,1,1],[3,3,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,2,2,1],[4,4,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,5,4,2,1,1],[4,4,2,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,6,5,3,2,1],[5,5,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,2,2,1,1,1],[2,1]] => ([(1,6),(2,3),(2,6),(3,5),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,2,2,1],[3,2,1,1,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3,3,2,1,1],[3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,3,2,1],[4,3,2,2,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,1,1,1],[3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,4,2,2,1],[4,3,2,1,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,4,2,1,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,5,3,2,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[4,3,2,1,1,1],[3,2]] => ([(2,4),(2,6),(5,3),(6,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,2,2,1],[4,3,1,1,1]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,2,1,1],[4,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,2,1],[5,4,2,2,1]] => ([(4,5),(4,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[5,4,3,1,1,1],[4,3,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,2,2,1],[5,4,2,1,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,5,4,2,1,1],[5,4,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[7,6,5,3,2,1],[6,5,3,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[4,4,4,4],[3,3,3]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[5,5,5,4],[4,4,4]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,4],[4,4,3]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[6,6,5,4],[5,5,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,4],[4,3,3]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[6,5,5,4],[5,4,4]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,4,4],[5,4,3]] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[7,6,5,4],[6,5,4]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[3,3,3,3,1],[2,2,2]] => ([(0,5),(1,2),(1,4),(3,6),(4,6),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,4,1],[3,3,3,1]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,3,1],[3,3,3]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,5,4,1],[4,4,4,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,4,3,3,1],[3,3,2]] => ([(0,6),(1,4),(2,3),(2,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,4,1],[4,4,3,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,3,1],[4,4,3]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,6,5,4,1],[5,5,4,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,3,1],[3,2,2]] => ([(1,5),(2,3),(2,4),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,4,1],[4,3,3,1]] => ([(2,5),(3,4),(4,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,4,3,1],[4,3,3]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,5,4,1],[5,4,4,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,3,1],[4,3,2]] => ([(2,6),(3,4),(3,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,4,1],[5,4,3,1]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,1],[5,4,3]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[7,6,5,4,1],[6,5,4,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[2,2,2,2,2],[1,1,1]] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,3,2],[2,2,2,1]] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,4,2],[3,3,3,2]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,2,2],[2,2,2]] => ([(0,5),(1,3),(1,4),(3,6),(4,6),(5,2)],7) => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [1,1,2,1,2] => 2
[[4,4,4,3,2],[3,3,3,1]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,5,4,2],[4,4,4,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[3,3,2,2,2],[2,2,1]] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [1,1,2,1,2] => 2
[[4,4,3,3,2],[3,3,2,1]] => ([(0,6),(1,5),(2,5),(2,6),(3,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,4,2],[4,4,3,2]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,2,2],[3,3,2]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[5,5,4,3,2],[4,4,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,6,5,4,2],[5,5,4,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[3,2,2,2,2],[2,1,1]] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [1,1,2,1,2] => 2
[[4,3,3,3,2],[3,2,2,1]] => ([(1,5),(2,5),(2,6),(3,4),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,4,2],[4,3,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,2,2],[3,2,2]] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [1,3,3] => 3
[[5,4,4,3,2],[4,3,3,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,5,4,2],[5,4,4,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[4,3,2,2,2],[3,2,1]] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,3,2],[4,3,2,1]] => ([(2,6),(3,5),(4,5),(4,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,4,2],[5,4,3,2]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,2,2],[4,3,2]] => ([(3,4),(3,5),(4,6),(5,6)],7) => ([(3,5),(3,6),(4,5),(4,6)],7) => [1,2,4] => 4
[[6,5,4,3,2],[5,4,3,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[7,6,5,4,2],[6,5,4,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[2,2,2,2,1,1],[1,1,1]] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,3,2,1],[2,2,2,1,1]] => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,3,1,1],[2,2,2,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,4,2,1],[3,3,3,2,1]] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[3,3,3,2,1,1],[2,2,2]] => ([(0,6),(1,4),(1,5),(5,3),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,3,2,1],[3,3,3,1,1]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,4,4,3,1,1],[3,3,3,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,5,4,2,1],[4,4,4,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,2,2,1,1],[2,2,1]] => ([(0,6),(1,3),(2,4),(2,6),(4,5)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,3,2,1],[3,3,2,1,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,3,1,1],[3,3,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,4,2,1],[4,4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,4,3,2,1,1],[3,3,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,3,2,1],[4,4,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,5,4,3,1,1],[4,4,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,6,5,4,2,1],[5,5,4,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,2,2,2,1,1],[2,1,1]] => ([(1,4),(2,3),(2,6),(3,5),(4,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,3,2,1],[3,2,2,1,1]] => ([(2,5),(3,4),(3,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3,3,3,1,1],[3,2,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,4,2,1],[4,3,3,2,1]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,2,1,1],[3,2,2]] => ([(1,5),(2,4),(2,6),(6,3)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,3,2,1],[4,3,3,1,1]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,4,3,1,1],[4,3,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[6,5,5,4,2,1],[5,4,4,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,3,2,2,1,1],[3,2,1]] => ([(2,6),(3,4),(3,6),(4,5)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,3,2,1],[4,3,2,1,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,3,1,1],[4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,4,2,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[5,4,3,2,1,1],[4,3,2]] => ([(3,4),(3,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,2,1],[5,4,3,1,1]] => ([(4,5),(4,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[6,5,4,3,1,1],[5,4,3,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[7,6,5,4,2,1],[6,5,4,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[3,3,3,3,3],[2,2,2,2]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[4,4,4,4,3],[3,3,3,3]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,3,3],[3,3,3,2]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,5,4,3],[4,4,4,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,4,3,3,3],[3,3,2,2]] => ([(0,5),(1,4),(2,3),(4,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[5,5,4,4,3],[4,4,3,3]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,3,3],[4,4,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,6,5,4,3],[5,5,4,3]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,3,3],[3,2,2,2]] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[5,4,4,4,3],[4,3,3,3]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,4,3,3],[4,3,3,2]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[6,5,5,4,3],[5,4,4,3]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,3,3],[4,3,2,2]] => ([(2,5),(3,4),(4,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[6,5,4,4,3],[5,4,3,3]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,3],[5,4,3,2]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[7,6,5,4,3],[6,5,4,3]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[2,2,2,2,2,1],[1,1,1,1]] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,3,3,1],[2,2,2,2,1]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,3,2,1],[2,2,2,2]] => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,4,3,1],[3,3,3,3,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[3,3,3,2,2,1],[2,2,2,1]] => ([(0,6),(1,4),(2,3),(2,6),(4,5)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,3,3,1],[3,3,3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,4,4,3,2,1],[3,3,3,2]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,5,5,4,3,1],[4,4,4,3,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,2,2,2,1],[2,2,1,1]] => ([(0,3),(1,5),(2,4),(2,6),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,3,3,1],[3,3,2,2,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,3,2,1],[3,3,2,2]] => ([(0,6),(1,5),(2,3),(2,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,4,3,1],[4,4,3,3,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[4,4,3,2,2,1],[3,3,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,3,3,1],[4,4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,5,4,3,2,1],[4,4,3,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,6,5,4,3,1],[5,5,4,3,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,2,2,2,2,1],[2,1,1,1]] => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,3,3,1],[3,2,2,2,1]] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3,3,3,2,1],[3,2,2,2]] => ([(1,6),(2,4),(2,5),(6,3)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,4,4,3,1],[4,3,3,3,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,2,2,1],[3,2,2,1]] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,3,3,1],[4,3,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,4,3,2,1],[4,3,3,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,5,4,3,1],[5,4,4,3,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,3,2,2,2,1],[3,2,1,1]] => ([(2,5),(3,4),(3,6),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,3,3,1],[4,3,2,2,1]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,3,2,1],[4,3,2,2]] => ([(2,6),(3,4),(3,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,4,3,1],[5,4,3,3,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,4,3,2,2,1],[4,3,2,1]] => ([(3,6),(4,5),(4,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,3,1],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[6,5,4,3,2,1],[5,4,3,2]] => ([(4,5),(4,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[7,6,5,4,3,1],[6,5,4,3,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[2,2,2,2,2,2],[1,1,1,1,1]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[3,3,3,3,3,2],[2,2,2,2,2]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,3,2,2],[2,2,2,2,1]] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,4,3,2],[3,3,3,3,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[3,3,3,2,2,2],[2,2,2,1,1]] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,4,3,3,2],[3,3,3,2,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,4,4,3,2,2],[3,3,3,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,5,5,4,3,2],[4,4,4,3,2]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,2,2,2,2],[2,2,1,1,1]] => ([(0,6),(1,3),(2,4),(4,5),(5,6)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[4,4,3,3,3,2],[3,3,2,2,2]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,3,2,2],[3,3,2,2,1]] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,4,3,2],[4,4,3,3,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[4,4,3,2,2,2],[3,3,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,5,4,3,3,2],[4,4,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,5,4,3,2,2],[4,4,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,6,5,4,3,2],[5,5,4,3,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,2,2,2,2,2],[2,1,1,1,1]] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[4,3,3,3,3,2],[3,2,2,2,2]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,3,2,2],[3,2,2,2,1]] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[5,4,4,4,3,2],[4,3,3,3,2]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,2,2,2],[3,2,2,1,1]] => ([(1,6),(2,4),(3,5),(5,6)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[5,4,4,3,3,2],[4,3,3,2,2]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,4,4,3,2,2],[4,3,3,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,5,4,3,2],[5,4,4,3,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,3,2,2,2,2],[3,2,1,1,1]] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[5,4,3,3,3,2],[4,3,2,2,2]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,3,2,2],[4,3,2,2,1]] => ([(2,6),(3,6),(4,5)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,4,3,2],[5,4,3,3,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,4,3,2,2,2],[4,3,2,1,1]] => ([(3,6),(4,5),(5,6)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[6,5,4,3,3,2],[5,4,3,2,2]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,5,4,3,2,2],[5,4,3,2,1]] => ([(4,6),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[7,6,5,4,3,2],[6,5,4,3,2]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[1,1,1,1,1,1,1],[]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [1,1,1,1,1,1,1] => 1
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[2,2,2,2,1,1,1],[1,1,1,1]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[2,2,2,1,1,1,1],[1,1,1]] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7) => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,3,2,1,1,1],[2,2,2,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[2,2,1,1,1,1,1],[1,1]] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7) => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [1,1,1,1,1,2] => 2
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[3,3,2,2,1,1,1],[2,2,1,1]] => ([(0,5),(1,4),(2,6),(6,3)],7) => ([(0,3),(1,2),(4,6),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[3,3,2,1,1,1,1],[2,2,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,4,3,2,1,1,1],[3,3,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[2,1,1,1,1,1,1],[1]] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [1,1,1,1,1,2] => 2
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[3,2,2,2,1,1,1],[2,1,1,1]] => ([(1,6),(2,5),(5,3),(6,4)],7) => ([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,3] => 3
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[3,2,2,1,1,1,1],[2,1,1]] => ([(1,6),(2,4),(5,3),(6,5)],7) => ([(1,2),(3,6),(4,5),(5,6)],7) => [1,2,1,3] => 3
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => ([(1,6),(2,5),(3,4)],7) => ([(1,6),(2,5),(3,4)],7) => [3,4] => 4
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[4,3,3,2,1,1,1],[3,2,2,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[3,2,1,1,1,1,1],[2,1]] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(2,6),(3,5),(4,5),(4,6)],7) => [1,1,1,1,3] => 3
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[4,3,2,2,1,1,1],[3,2,1,1]] => ([(2,4),(3,5),(5,6)],7) => ([(2,3),(4,6),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[4,3,2,1,1,1,1],[3,2,1]] => ([(3,4),(4,6),(6,5)],7) => ([(3,6),(4,5),(5,6)],7) => [1,1,1,4] => 4
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[5,4,3,2,2,1,1],[4,3,2,1,1]] => ([(3,6),(4,5)],7) => ([(3,6),(4,5)],7) => [2,5] => 5
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[5,4,3,2,1,1,1],[4,3,2,1]] => ([(4,5),(5,6)],7) => ([(4,6),(5,6)],7) => [1,1,5] => 5
[[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[6,5,4,3,2,1,1],[5,4,3,2,1]] => ([(5,6)],7) => ([(5,6)],7) => [1,6] => 6
[[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => ([],7) => ([],7) => [7] => 7
[[8],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[7,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[6,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,3],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,2,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => [1,1,1,1,2,1,1] => 1
[[4,3,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,2,2],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,2,1,1],[]] => ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8) => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8) => [1,1,1,2,1,1,1] => 1
[[4,1,1,1,1],[]] => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,1,1],[]] => ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,2,2,1],[]] => ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,2,1,1,1],[]] => ([(0,5),(0,6),(3,4),(4,2),(5,3),(5,7),(6,1),(6,7)],8) => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,1,1,1,1,1],[]] => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[2,2,2,2],[]] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => [1,1,1,1,2,1,1] => 1
[[2,2,2,1,1],[]] => ([(0,2),(0,5),(2,6),(3,4),(3,7),(4,1),(5,3),(5,6),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[2,1,1,1,1,1,1],[]] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[1,1,1,1,1,1,1,1],[]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,3,2],[]] => ([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10) => ([(0,5),(1,2),(1,9),(2,6),(3,7),(3,9),(4,6),(4,8),(5,7),(6,9),(7,8),(8,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
[[4,3,3],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
[[4,3,2,1],[]] => ([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10) => ([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
[[3,3,3,1],[]] => ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8),(7,9),(8,9)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
[[3,3,2,1,1],[]] => ([(0,5),(0,6),(2,9),(3,1),(4,3),(4,8),(5,4),(5,7),(6,2),(6,7),(7,8),(7,9)],10) => ([(0,5),(1,2),(1,9),(2,6),(3,7),(3,9),(4,6),(4,8),(5,7),(6,9),(7,8),(8,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
[[2,2,2,1,1,1,1],[1,1]] => ([(0,3),(1,6),(1,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,2,1,1,1,1],[1]] => ([(0,6),(0,7),(1,3),(1,7),(4,5),(5,2),(6,4)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[2,2,2,2,2,1,1],[1,1,1,1]] => ([(0,5),(1,6),(1,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,3,3,3,2],[2,2,2,2,1]] => ([(0,3),(1,6),(2,6),(2,7),(3,5),(4,7),(5,4)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,3,3,2],[3,2,2,1]] => ([(0,5),(1,6),(2,5),(2,7),(3,4),(3,6),(4,7)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,5,4,2],[4,3,1]] => ([(0,5),(1,6),(2,5),(2,7),(3,4),(3,6),(4,7)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,3,3,3],[2,2,2]] => ([(0,4),(1,5),(1,6),(3,7),(4,7),(5,2),(6,3)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,4,4,4],[3,3,3,3]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,5,5,5],[4,4,4]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,3,1],[1,1]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(5,6),(7,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,1],[1]] => ([(0,3),(0,7),(1,4),(1,7),(2,6),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[2,2,2,2,1],[1]] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,3,1],[2]] => ([(0,7),(1,3),(1,4),(3,5),(3,7),(4,2),(4,5),(5,6),(7,6)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,3,2],[1,1,1]] => ([(0,7),(1,3),(1,4),(2,6),(2,7),(3,5),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,2],[1,1]] => ([(0,7),(1,3),(1,4),(2,6),(3,5),(3,7),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,4],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,5],[2]] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,3,3],[2,1,1]] => ([(0,7),(1,6),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,3,3],[1,1]] => ([(0,7),(1,3),(1,4),(3,5),(3,7),(4,2),(4,5),(5,6),(7,6)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,4],[3,1]] => ([(0,7),(1,6),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[5,4],[1]] => ([(0,7),(1,4),(1,7),(3,2),(3,6),(4,3),(4,5),(5,6),(7,5)],8) => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,4],[1,1]] => ([(0,3),(0,4),(1,7),(2,8),(3,2),(3,9),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
[[2,2,2,2,2],[1,1]] => ([(0,3),(1,4),(1,7),(2,6),(3,7),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,2,2,2],[1]] => ([(0,3),(0,7),(1,4),(1,7),(2,6),(4,2),(4,5),(5,6),(7,5)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,2,2],[2]] => ([(0,7),(1,3),(1,4),(2,6),(3,5),(3,7),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,3,3],[2,2]] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,3,3],[2]] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(3,7),(5,6),(7,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[4,4,3],[3]] => ([(0,7),(1,3),(1,4),(2,6),(2,7),(3,5),(4,2),(4,5),(5,6)],8) => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8) => [1,1,1,1,1,1,1,1] => 1
[[3,3,3,3],[2]] => ([(0,3),(0,4),(1,7),(2,8),(3,2),(3,9),(4,7),(4,9),(6,5),(7,6),(8,5),(9,6),(9,8)],10) => ([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
[[4,4,4,4],[3,2,1]] => ([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10) => ([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10) => [1,1,1,1,1,1,1,1,1,1] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 4,4,1 9,12,6,1 20,34,24,8,1 46,92,83,40,10,1 105,244,264,164,60,12,1
$F_{1} = q$
$F_{2} = 2\ q + q^{2}$
$F_{3} = 4\ q + 4\ q^{2} + q^{3}$
$F_{4} = 9\ q + 12\ q^{2} + 6\ q^{3} + q^{4}$
$F_{5} = 20\ q + 34\ q^{2} + 24\ q^{3} + 8\ q^{4} + q^{5}$
$F_{6} = 46\ q + 92\ q^{2} + 83\ q^{3} + 40\ q^{4} + 10\ q^{5} + q^{6}$
$F_{7} = 105\ q + 244\ q^{2} + 264\ q^{3} + 164\ q^{4} + 60\ q^{5} + 12\ q^{6} + q^{7}$
Description
The last part of an integer composition.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
cell poset
Description
The Young diagram of a skew partition regarded as a poset.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
This is the poset on the cells of the Young diagram, such that a cell $d$ is greater than a cell $c$ if the entry in $d$ must be larger than the entry of $c$ in any standard Young tableau on the skew partition.
Map
Laplacian multiplicities
Description
The composition of multiplicities of the Laplacian eigenvalues.
Let $\lambda_1 > \lambda_2 > \dots$ be the eigenvalues of the Laplacian matrix of a graph on $n$ vertices. Then this map returns the composition $a_1,\dots,a_k$ of $n$ where $a_i$ is the multiplicity of $\lambda_i$.
Let $\lambda_1 > \lambda_2 > \dots$ be the eigenvalues of the Laplacian matrix of a graph on $n$ vertices. Then this map returns the composition $a_1,\dots,a_k$ of $n$ where $a_i$ is the multiplicity of $\lambda_i$.
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