Identifier
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
[[1,2]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[2,2]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[2]] => [2,1] => [2,1] => [2,1] => ([],2)
[[1,3]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[2,3]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[3,3]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[3]] => [2,1] => [2,1] => [2,1] => ([],2)
[[2],[3]] => [2,1] => [2,1] => [2,1] => ([],2)
[[1,1,2]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,2,2]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,2,2]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,1],[2]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,2],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,4]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[2,4]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[3,4]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[4,4]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[4]] => [2,1] => [2,1] => [2,1] => ([],2)
[[2],[4]] => [2,1] => [2,1] => [2,1] => ([],2)
[[3],[4]] => [2,1] => [2,1] => [2,1] => ([],2)
[[1,1,3]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,2,3]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,3,3]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,2,3]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,3,3]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,3,3]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,1],[3]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,2],[3]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,3],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,3],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,2],[3]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,3],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1],[2],[3]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1,1,1,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,2,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,2,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,2]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,1],[2]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,2],[2]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,2,2],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,1],[2,2]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,5]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[2,5]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[3,5]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[4,5]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[5,5]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[5]] => [2,1] => [2,1] => [2,1] => ([],2)
[[2],[5]] => [2,1] => [2,1] => [2,1] => ([],2)
[[3],[5]] => [2,1] => [2,1] => [2,1] => ([],2)
[[4],[5]] => [2,1] => [2,1] => [2,1] => ([],2)
[[1,1,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,2,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,3,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,2,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,3,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,3,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,4,4]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,1],[4]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,2],[4]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,4],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,3],[4]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,4],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,4],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,2],[4]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,3],[4]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,4],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,4],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,3],[4]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,4],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1],[2],[4]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[3],[4]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[3],[4]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1,1,1,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,2,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,2,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,3]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,1],[3]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,2],[3]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,3],[2]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,3],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,2,2],[3]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,3],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,3],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,3,3],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,3],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,2,2],[3]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,3],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,3,3],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,1],[2,3]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[3,3]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,2],[2,3]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[3,3]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
>>> Load all 2463 entries. <<<
[[2,2],[3,3]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[2],[3]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,2],[2],[3]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,3],[2],[3]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,1,1,1,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,2,2]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,1],[2]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,2],[2]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,2,2],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,2,2,2],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,1,1],[2,2]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,2],[2,2]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,6]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[2,6]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[3,6]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[4,6]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[5,6]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[6,6]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[6]] => [2,1] => [2,1] => [2,1] => ([],2)
[[2],[6]] => [2,1] => [2,1] => [2,1] => ([],2)
[[3],[6]] => [2,1] => [2,1] => [2,1] => ([],2)
[[4],[6]] => [2,1] => [2,1] => [2,1] => ([],2)
[[5],[6]] => [2,1] => [2,1] => [2,1] => ([],2)
[[1,1,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,2,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,3,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,2,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,3,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,3,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,4,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[5,5,5]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,1],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,2],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,5],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,3],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,5],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,4],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,5],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,2],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,3],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,5],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,4],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,5],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,3],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,4],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,5],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[4,4],[5]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[4,5],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1],[2],[5]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[3],[5]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[4],[5]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[3],[5]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[4],[5]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[3],[4],[5]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1,1,1,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,2,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,2,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,1],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,2],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,4],[2]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,3],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,4],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,4],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,2,2],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,4],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,3],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,4],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,3,4],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,4],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,4,4],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,3],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,3,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,4],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,4,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,4,4],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,2,2],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,3],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,4],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,2,4],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,3,3],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,3,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,3,4],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,4,4],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,4,4],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,3,3],[4]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,3,4],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,4,4],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,1],[2,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[3,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[4,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,2],[2,4]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[3,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,3],[2,4]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[4,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,3],[3,4]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,3],[4,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[3,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[4,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,3],[3,4]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,3],[4,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,3],[4,4]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[2],[4]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,1],[3],[4]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,2],[2],[4]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,2],[3],[4]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,3],[2],[4]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,4],[2],[3]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,4],[2],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,3],[3],[4]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,4],[3],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,2],[3],[4]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,3],[3],[4]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,4],[3],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1],[2],[3],[4]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1,1,1,1,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,2,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,3,3]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,1],[3]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,2],[3]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,3],[2]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,1,3],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,2,2],[3]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,2,3],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,2,3],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,3,3],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,3,3],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,2,2,2],[3]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,2,3],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,2,3],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,3,3],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,3,3],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,3,3,3],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,3,3],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,2,2,2],[3]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,2,3],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,3,3],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,3,3,3],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,1,1],[2,3]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,1],[3,3]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,2],[2,3]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,3],[2,2]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,2],[3,3]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,3],[2,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,3],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,2,2],[2,3]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,2],[3,3]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,3],[2,3]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,3],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,2],[3,3]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,3],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,1],[2],[3]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,2],[2],[3]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,3],[2],[3]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,2],[2],[3]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,2,3],[2],[3]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,3,3],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,1],[2,2],[3]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[2,3],[3]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,2],[2,3],[3]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1,1,1,1,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2,2,2]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,1],[2]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,1,2],[2]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,2,2],[2]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,2,2,2],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,2,2,2,2],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,1,1,1],[2,2]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,2],[2,2]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,2,2],[2,2]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,1],[2,2,2]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,7]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[2,7]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[3,7]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[4,7]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[5,7]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[6,7]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[7,7]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[7]] => [2,1] => [2,1] => [2,1] => ([],2)
[[2],[7]] => [2,1] => [2,1] => [2,1] => ([],2)
[[3],[7]] => [2,1] => [2,1] => [2,1] => ([],2)
[[4],[7]] => [2,1] => [2,1] => [2,1] => ([],2)
[[5],[7]] => [2,1] => [2,1] => [2,1] => ([],2)
[[6],[7]] => [2,1] => [2,1] => [2,1] => ([],2)
[[1,1,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,2,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,3,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,2,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,3,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,3,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,4,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[5,5,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[5,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[6,6,6]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,1],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,2],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,6],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,3],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,6],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,4],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,6],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,5],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,2],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,3],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,6],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,4],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,6],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,5],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,3],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,4],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,6],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,5],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[4,4],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[4,5],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[4,6],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[4,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[5,5],[6]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[5,6],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1],[2],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[3],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[4],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[5],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[3],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[4],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[5],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[3],[4],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[3],[5],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[4],[5],[6]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1,1,1,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,2,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,2,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,4,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[5,5,5,5]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,1],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,2],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,5],[2]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,3],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,5],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,5],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,2,2],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,3],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,5],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,3,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,5],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,4,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,5,5],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,3],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,3,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,3,5],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,4,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,5,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,4,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,4,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,4,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,5,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,2,2],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,3],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,5],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,2,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,5],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,2,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,3,3],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,3,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,3,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,3,5],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,4,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,3,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,5,5],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,4,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,4,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,4,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,5,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,3,3],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,3,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,3,5],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,3,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,4,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,4,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,4,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,5,5],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[4,4,4],[5]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[4,4,5],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[4,5,5],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,1],[2,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[3,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[4,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,2],[2,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[3,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,3],[2,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[4,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,4],[2,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,3],[3,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,3],[4,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,4],[3,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,3],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,4],[4,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,4],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[3,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[4,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,3],[3,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,3],[4,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,4],[3,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,3],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,4],[4,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,4],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,3],[4,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,3],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,4],[4,5]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[3,4],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[4,4],[5,5]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[2],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,1],[3],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,1],[4],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,2],[2],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,2],[3],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,3],[2],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,5],[2],[3]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,2],[4],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,4],[2],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,5],[2],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,5],[2],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,3],[3],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,3],[4],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,4],[3],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,5],[3],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,5],[3],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,4],[4],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,5],[4],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,2],[3],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,2],[4],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,3],[3],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,3],[4],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,4],[3],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,5],[3],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,5],[3],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,4],[4],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,5],[4],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[3,3],[4],[5]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[3,4],[4],[5]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[3,5],[4],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1],[2],[3],[5]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1],[2],[4],[5]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1],[3],[4],[5]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[2],[3],[4],[5]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1,1,1,1,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,2,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,3,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,4,4,4]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,1],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,2],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,4],[2]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,1,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,4],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,1,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,2,2],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,2,4],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,2,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,2,4],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,3,4],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,2,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,4,4],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,3,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,3,4],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,3,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,4,4],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,4,4],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,2,2,2],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,2,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,2,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,2,4],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,3,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,2,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,4,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,3,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,3,4],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,3,3,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,3,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,4,4],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,3,4,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,4,4],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,4,4,4],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,3,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,3,3,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,3,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,3,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,4,4],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,4,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,4,4,4],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,2,2,2],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,2,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,2,4],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,2,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,3,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,3,4],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,2,3,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,4,4],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,2,4,4],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,3,3,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,3,3,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,3,3,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,3,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,3,4,4],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,4,4,4],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,4,4,4],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[3,3,3,3],[4]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[3,3,3,4],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[3,3,4,4],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[3,4,4,4],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,1,1],[2,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,1],[3,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,1],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,2],[2,4]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,4],[2,2]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,2],[3,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,3],[2,4]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,4],[2,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,2],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,4],[2,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,3],[3,4]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,4],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,3],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,4],[3,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,4],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,2,2],[2,4]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,2],[3,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,3],[2,4]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,4],[2,3]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,2],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,4],[2,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,3],[3,4]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,2,4],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,3,3],[2,4]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,3],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,4],[3,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,3,4],[2,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,4],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,3,3],[3,4]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,3,3],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,3,4],[3,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,3,4],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,2],[3,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,2],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,3],[3,4]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[2,2,4],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,3],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,4],[3,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,4],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,3,3],[3,4]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[2,3,3],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,3,4],[3,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[2,3,4],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[3,3,3],[4,4]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[3,3,4],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,1],[2],[4]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,1],[3],[4]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,2],[2],[4]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,2],[3],[4]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,3],[2],[4]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,4],[2],[3]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,4],[2],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,3],[3],[4]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,4],[3],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,2],[2],[4]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,2,2],[3],[4]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,2,3],[2],[4]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,2,4],[2],[3]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,2,4],[2],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,2,3],[3],[4]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,3,3],[2],[4]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,3,4],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,2,4],[3],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,4],[2],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,4,4],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,4,4],[2],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,3,3],[3],[4]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,3,4],[3],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,4,4],[3],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[2,2,2],[3],[4]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[2,2,3],[3],[4]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[2,2,4],[3],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[2,3,3],[3],[4]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[2,3,4],[3],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[2,4,4],[3],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,1],[2,2],[4]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[2,3],[4]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[2,4],[3]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,1],[2,4],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,1],[3,3],[4]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[3,4],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,2],[2,3],[4]] => [5,2,4,1,3] => [2,4,5,3,1] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
[[1,2],[2,4],[3]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[2,4],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[3,3],[4]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,3],[2,4],[3]] => [3,2,5,1,4] => [2,1,4,5,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,2],[3,4],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,3],[2,4],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[3,4],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[2,2],[3,3],[4]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[2,2],[3,4],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[2,3],[3,4],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1],[2],[3],[4]] => [5,4,3,1,2] => [4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5)
[[1,2],[2],[3],[4]] => [5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
[[1,3],[2],[3],[4]] => [5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[[1,4],[2],[3],[4]] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[[1,1,1,1,1,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2,2,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,3,3,3,3]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,1],[3]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,1,2],[3]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,1,3],[2]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,1,3],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,2,2],[3]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,2,3],[2]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,1,2,3],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,3,3],[2]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,1,3,3],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,2,2,2],[3]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,2,2,3],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,2,2,3],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,2,3,3],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,2,3,3],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,3,3,3],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,3,3,3],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,2,2,2,2],[3]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,2,2,2,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,2,2,3],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,2,2,3,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,2,3,3],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,2,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,3,3,3],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,3,3,3,3],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[2,2,2,2,2],[3]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[2,2,2,2,3],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[2,2,2,3,3],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[2,2,3,3,3],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[2,3,3,3,3],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,1,1,1],[2,3]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,1],[3,3]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,2],[2,3]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,1,1,3],[2,2]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,1,2],[3,3]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,3],[2,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,1,3],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,2,2],[2,3]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[1,1,2,3],[2,2]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,2,3],[2,3]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[1,1,3,3],[2,2]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,2,3],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,3,3],[2,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,3,3],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,2,2,2],[2,3]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,2,2,2],[3,3]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,2,2,3],[2,3]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,2,2,3],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,2,3,3],[2,3]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,2,3,3],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[2,2,2,2],[3,3]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[2,2,2,3],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[2,2,3,3],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,1,1],[2],[3]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[1,1,1,2],[2],[3]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,3],[2],[3]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,2,2],[2],[3]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,2,3],[2],[3]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[1,1,3,3],[2],[3]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[1,2,2,2],[2],[3]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,2,2,3],[2],[3]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,2,3,3],[2],[3]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,3,3,3],[2],[3]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[1,1,1],[2,2,3]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[2,3,3]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[3,3,3]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,2],[2,2,3]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,1,2],[2,3,3]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[1,1,2],[3,3,3]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,2,2],[2,3,3]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[1,2,2],[3,3,3]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[2,2,2],[3,3,3]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[2,2],[3]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[1,1,1],[2,3],[3]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[1,1,2],[2,2],[3]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,2],[2,3],[3]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,1,3],[2,2],[3]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,3],[2,3],[3]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[1,2,2],[2,3],[3]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[1,2,3],[2,3],[3]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[1,1],[2,2],[3,3]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,1,1],[2]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,1,1,1,1,2],[2]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,1,1,1,2,2],[2]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,1,1,2,2,2],[2]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,1,2,2,2,2],[2]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[1,1,1,1,1],[2,2]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,1,1,1,2],[2,2]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[1,1,1,2,2],[2,2]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,1,2,2,2],[2,2]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[1,1,1,1],[2,2,2]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,1,1,2],[2,2,2]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[1,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[2,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[3,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[4,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[5,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[6,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[7,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[8,8]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[8]] => [2,1] => [2,1] => [2,1] => ([],2)
[[2],[8]] => [2,1] => [2,1] => [2,1] => ([],2)
[[3],[8]] => [2,1] => [2,1] => [2,1] => ([],2)
[[4],[8]] => [2,1] => [2,1] => [2,1] => ([],2)
[[5],[8]] => [2,1] => [2,1] => [2,1] => ([],2)
[[6],[8]] => [2,1] => [2,1] => [2,1] => ([],2)
[[7],[8]] => [2,1] => [2,1] => [2,1] => ([],2)
[[1,1,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,2,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,3,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,2,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,3,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[2,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,3,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[3,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,4,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[5,5,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[5,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[5,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[6,6,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[6,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[7,7,7]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,1],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,2],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,7],[2]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,3],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,7],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,4],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,7],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,5],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,6],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[1,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,2],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,3],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,7],[3]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,4],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,7],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,5],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,6],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[2,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[2,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,3],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,4],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,7],[4]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,5],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,6],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[3,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[3,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[4,4],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[4,5],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[4,7],[5]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[4,6],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[4,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[4,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[5,5],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[5,6],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[5,7],[6]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[5,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[6,6],[7]] => [3,1,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
[[6,7],[7]] => [2,1,3] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1],[2],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[3],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[4],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[5],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1],[6],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[3],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[4],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[5],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[2],[6],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[3],[4],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[3],[5],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[3],[6],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[4],[5],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[4],[6],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[5],[6],[7]] => [3,2,1] => [3,2,1] => [3,2,1] => ([],3)
[[1,1,1,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,2,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,2,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,2,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,2,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,2,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,3,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[2,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,3,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,3,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[3,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,4,4,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,4,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,4,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[4,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[5,5,5,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[5,5,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[5,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[6,6,6,6]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,1,1],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,2],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,6],[2]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,3],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,6],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,6],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,1,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,1,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,2,2],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,3],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,6],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,3,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,6],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,4,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,2,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,5,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,6,6],[2]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,3],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,3,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,3,6],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,4,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,3,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,5,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,3,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,6,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,4,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,4,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,4,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,4,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,5,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,4,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,6,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,5,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[1,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,5,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,2,2],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,3],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,6],[3]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,2,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,6],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,2,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,2,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,2,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,3,3],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,3,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,3,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,3,6],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,4,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,3,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,3,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,5,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,3,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,6,6],[3]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,4,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,4,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,4,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,4,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,5,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,4,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,6,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,5,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[2,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,5,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[2,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[2,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,3,3],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,3,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,3,6],[4]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,3,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,3,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,3,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,4,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,4,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,4,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,4,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,5,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,4,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,6,6],[4]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,5,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[3,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,5,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[3,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[3,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[4,4,4],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[4,4,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[4,4,6],[5]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[4,4,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[4,5,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[4,5,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[4,5,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[4,6,6],[5]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[4,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[5,5,5],[6]] => [4,1,2,3] => [2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[5,5,6],[6]] => [3,1,2,4] => [2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[5,6,6],[6]] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,1],[2,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[3,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[4,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,2],[2,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[3,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,3],[2,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[4,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,4],[2,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,5],[2,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,3],[3,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,3],[4,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,4],[3,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,3],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,5],[3,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,3],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,4],[4,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,4],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,5],[4,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,4],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,5],[5,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1,5],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[3,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[4,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,2],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,3],[3,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,3],[4,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,4],[3,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,3],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,5],[3,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,3],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,4],[4,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,4],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,5],[4,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,4],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[2,5],[5,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[2,5],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,3],[4,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,3],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,3],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,4],[4,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[3,4],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,5],[4,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[3,4],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[3,5],[5,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[3,5],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[4,4],[5,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[4,4],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[4,5],[5,6]] => [2,4,1,3] => [1,3,4,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[4,5],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[5,5],[6,6]] => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => ([(0,3),(1,2)],4)
[[1,1],[2],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,1],[3],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,1],[4],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,1],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,2],[2],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,2],[3],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,3],[2],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,6],[2],[3]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,2],[4],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,4],[2],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,6],[2],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,2],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,5],[2],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,6],[2],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,6],[2],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,3],[3],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,3],[4],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,4],[3],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,6],[3],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,3],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,5],[3],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,6],[3],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,6],[3],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,4],[4],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,4],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[1,5],[4],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,6],[4],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,6],[4],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1,5],[5],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[1,6],[5],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,2],[3],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,2],[4],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,2],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,3],[3],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,3],[4],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,4],[3],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,6],[3],[4]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,3],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,5],[3],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,6],[3],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,6],[3],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,4],[4],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,4],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[2,5],[4],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,6],[4],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,6],[4],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[2,5],[5],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[2,6],[5],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[3,3],[4],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[3,3],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[3,4],[4],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[3,4],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[3,5],[4],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[3,6],[4],[5]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[3,6],[4],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[3,5],[5],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[3,6],[5],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[4,4],[5],[6]] => [4,3,1,2] => [3,4,2,1] => [3,4,2,1] => ([(2,3)],4)
[[4,5],[5],[6]] => [4,2,1,3] => [3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[4,6],[5],[6]] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[1],[2],[3],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1],[2],[4],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1],[2],[5],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1],[3],[4],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1],[3],[5],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1],[4],[5],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[2],[3],[4],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[2],[3],[5],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[2],[4],[5],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[3],[4],[5],[6]] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => ([],4)
[[1,1,1,1,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,2,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,2,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,2,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,3,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,2,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,2,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,2,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,3,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[2,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,3,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,3,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,3,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[3,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,4,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,4,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,4,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[4,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[5,5,5,5,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[1,1,1,1],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,2],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,5],[2]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,1,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,5],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,1,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,1,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,1,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,2,2],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,2,5],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,2,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,2,5],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,3,5],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,2,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,2,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,4,5],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,2,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,5,5],[2]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,3,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,3,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,3,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,3,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,4,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,3,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,5,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,1,4,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,1,5,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,1,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,2,2,2],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,2,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,2,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,2,5],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,3,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,2,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,2,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,2,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,3,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,3,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,3,3,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,3,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,3,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,4,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,3,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,5,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,3,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,2,4,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,4,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,5,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,4,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,5,5,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,3,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,3,3,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,3,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,3,3,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,3,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,3,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,3,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,3,4,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,4,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,3,5,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,4,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,3,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,5,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,4,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[1,4,4,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,4,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,4,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,4,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,5,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,2,2,2],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,2,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,2,5],[3]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,2,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,2,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,2,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,3,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,3,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,2,3,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,3,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,4,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,2,3,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,5,5],[3]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,2,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,2,4,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,2,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,2,5,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,2,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,3,3,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,3,3,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,3,3,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,3,3,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,3,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,3,3,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,3,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,3,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,3,4,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,4,4,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,3,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,3,5,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,4,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,3,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,5,5,5],[3]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,4,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[2,4,4,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,4,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[2,4,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,4,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[2,5,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[2,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[3,3,3,3],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[3,3,3,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[3,3,3,5],[4]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[3,3,3,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[3,3,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[3,3,4,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[3,3,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[3,3,5,5],[4]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[3,3,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[3,4,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[3,4,4,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[3,4,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[3,4,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[3,4,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[3,5,5,5],[4]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[3,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[4,4,4,4],[5]] => [5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[4,4,4,5],[5]] => [4,1,2,3,5] => [2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[4,4,5,5],[5]] => [3,1,2,4,5] => [2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[4,5,5,5],[5]] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,1,1],[2,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,1],[3,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,1],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,1],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,2],[2,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,5],[2,2]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,2],[3,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,3],[2,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,5],[2,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,2],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,4],[2,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,5],[2,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,2],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,5],[2,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,3],[3,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,5],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,3],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,4],[3,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,5],[3,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,3],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,5],[3,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,4],[4,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,1,5],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,1,5],[4,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,2,2],[2,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,2],[3,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,3],[2,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,5],[2,3]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,2],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,4],[2,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,5],[2,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,2],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,5],[2,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,3],[3,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,2,5],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,3,3],[2,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,3],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,4],[3,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,2,5],[3,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,3,4],[2,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,3,5],[2,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,3],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,5],[3,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,3,5],[2,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,4],[4,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,2,5],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,4,4],[2,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,2,5],[4,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,4,5],[2,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,3,3],[3,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,3,3],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,3,4],[3,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,3,5],[3,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,3,3],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,3,5],[3,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,3,4],[4,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[1,3,5],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,4,4],[3,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,3,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,3,5],[4,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,4,5],[3,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,3,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,4,4],[4,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,4,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[1,4,5],[4,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,4,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,2],[3,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,2],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,2],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,3],[3,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[2,2,5],[3,3]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,3],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,4],[3,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[2,2,5],[3,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,3],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,5],[3,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,4],[4,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[2,2,5],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,2,5],[4,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,2,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,3,3],[3,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[2,3,3],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,3,4],[3,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[2,3,5],[3,4]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[2,3,3],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,3,5],[3,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[2,3,4],[4,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[2,3,5],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,4,4],[3,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[2,3,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,3,5],[4,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,4,5],[3,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[2,3,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[2,4,4],[4,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[2,4,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[2,4,5],[4,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[2,4,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[3,3,3],[4,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[3,3,3],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[3,3,4],[4,5]] => [3,5,1,2,4] => [3,1,4,5,2] => [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
[[3,3,5],[4,4]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[3,3,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[3,3,5],[4,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[3,3,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[3,4,4],[4,5]] => [2,5,1,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[3,4,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[3,4,5],[4,5]] => [2,4,1,3,5] => [1,3,4,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[3,4,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[4,4,4],[5,5]] => [4,5,1,2,3] => [3,4,1,5,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
[[4,4,5],[5,5]] => [3,4,1,2,5] => [3,1,4,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
[[1,1,1],[2],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,1],[3],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,1],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,2],[2],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,2],[3],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,3],[2],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,5],[2],[3]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,2],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,4],[2],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,5],[2],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,5],[2],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,3],[3],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,3],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,1,4],[3],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,5],[3],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,5],[3],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,1,4],[4],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,1,5],[4],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,2],[2],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,2,2],[3],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,2,3],[2],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,2,5],[2],[3]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,2,2],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,2,4],[2],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,2,5],[2],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,2,5],[2],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,2,3],[3],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,3,3],[2],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,3,5],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,2,5],[3],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,3,5],[2],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,5,5],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,2,4],[4],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,4,4],[2],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,4,5],[2],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,2,5],[4],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,4,5],[2],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,5,5],[2],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,5,5],[2],[5]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,3,3],[3],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,3,3],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[1,3,4],[3],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,3,5],[3],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,3,5],[3],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,3,4],[4],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[1,4,4],[3],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,4,5],[3],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,3,5],[4],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[1,4,5],[3],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,5,5],[3],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,5,5],[3],[5]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,4,4],[4],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[1,4,5],[4],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,5,5],[4],[5]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[2,2,2],[3],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[2,2,2],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[2,2,3],[3],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[2,2,3],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[2,2,4],[3],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[2,2,5],[3],[4]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[2,2,5],[3],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[2,2,4],[4],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[2,2,5],[4],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[2,3,3],[3],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[2,3,3],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[2,3,4],[3],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[2,3,5],[3],[4]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[2,3,5],[3],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[2,3,4],[4],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[2,4,4],[3],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[2,4,5],[3],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[2,3,5],[4],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[2,4,5],[3],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[2,5,5],[3],[4]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[2,5,5],[3],[5]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[2,4,4],[4],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[2,4,5],[4],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[2,5,5],[4],[5]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[3,3,3],[4],[5]] => [5,4,1,2,3] => [3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5)
[[3,3,4],[4],[5]] => [5,3,1,2,4] => [3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
[[3,3,5],[4],[5]] => [4,3,1,2,5] => [3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[3,4,4],[4],[5]] => [5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[3,4,5],[4],[5]] => [4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[3,5,5],[4],[5]] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[1,1],[2,2],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[2,3],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[2,5],[3]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,1],[2,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[2,5],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,1],[2,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,1],[3,3],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[3,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[3,5],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,1],[3,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,1],[4,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,1],[4,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,2],[2,3],[5]] => [5,2,4,1,3] => [2,4,5,3,1] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
[[1,2],[2,5],[3]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[2,4],[5]] => [5,2,4,1,3] => [2,4,5,3,1] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
[[1,2],[2,5],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[2,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[3,3],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,3],[2,5],[3]] => [3,2,5,1,4] => [2,1,4,5,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [2,4,5,3,1] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [2,1,4,5,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,2],[3,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,3],[2,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,2],[4,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,4],[2,5],[4]] => [3,2,5,1,4] => [2,1,4,5,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,2],[4,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,4],[2,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[3,4],[5]] => [5,2,4,1,3] => [2,4,5,3,1] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
[[1,3],[3,5],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[3,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,3],[4,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[1,4],[3,5],[4]] => [3,2,5,1,4] => [2,1,4,5,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,3],[4,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[1,4],[3,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,4],[4,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[2,2],[3,3],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[2,2],[3,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[2,2],[3,5],[4]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[2,2],[3,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[2,2],[4,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[2,2],[4,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[2,3],[3,4],[5]] => [5,2,4,1,3] => [2,4,5,3,1] => [4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
[[2,3],[3,5],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[2,3],[3,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[2,3],[4,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[2,4],[3,5],[4]] => [3,2,5,1,4] => [2,1,4,5,3] => [4,2,1,5,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[2,3],[4,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[2,4],[3,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[2,4],[4,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[3,3],[4,4],[5]] => [5,3,4,1,2] => [4,2,5,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5)
[[3,3],[4,5],[5]] => [4,3,5,1,2] => [4,2,1,5,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
[[3,4],[4,5],[5]] => [4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
[[1,1],[2],[3],[5]] => [5,4,3,1,2] => [4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5)
[[1,1],[2],[4],[5]] => [5,4,3,1,2] => [4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5)
[[1,1],[3],[4],[5]] => [5,4,3,1,2] => [4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5)
[[1,2],[2],[3],[5]] => [5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
[[1,2],[2],[4],[5]] => [5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
[[1,3],[2],[3],[5]] => [5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5)
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[[1,5],[2],[3],[5]] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[[1,4],[2],[4],[5]] => [5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[[1,5],[2],[4],[5]] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[[1,3],[3],[4],[5]] => [5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
[[1,4],[3],[4],[5]] => [5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[[1,5],[3],[4],[5]] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[[2,2],[3],[4],[5]] => [5,4,3,1,2] => [4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5)
[[2,3],[3],[4],[5]] => [5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5)
[[2,4],[3],[4],[5]] => [5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[[2,5],[3],[4],[5]] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ([],5)
[[1,1,1,1,1,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,2,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2,2,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,2,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,2,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,2,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[2,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,3,3,3,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,3,3,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,3,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,3,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[3,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[4,4,4,4,4,4]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,1,1,1,1],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,1,2],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,1,4],[2]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,1,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,1,4],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,1,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,2,2],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,2,4],[2]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,1,2,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,2,4],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,3,4],[2]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,1,2,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,4,4],[2]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,1,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,1,3,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,1,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,1,4,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,1,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,2,2,2],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,2,2,4],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,2,2,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,2,2,4],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,2,3,4],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,2,2,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,2,4,4],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,2,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,2,3,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,3,3,4],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,2,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,2,4,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,3,4,4],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,2,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,4,4,4],[2]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,3,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,1,3,3,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,3,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,1,3,4,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,3,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,1,4,4,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,1,4,4,4],[4]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,2,2,2,2],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,2,2,2,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,2,2,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,2,2,2,4],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,2,2,3,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,2,2,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,2,2,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,2,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,2,2,3,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,2,3,3,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,2,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,2,2,4,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,2,3,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,2,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,2,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,3,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,2,3,3,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,3,3,3,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,3,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,2,3,4,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,3,3,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,3,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,2,4,4,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,3,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,4,4,4],[4]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,4,4,4,4],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,3,3,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,3,3,3,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,3,3,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,3,3,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,3,3,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,3,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,3,4,4,4],[4]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,4,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[2,2,2,2,2],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[2,2,2,2,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[2,2,2,2,4],[3]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[2,2,2,2,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[2,2,2,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[2,2,2,3,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[2,2,2,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[2,2,2,4,4],[3]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[2,2,2,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[2,2,3,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[2,2,3,3,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[2,2,3,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[2,2,3,4,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[2,2,3,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[2,2,4,4,4],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[2,2,4,4,4],[4]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[2,3,3,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[2,3,3,3,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[2,3,3,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[2,3,3,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[2,3,3,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[2,3,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[2,3,4,4,4],[4]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[2,4,4,4,4],[3]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[2,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[3,3,3,3,3],[4]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[3,3,3,3,4],[4]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[3,3,3,4,4],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[3,3,4,4,4],[4]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[3,4,4,4,4],[4]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,1,1,1],[2,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,1],[3,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,1],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,2],[2,4]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,1,1,4],[2,2]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,1,2],[3,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,3],[2,4]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,1,1,4],[2,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,1,2],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,4],[2,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,1,3],[3,4]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,1,1,4],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,1,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,1,4],[3,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,1,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,2,2],[2,4]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[1,1,2,4],[2,2]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,2,3],[2,4]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[1,1,2,4],[2,3]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[1,1,3,4],[2,2]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,2,4],[2,4]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[1,1,4,4],[2,2]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,2,3],[3,4]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,1,2,4],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,3,3],[2,4]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[1,1,3,4],[2,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,2,4],[3,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,3,4],[2,4]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[1,1,4,4],[2,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,2,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,4,4],[2,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,3,3],[3,4]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[1,1,3,4],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,1,3,4],[3,4]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[1,1,4,4],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,3,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,1,4,4],[3,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,4,4],[4,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,2,2,2],[2,4]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,2,2,2],[3,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,2,2,3],[2,4]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,2,2,4],[2,3]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,2,2,2],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,2,2,4],[2,4]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,2,2,3],[3,4]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,2,2,4],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,2,3,3],[2,4]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,2,3,4],[2,3]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,2,2,4],[3,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,2,3,4],[2,4]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,2,4,4],[2,3]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,2,2,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,2,4,4],[2,4]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,2,3,3],[3,4]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[1,2,3,4],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,3,3,3],[2,4]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,2,3,4],[3,4]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[1,2,4,4],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,3,3,4],[2,4]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,2,3,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,2,4,4],[3,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,3,4,4],[2,4]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,2,4,4],[4,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,3,3,3],[3,4]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,3,3,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,3,3,4],[3,4]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,3,3,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,3,4,4],[3,4]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,3,4,4],[4,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[2,2,2,2],[3,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[2,2,2,2],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[2,2,2,3],[3,4]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[2,2,2,4],[3,3]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[2,2,2,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[2,2,2,4],[3,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[2,2,2,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[2,2,3,3],[3,4]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[2,2,3,4],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[2,2,3,4],[3,4]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[2,2,4,4],[3,3]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[2,2,3,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[2,2,4,4],[3,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[2,2,4,4],[4,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[2,3,3,3],[3,4]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[2,3,3,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[2,3,3,4],[3,4]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[2,3,3,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[2,3,4,4],[3,4]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[2,3,4,4],[4,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[3,3,3,3],[4,4]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[3,3,3,4],[4,4]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[3,3,4,4],[4,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,1,1,1],[2],[4]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[1,1,1,1],[3],[4]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[1,1,1,2],[2],[4]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,2],[3],[4]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[1,1,1,3],[2],[4]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,4],[2],[3]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,4],[2],[4]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,3],[3],[4]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,1,4],[3],[4]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,2,2],[2],[4]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[1,1,2,3],[2],[4]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,2,4],[2],[3]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[1,1,2,4],[2],[4]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,3,3],[2],[4]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,3,4],[2],[3]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,1,3,4],[2],[4]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[1,1,4,4],[2],[3]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,4,4],[2],[4]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,3,3],[3],[4]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[1,1,3,4],[3],[4]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[1,1,4,4],[3],[4]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[1,2,2,2],[2],[4]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,2,2,2],[3],[4]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[1,2,2,3],[2],[4]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,2,2,4],[2],[3]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,2,2,4],[2],[4]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,3,3],[2],[4]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,2,3,4],[2],[3]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,3,4],[2],[4]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,2,4,4],[2],[3]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,2,4,4],[2],[4]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,2,3,3],[3],[4]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[1,3,3,3],[2],[4]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,3,3,4],[2],[3]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[1,2,3,4],[3],[4]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[1,3,3,4],[2],[4]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,3,4,4],[2],[3]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[1,2,4,4],[3],[4]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[1,3,4,4],[2],[4]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,4,4,4],[2],[3]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[1,4,4,4],[2],[4]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[1,3,3,3],[3],[4]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,3,3,4],[3],[4]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,3,4,4],[3],[4]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,4,4,4],[3],[4]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[2,2,2,2],[3],[4]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[2,2,2,3],[3],[4]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[2,2,2,4],[3],[4]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[2,2,3,3],[3],[4]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[2,2,3,4],[3],[4]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[2,2,4,4],[3],[4]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[2,3,3,3],[3],[4]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[2,3,3,4],[3],[4]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[2,3,4,4],[3],[4]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[2,4,4,4],[3],[4]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[1,1,1],[2,2,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[2,3,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[2,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[3,3,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[3,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,2],[2,2,4]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,1,2],[2,3,4]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[1,1,3],[2,2,4]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,1,2],[2,4,4]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[1,1,2],[3,3,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,3],[2,3,4]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,1,2],[3,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,3],[2,4,4]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[1,1,2],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,3],[3,3,4]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,1,3],[3,4,4]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[1,1,3],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,2,2],[2,3,4]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[1,2,2],[2,4,4]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[1,2,2],[3,3,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,2,3],[2,3,4]] => [2,4,6,1,3,5] => [4,1,2,5,6,3] => [4,1,5,2,6,3] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
[[1,2,2],[3,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,2,3],[2,4,4]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[1,2,2],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,2,3],[3,3,4]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,2,3],[3,4,4]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[1,3,3],[2,4,4]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[1,2,3],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,3,3],[3,4,4]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[1,3,3],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[2,2,2],[3,3,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[2,2,2],[3,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[2,2,2],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[2,2,3],[3,3,4]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[2,2,3],[3,4,4]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[2,2,3],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[2,3,3],[3,4,4]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[2,3,3],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[3,3,3],[4,4,4]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,1,1],[2,2],[4]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[1,1,1],[2,3],[4]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[1,1,1],[2,4],[3]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[1,1,1],[2,4],[4]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[1,1,1],[3,3],[4]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[1,1,1],[3,4],[4]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[1,1,2],[2,2],[4]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,2],[2,3],[4]] => [6,3,5,1,2,4] => [4,2,5,6,3,1] => [4,5,2,6,3,1] => ([(1,4),(2,3),(2,5),(4,5)],6)
[[1,1,2],[2,4],[3]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,1,3],[2,2],[4]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,4],[2,2],[3]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,2],[2,4],[4]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,1,4],[2,2],[4]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,2],[3,3],[4]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[1,1,3],[2,3],[4]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,3],[2,4],[3]] => [4,3,6,1,2,5] => [4,2,1,5,6,3] => [4,5,2,1,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)
[[1,1,4],[2,3],[3]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,2],[3,4],[4]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[1,1,3],[2,4],[4]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,1,4],[2,3],[4]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,4],[2,4],[3]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,4],[2,4],[4]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,3],[3,3],[4]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,3],[3,4],[4]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,1,4],[3,3],[4]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,1,4],[3,4],[4]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[1,2,2],[2,3],[4]] => [6,2,5,1,3,4] => [2,4,5,6,3,1] => [4,2,5,6,3,1] => ([(1,5),(2,3),(2,5),(5,4)],6)
[[1,2,2],[2,4],[3]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[1,2,2],[2,4],[4]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[1,2,2],[3,3],[4]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[1,2,3],[2,3],[4]] => [6,2,4,1,3,5] => [2,4,5,3,6,1] => [4,2,5,3,6,1] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,3],[2,4],[3]] => [4,2,6,1,3,5] => [2,4,1,5,6,3] => [4,2,5,1,6,3] => ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)
[[1,2,4],[2,3],[3]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[1,2,3],[2,4],[4]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[1,2,4],[2,3],[4]] => [5,2,4,1,3,6] => [2,4,5,3,1,6] => [4,2,5,3,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,4],[2,4],[3]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,4],[2,4],[4]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,3],[3,3],[4]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[1,3,3],[2,4],[3]] => [3,2,6,1,4,5] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[1,2,3],[3,4],[4]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,2,4],[3,3],[4]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,3,3],[2,4],[4]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[1,3,4],[2,4],[3]] => [3,2,5,1,4,6] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
[[1,2,4],[3,4],[4]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[1,3,4],[2,4],[4]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[1,3,3],[3,4],[4]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[1,3,4],[3,4],[4]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[2,2,2],[3,3],[4]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[2,2,2],[3,4],[4]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[2,2,3],[3,3],[4]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[2,2,3],[3,4],[4]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[2,2,4],[3,3],[4]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[2,2,4],[3,4],[4]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[2,3,3],[3,4],[4]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[2,3,4],[3,4],[4]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[1,1,1],[2],[3],[4]] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6)
[[1,1,2],[2],[3],[4]] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6)
[[1,1,3],[2],[3],[4]] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6)
[[1,1,4],[2],[3],[4]] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,2],[2],[3],[4]] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6)
[[1,2,3],[2],[3],[4]] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6)
[[1,2,4],[2],[3],[4]] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[1,3,3],[2],[3],[4]] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6)
[[1,3,4],[2],[3],[4]] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[1,4,4],[2],[3],[4]] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[[1,1],[2,2],[3,4]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[1,1],[2,2],[4,4]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[1,1],[2,3],[3,4]] => [4,6,3,5,1,2] => [1,5,3,6,4,2] => [5,6,3,1,4,2] => ([(0,5),(1,3),(2,4),(2,5)],6)
[[1,1],[2,3],[4,4]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[1,1],[3,3],[4,4]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[1,2],[2,3],[3,4]] => [4,6,2,5,1,3] => [3,1,5,6,4,2] => [5,3,6,1,4,2] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
[[1,2],[2,3],[4,4]] => [5,6,2,4,1,3] => [3,5,1,6,4,2] => [5,3,6,4,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6)
[[1,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[2,2],[3,3],[4,4]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[1,1],[2,2],[3],[4]] => [6,5,3,4,1,2] => [5,3,6,4,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6)
[[1,1],[2,3],[3],[4]] => [6,4,3,5,1,2] => [5,3,2,6,4,1] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6)
[[1,1],[2,4],[3],[4]] => [5,4,3,6,1,2] => [5,3,2,1,6,4] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6)
[[1,2],[2,3],[3],[4]] => [6,4,2,5,1,3] => [3,5,2,6,4,1] => [5,3,6,2,4,1] => ([(1,5),(2,4),(3,4),(3,5)],6)
[[1,2],[2,4],[3],[4]] => [5,4,2,6,1,3] => [3,5,2,1,6,4] => [5,3,6,2,1,4] => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
[[1,3],[2,4],[3],[4]] => [5,3,2,6,1,4] => [3,2,5,1,6,4] => [5,3,2,6,1,4] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[[1,1,1,1,1,1,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,1,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,1,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,2,2,2,2,2,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,2,2,2,2,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,2,2,2,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,2,2,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,2,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[2,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[3,3,3,3,3,3,3]] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[1,1,1,1,1,1],[3]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,1,1,1,1,2],[3]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,1,1,1,1,3],[2]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,1,1,1,1,3],[3]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,1,1,1,2,2],[3]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,1,1,1,2,3],[2]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,1,1,1,2,3],[3]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,1,1,1,3,3],[2]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,1,1,1,3,3],[3]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,1,1,2,2,2],[3]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,1,1,2,2,3],[2]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,1,1,2,2,3],[3]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,1,1,2,3,3],[2]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,1,1,2,3,3],[3]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,1,1,3,3,3],[2]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,1,1,3,3,3],[3]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,1,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,1,2,2,2,3],[2]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,1,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,1,2,2,3,3],[2]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,1,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,1,2,3,3,3],[2]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,1,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,1,3,3,3,3],[2]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,1,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,2,2,2,2,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[1,2,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,2,2,2,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[1,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,2,2,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[1,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,2,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[1,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,3,3,3,3,3],[2]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[1,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[2,2,2,2,2,2],[3]] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[2,2,2,2,2,3],[3]] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[2,2,2,2,3,3],[3]] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[2,2,2,3,3,3],[3]] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[2,2,3,3,3,3],[3]] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[2,3,3,3,3,3],[3]] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[1,1,1,1,1],[2,3]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,1,1,1,1],[3,3]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,1,1,1,2],[2,3]] => [5,7,1,2,3,4,6] => [3,4,5,1,6,7,2] => [3,4,5,6,1,7,2] => ([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)
[[1,1,1,1,3],[2,2]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[1,1,1,1,2],[3,3]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,1,1,1,3],[2,3]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[1,1,1,1,3],[3,3]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[1,1,1,2,2],[2,3]] => [4,7,1,2,3,5,6] => [3,4,1,5,6,7,2] => [3,4,5,1,6,7,2] => ([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
[[1,1,1,2,3],[2,2]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,1,1,2,2],[3,3]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,1,1,2,3],[2,3]] => [4,6,1,2,3,5,7] => [3,4,1,5,6,2,7] => [3,4,5,1,6,2,7] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7)
[[1,1,1,3,3],[2,2]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,1,1,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[1,1,1,3,3],[2,3]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,1,1,3,3],[3,3]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,1,2,2,2],[2,3]] => [3,7,1,2,4,5,6] => [3,1,4,5,6,7,2] => [3,4,1,5,6,7,2] => ([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7)
[[1,1,2,2,3],[2,2]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[1,1,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,1,2,2,3],[2,3]] => [3,6,1,2,4,5,7] => [3,1,4,5,6,2,7] => [3,4,1,5,6,2,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7)
[[1,1,2,3,3],[2,2]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[1,1,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[1,1,2,3,3],[2,3]] => [3,5,1,2,4,6,7] => [3,1,4,5,2,6,7] => [3,4,1,5,2,6,7] => ([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)
[[1,1,3,3,3],[2,2]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[1,1,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,1,3,3,3],[2,3]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[1,1,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[1,2,2,2,2],[2,3]] => [2,7,1,3,4,5,6] => [1,3,4,5,6,7,2] => [3,1,4,5,6,7,2] => ([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[[1,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,2,2,2,3],[2,3]] => [2,6,1,3,4,5,7] => [1,3,4,5,6,2,7] => [3,1,4,5,6,2,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)
[[1,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[1,2,2,3,3],[2,3]] => [2,5,1,3,4,6,7] => [1,3,4,5,2,6,7] => [3,1,4,5,2,6,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)
[[1,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,2,3,3,3],[2,3]] => [2,4,1,3,5,6,7] => [1,3,4,2,5,6,7] => [3,1,4,2,5,6,7] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
[[1,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[2,2,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => [3,4,5,6,1,7,2] => [3,4,5,6,7,1,2] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[2,2,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => [3,4,5,1,6,2,7] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[[2,2,2,3,3],[3,3]] => [4,5,1,2,3,6,7] => [3,4,1,5,2,6,7] => [3,4,5,1,2,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[2,2,3,3,3],[3,3]] => [3,4,1,2,5,6,7] => [3,1,4,2,5,6,7] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[[1,1,1,1,1],[2],[3]] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => ([(2,6),(4,5),(5,3),(6,4)],7)
[[1,1,1,1,2],[2],[3]] => [7,5,1,2,3,4,6] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[[1,1,1,1,3],[2],[3]] => [6,5,1,2,3,4,7] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[1,1,1,2,2],[2],[3]] => [7,4,1,2,3,5,6] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[1,1,1,2,3],[2],[3]] => [6,4,1,2,3,5,7] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[1,1,1,3,3],[2],[3]] => [5,4,1,2,3,6,7] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[1,1,2,2,2],[2],[3]] => [7,3,1,2,4,5,6] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[1,1,2,2,3],[2],[3]] => [6,3,1,2,4,5,7] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[1,1,2,3,3],[2],[3]] => [5,3,1,2,4,6,7] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[1,1,3,3,3],[2],[3]] => [4,3,1,2,5,6,7] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[1,2,2,2,2],[2],[3]] => [7,2,1,3,4,5,6] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[1,2,2,2,3],[2],[3]] => [6,2,1,3,4,5,7] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[[1,2,2,3,3],[2],[3]] => [5,2,1,3,4,6,7] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[[1,2,3,3,3],[2],[3]] => [4,2,1,3,5,6,7] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[[1,3,3,3,3],[2],[3]] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[1,1,1,1],[2,2,3]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,1,1,1],[2,3,3]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,1,1,1],[3,3,3]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,1,1,2],[2,2,3]] => [4,5,7,1,2,3,6] => [4,1,5,2,6,7,3] => [4,5,6,1,2,7,3] => ([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7)
[[1,1,1,3],[2,2,2]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[1,1,1,2],[2,3,3]] => [4,6,7,1,2,3,5] => [4,1,5,6,2,7,3] => [4,5,6,1,7,2,3] => ([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)
[[1,1,1,3],[2,2,3]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[1,1,1,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,1,1,3],[2,3,3]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[1,1,1,3],[3,3,3]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[1,1,2,2],[2,2,3]] => [3,4,7,1,2,5,6] => [1,4,2,5,6,7,3] => [4,5,1,2,6,7,3] => ([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
[[1,1,2,2],[2,3,3]] => [3,6,7,1,2,4,5] => [1,4,5,6,2,7,3] => [4,5,1,6,7,2,3] => ([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)
[[1,1,2,3],[2,2,3]] => [3,4,6,1,2,5,7] => [1,4,2,5,6,3,7] => [4,5,1,2,6,3,7] => ([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7)
[[1,1,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,1,2,3],[2,3,3]] => [3,5,6,1,2,4,7] => [1,4,5,2,6,3,7] => [4,5,1,6,2,3,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)
[[1,1,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[1,2,2,2],[2,3,3]] => [2,6,7,1,3,4,5] => [4,5,6,1,2,7,3] => [4,1,5,6,7,2,3] => ([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)
[[1,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,2,2,3],[2,3,3]] => [2,5,6,1,3,4,7] => [4,5,1,2,6,3,7] => [4,1,5,6,2,3,7] => ([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7)
[[1,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[2,2,2,2],[3,3,3]] => [5,6,7,1,2,3,4] => [4,5,1,6,2,7,3] => [4,5,6,7,1,2,3] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[2,2,2,3],[3,3,3]] => [4,5,6,1,2,3,7] => [4,1,5,2,6,3,7] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[[1,1,1,1],[2,2],[3]] => [7,5,6,1,2,3,4] => [4,5,6,2,7,3,1] => [4,5,6,7,2,3,1] => ([(1,6),(2,4),(5,3),(6,5)],7)
[[1,1,1,1],[2,3],[3]] => [6,5,7,1,2,3,4] => [4,5,6,2,1,7,3] => [4,5,6,7,2,1,3] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7)
[[1,1,1,2],[2,2],[3]] => [7,4,5,1,2,3,6] => [4,5,2,6,3,7,1] => [4,5,6,2,3,7,1] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[[1,1,1,2],[2,3],[3]] => [6,4,7,1,2,3,5] => [4,5,2,6,1,7,3] => [4,5,6,2,7,1,3] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7)
[[1,1,1,3],[2,2],[3]] => [6,4,5,1,2,3,7] => [4,5,2,6,3,1,7] => [4,5,6,2,3,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
[[1,1,1,3],[2,3],[3]] => [5,4,6,1,2,3,7] => [4,5,2,1,6,3,7] => [4,5,6,2,1,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[[1,1,2,2],[2,2],[3]] => [7,3,4,1,2,5,6] => [4,2,5,3,6,7,1] => [4,5,2,3,6,7,1] => ([(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[[1,1,2,2],[2,3],[3]] => [6,3,7,1,2,4,5] => [4,2,5,6,1,7,3] => [4,5,2,6,7,1,3] => ([(0,5),(1,5),(1,6),(2,3),(3,6),(6,4)],7)
[[1,1,2,3],[2,2],[3]] => [6,3,4,1,2,5,7] => [4,2,5,3,6,1,7] => [4,5,2,3,6,1,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[[1,1,2,3],[2,3],[3]] => [5,3,6,1,2,4,7] => [4,2,5,1,6,3,7] => [4,5,2,6,1,3,7] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7)
[[1,1,3,3],[2,2],[3]] => [5,3,4,1,2,6,7] => [4,2,5,3,1,6,7] => [4,5,2,3,1,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[[1,1,3,3],[2,3],[3]] => [4,3,5,1,2,6,7] => [4,2,1,5,3,6,7] => [4,5,2,1,3,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[[1,2,2,2],[2,3],[3]] => [6,2,7,1,3,4,5] => [2,4,5,6,1,7,3] => [4,2,5,6,7,1,3] => ([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)
[[1,2,2,3],[2,3],[3]] => [5,2,6,1,3,4,7] => [2,4,5,1,6,3,7] => [4,2,5,6,1,3,7] => ([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[[1,2,3,3],[2,3],[3]] => [4,2,5,1,3,6,7] => [2,4,1,5,3,6,7] => [4,2,5,1,3,6,7] => ([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[1,1,1],[2,2,2],[3]] => [7,4,5,6,1,2,3] => [5,2,6,3,7,4,1] => [5,6,7,2,3,4,1] => ([(1,6),(2,5),(5,3),(6,4)],7)
[[1,1,1],[2,2,3],[3]] => [6,4,5,7,1,2,3] => [5,2,6,3,1,7,4] => [5,6,7,2,3,1,4] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7)
[[1,1,1],[2,3,3],[3]] => [5,4,6,7,1,2,3] => [5,2,1,6,3,7,4] => [5,6,7,2,1,3,4] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7)
[[1,1,2],[2,2,3],[3]] => [6,3,4,7,1,2,5] => [2,5,3,6,1,7,4] => [5,6,2,3,7,1,4] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(4,6)],7)
[[1,1,2],[2,3,3],[3]] => [5,3,6,7,1,2,4] => [2,5,1,6,3,7,4] => [5,6,2,7,1,3,4] => ([(0,5),(1,5),(1,6),(2,3),(3,6),(5,4)],7)
[[1,2,2],[2,3,3],[3]] => [5,2,6,7,1,3,4] => [5,6,2,1,3,7,4] => [5,2,6,7,1,3,4] => ([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)
[[1,1,1],[2,2],[3,3]] => [6,7,4,5,1,2,3] => [5,6,3,1,7,4,2] => [5,6,7,3,4,1,2] => ([(0,5),(1,4),(2,6),(6,3)],7)
[[1,1,2],[2,2],[3,3]] => [6,7,3,4,1,2,5] => [5,3,6,4,1,7,2] => [5,6,3,4,7,1,2] => ([(0,5),(1,4),(2,3),(4,6),(5,6)],7)
[[1,1,3],[2,2],[3,3]] => [5,6,3,4,1,2,7] => [5,3,1,6,4,2,7] => [5,6,3,4,1,2,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[[1,1,1,1,1,1,1,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[1,1,1,1,1,1,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[1,1,1,1,1,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[1,1,1,1,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[1,1,1,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[1,1,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[1,2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[2,2,2,2,2,2,2,2]] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[1,1,1,1,1,1,1],[2]] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[1,1,1,1,1,1,2],[2]] => [7,1,2,3,4,5,6,8] => [2,3,4,5,6,7,1,8] => [2,3,4,5,6,7,1,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[1,1,1,1,1,2,2],[2]] => [6,1,2,3,4,5,7,8] => [2,3,4,5,6,1,7,8] => [2,3,4,5,6,1,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[1,1,1,1,2,2,2],[2]] => [5,1,2,3,4,6,7,8] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[1,1,1,2,2,2,2],[2]] => [4,1,2,3,5,6,7,8] => [2,3,4,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[1,1,2,2,2,2,2],[2]] => [3,1,2,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[1,2,2,2,2,2,2],[2]] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[[1,1,1,1,1,1],[2,2]] => [7,8,1,2,3,4,5,6] => [3,4,5,6,7,1,8,2] => [3,4,5,6,7,8,1,2] => ([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8)
[[1,1,1,1,1,2],[2,2]] => [6,7,1,2,3,4,5,8] => [3,4,5,6,1,7,2,8] => [3,4,5,6,7,1,2,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[1,1,1,1,2,2],[2,2]] => [5,6,1,2,3,4,7,8] => [3,4,5,1,6,2,7,8] => [3,4,5,6,1,2,7,8] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[[1,1,1,2,2,2],[2,2]] => [4,5,1,2,3,6,7,8] => [3,4,1,5,2,6,7,8] => [3,4,5,1,2,6,7,8] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[[1,1,2,2,2,2],[2,2]] => [3,4,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => [3,4,1,2,5,6,7,8] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[1,1,1,1,1],[2,2,2]] => [6,7,8,1,2,3,4,5] => [4,5,6,1,7,2,8,3] => [4,5,6,7,8,1,2,3] => ([(0,7),(1,6),(4,5),(5,3),(6,4),(7,2)],8)
[[1,1,1,1,2],[2,2,2]] => [5,6,7,1,2,3,4,8] => [4,5,1,6,2,7,3,8] => [4,5,6,7,1,2,3,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[[1,1,1,2,2],[2,2,2]] => [4,5,6,1,2,3,7,8] => [4,1,5,2,6,3,7,8] => [4,5,6,1,2,3,7,8] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[[1,1,1,1],[2,2,2,2]] => [5,6,7,8,1,2,3,4] => [5,1,6,2,7,3,8,4] => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
[[1]] => [1] => [1] => [1] => ([],1)
[[2]] => [1] => [1] => [1] => ([],1)
[[1,1]] => [1,2] => [1,2] => [1,2] => ([(0,1)],2)
[[3]] => [1] => [1] => [1] => ([],1)
[[1,1,1]] => [1,2,3] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[4]] => [1] => [1] => [1] => ([],1)
[[1,1,1,1]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[5]] => [1] => [1] => [1] => ([],1)
[[1,1,1,1,1]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[6]] => [1] => [1] => [1] => ([],1)
[[1,1,1,1,1,1]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [3,4,1,5,6,2] => [3,4,5,1,6,2] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [3,4,5,1,6,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6)
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6)
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [3,1,4,5,6,2] => [3,4,1,5,6,2] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [3,1,4,5,2,6] => [3,4,1,5,2,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [4,2,5,6,3,1] => [4,5,2,6,3,1] => ([(1,4),(2,3),(2,5),(4,5)],6)
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6)
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [3,4,1,5,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [4,5,2,6,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [4,2,1,5,6,3] => [4,5,2,1,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [4,5,2,1,6,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [4,2,5,1,6,3] => [4,5,2,6,1,3] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => ([(4,5)],6)
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [2,4,5,6,3,1] => [4,2,5,6,3,1] => ([(1,5),(2,3),(2,5),(5,4)],6)
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [4,1,2,5,6,3] => [4,1,5,2,6,3] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [2,4,5,3,6,1] => [4,2,5,3,6,1] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [4,5,1,2,6,3] => [4,1,5,6,2,3] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [2,4,5,3,1,6] => [4,2,5,3,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [3,5,6,4,2,1] => [5,3,6,4,2,1] => ([(2,5),(3,4),(3,5)],6)
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6)
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [2,4,1,5,6,3] => [4,2,5,1,6,3] => ([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6)
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [2,4,5,1,6,3] => [4,2,5,6,1,3] => ([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6)
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [1,4,2,5,6,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [4,2,5,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [1,4,5,2,6,3] => [4,5,1,6,2,3] => ([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [4,2,5,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [5,3,6,4,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6)
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [2,1,4,5,6,3] => [4,2,1,5,6,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [2,1,4,5,3,6] => [4,2,1,5,3,6] => ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [1,3,5,6,4,2] => [5,3,1,6,4,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [3,2,5,6,4,1] => [5,3,2,6,4,1] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6)
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6)
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6)
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [4,2,1,5,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [5,3,2,6,4,1] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6)
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [3,1,5,6,4,2] => [5,3,6,1,4,2] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [3,5,2,6,4,1] => [5,3,6,2,4,1] => ([(1,5),(2,4),(3,4),(3,5)],6)
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [1,5,3,6,4,2] => [5,6,3,1,4,2] => ([(0,5),(1,3),(2,4),(2,5)],6)
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [3,2,1,5,6,4] => [5,3,2,1,6,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [5,3,2,1,6,4] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6)
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [3,5,1,6,4,2] => [5,3,6,4,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6)
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [3,5,2,1,6,4] => [5,3,6,2,1,4] => ([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6)
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [3,2,5,1,6,4] => [5,3,2,6,1,4] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([],6)
[[1,1,1,1,2,2,2],[3,3],[4]] => [10,8,9,1,2,3,4,5,6,7] => [4,5,6,7,8,9,2,10,3,1] => [4,5,6,7,8,9,10,2,3,1] => ([(1,9),(2,4),(5,6),(6,8),(7,5),(8,3),(9,7)],10)
[[1,1,1,2,2,2,2],[3,3],[4]] => [10,8,9,1,2,3,4,5,6,7] => [4,5,6,7,8,9,2,10,3,1] => [4,5,6,7,8,9,10,2,3,1] => ([(1,9),(2,4),(5,6),(6,8),(7,5),(8,3),(9,7)],10)
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation $\sigma$ is given by $L(\sigma) = l_1 \ldots l_n$ with $l_i = \# \{ j > i : \sigma_j < \sigma_i \}$. In particular, $l_i$ is the number of boxes in the $i$-th column of the Rothe diagram. For example, the Lehmer code of $\sigma = [4,3,1,5,2]$ is $32010$. The Lehmer code $L : \mathfrak{S}_n\ \tilde\longrightarrow\ S_n$ is a bijection between permutations of size $n$ and sequences $l_1\ldots l_n \in \mathbf{N}^n$ with $l_i \leq i$.
* The major code $M(\sigma)$ of a permutation $\sigma \in \mathfrak{S}_n$ is a way to encode a permutation as a sequence $m_1 m_2 \ldots m_n$ with $m_i \geq i$. To define $m_i$, let $\operatorname{del}_i(\sigma)$ be the normalized permutation obtained by removing all $\sigma_j < i$ from the one-line notation of $\sigma$. The $i$-th index is then given by
$$m_i = \operatorname{maj}(\operatorname{del}_i(\sigma)) - \operatorname{maj}(\operatorname{del}_{i-1}(\sigma)).$$
For example, the permutation $[9,3,5,7,2,1,4,6,8]$ has major code $[5, 0, 1, 0, 1, 2, 0, 1, 0]$ since
$$\operatorname{maj}([8,2,4,6,1,3,5,7]) = 5, \quad \operatorname{maj}([7,1,3,5,2,4,6]) = 5, \quad \operatorname{maj}([6,2,4,1,3,5]) = 4,$$
$$\operatorname{maj}([5,1,3,2,4]) = 4, \quad \operatorname{maj}([4,2,1,3]) = 3, \quad \operatorname{maj}([3,1,2]) = 1, \quad \operatorname{maj}([2,1]) = 1.$$
Observe that the sum of the major code of $\sigma$ equals the major index of $\sigma$.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
- If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
- If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
- $1$
- $|1|4 \to 14$
- $|14|2 \to 412$
- $|4|1|2|5 \to 4125$
- $|4|125|3 \to 45123.$
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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