Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
[[1]] => [1] => [1] => ([],1)
[[1,2]] => [1,2] => [1,2] => ([(0,1)],2)
[[1],[2]] => [2,1] => [2,1] => ([],2)
[[1,2,3]] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
[[1,3],[2]] => [2,1,3] => [2,1,3] => ([(0,2),(1,2)],3)
[[1,2],[3]] => [3,1,2] => [3,1,2] => ([(1,2)],3)
[[1],[2],[3]] => [3,2,1] => [2,3,1] => ([(1,2)],3)
[[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[1,3,4],[2]] => [2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[1,2,4],[3]] => [3,1,2,4] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
[[1,2,3],[4]] => [4,1,2,3] => [4,1,2,3] => ([(1,2),(2,3)],4)
[[1,3],[2,4]] => [2,4,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4)
[[1,2],[3,4]] => [3,4,1,2] => [4,1,3,2] => ([(1,2),(1,3)],4)
[[1,4],[2],[3]] => [3,2,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[1,3],[2],[4]] => [4,2,1,3] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
[[1,2],[3],[4]] => [4,3,1,2] => [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
[[1],[2],[3],[4]] => [4,3,2,1] => [2,3,4,1] => ([(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)
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[1,2,4,5],[3]] => [3,1,2,4,5] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,2,3,5],[4]] => [4,1,2,3,5] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,2,3,4],[5]] => [5,1,2,3,4] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
[[1,3,5],[2,4]] => [2,4,1,3,5] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[1,2,5],[3,4]] => [3,4,1,2,5] => [4,1,3,2,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[[1,3,4],[2,5]] => [2,5,1,3,4] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
[[1,2,4],[3,5]] => [3,5,1,2,4] => [5,1,3,2,4] => ([(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,3],[4,5]] => [4,5,1,2,3] => [5,1,2,4,3] => ([(1,4),(4,2),(4,3)],5)
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5)
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [5,4,1,2,3] => ([(2,3),(3,4)],5)
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [5,1,4,3,2] => ([(1,2),(1,3),(1,4)],5)
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(1,4)],5)
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [2,3,5,1,4] => ([(0,4),(1,2),(2,3),(2,4)],5)
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[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)
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => ([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => ([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => ([(1,4),(4,5),(5,2),(5,3)],6)
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [3,1,5,2,4,6] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [4,1,2,5,3,6] => ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [3,1,6,2,4,5] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [4,1,2,6,3,5] => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [5,1,2,3,6,4] => ([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => ([(1,5),(2,5),(5,3),(5,4)],6)
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => ([(1,5),(4,3),(5,2),(5,4)],6)
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [5,1,4,3,2,6] => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [4,1,5,3,2,6] => ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6)
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [6,1,4,3,2,5] => ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [6,5,1,3,2,4] => ([(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [6,1,5,2,3,4] => ([(1,3),(1,5),(4,2),(5,4)],6)
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [6,1,2,5,4,3] => ([(1,5),(5,2),(5,3),(5,4)],6)
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [4,6,1,2,3,5] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6)
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [4,1,6,3,2,5] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [5,6,1,3,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5)],6)
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [5,1,2,6,4,3] => ([(0,5),(1,4),(4,2),(4,3),(4,5)],6)
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [2,3,5,1,4,6] => ([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [2,4,1,5,3,6] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [3,1,4,5,2,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [2,3,6,1,4,5] => ([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [2,4,1,6,3,5] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [3,1,4,6,2,5] => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [2,5,1,3,6,4] => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [3,1,5,2,6,4] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [4,1,2,5,6,3] => ([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6)
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [5,6,1,4,2,3] => ([(0,4),(1,3),(1,5),(5,2)],6)
>>> Load all 1021 entries. <<<
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [5,1,6,4,3,2] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [4,6,1,2,5,3] => ([(0,4),(1,3),(1,5),(4,2),(4,5)],6)
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [4,1,6,3,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => ([(1,4),(2,3),(2,5),(4,5)],6)
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [6,4,1,5,2,3] => ([(1,5),(2,3),(2,5),(3,4)],6)
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [6,1,4,5,3,2] => ([(1,3),(1,4),(1,5),(5,2)],6)
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [5,3,6,1,2,4] => ([(0,4),(1,4),(1,5),(2,3),(3,5)],6)
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [5,4,1,6,2,3] => ([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [5,1,4,6,3,2] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [4,5,1,2,6,3] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6)
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [4,1,5,3,6,2] => ([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [2,3,4,6,1,5] => ([(0,5),(1,3),(3,4),(4,2),(4,5)],6)
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [2,3,5,1,6,4] => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [2,4,1,5,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [3,1,4,5,6,2] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6)
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[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)
[[1,3,4,5,6,7],[2]] => [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)
[[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [4,2,1,3,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => [4,1,3,2,5,6,7] => ([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => [5,2,1,3,4,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => [5,1,3,2,4,6,7] => ([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)
[[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => [5,1,2,4,3,6,7] => ([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => [6,2,1,3,4,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => [6,1,3,2,4,5,7] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
[[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => [6,1,2,4,3,5,7] => ([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)
[[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => [6,1,2,3,5,4,7] => ([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => [7,2,1,3,4,5,6] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => [7,1,3,2,4,5,6] => ([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => [7,1,2,4,3,5,6] => ([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => [7,1,2,3,5,4,6] => ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => ([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
[[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
[[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => [3,1,4,2,5,6,7] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
[[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => [2,5,1,3,4,6,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)
[[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => [3,1,5,2,4,6,7] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)
[[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => [4,1,2,5,3,6,7] => ([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)
[[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => [2,6,1,3,4,5,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)
[[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => [3,1,6,2,4,5,7] => ([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7)
[[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => [4,1,2,6,3,5,7] => ([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7)
[[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => [5,1,2,3,6,4,7] => ([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)
[[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => [2,7,1,3,4,5,6] => ([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => [3,1,7,2,4,5,6] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)
[[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => [4,1,2,7,3,5,6] => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)
[[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => [5,1,2,3,7,4,6] => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)
[[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => [6,1,2,3,4,7,5] => ([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)
[[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [6,2,1,4,3,5,7] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => [6,1,3,4,2,5,7] => ([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)
[[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [6,2,1,3,5,4,7] => ([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => [6,1,3,2,5,4,7] => ([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => [6,1,2,4,5,3,7] => ([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [7,2,1,4,3,5,6] => ([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => [7,1,3,4,2,5,6] => ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => [7,2,1,3,5,4,6] => ([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => [7,1,3,2,5,4,6] => ([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[1,2,3,6],[4,5,7]] => [4,5,7,1,2,3,6] => [7,1,2,4,5,3,6] => ([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => [7,2,1,3,4,6,5] => ([(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[[1,2,4,5],[3,6,7]] => [3,6,7,1,2,4,5] => [7,1,3,2,4,6,5] => ([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[[1,2,3,5],[4,6,7]] => [4,6,7,1,2,3,5] => [7,1,2,4,3,6,5] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => ([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [5,3,2,1,4,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => [5,1,4,3,2,6,7] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [4,5,1,2,3,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => [4,1,5,3,2,6,7] => ([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7)
[[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [6,3,2,1,4,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [6,4,1,2,3,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => [6,1,4,3,2,5,7] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [6,5,1,3,2,4,7] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
[[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => [6,1,5,2,3,4,7] => ([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => [6,1,2,5,4,3,7] => ([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [4,6,1,2,3,5,7] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7)
[[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => [4,1,6,3,2,5,7] => ([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)
[[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => [5,6,1,3,2,4,7] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,6),(5,6)],7)
[[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => [5,1,6,2,3,4,7] => ([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7)
[[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => [5,1,2,6,4,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5),(5,6)],7)
[[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [7,3,2,1,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [7,4,1,2,3,5,6] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => [7,1,4,3,2,5,6] => ([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [7,5,1,3,2,4,6] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => [7,1,5,2,3,4,6] => ([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => [7,1,2,5,4,3,6] => ([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => [7,6,1,3,4,2,5] => ([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => [7,1,6,2,4,3,5] => ([(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)
[[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => [7,1,2,6,3,4,5] => ([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => [7,1,2,3,6,5,4] => ([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
[[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [4,7,1,2,3,5,6] => ([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)
[[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => [4,1,7,3,2,5,6] => ([(0,5),(0,6),(1,2),(1,3),(1,5),(2,6),(3,6),(6,4)],7)
[[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => [5,7,1,3,2,4,6] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(3,5),(5,6)],7)
[[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => [5,1,7,2,3,4,6] => ([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)
[[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => [5,1,2,7,4,3,6] => ([(0,5),(0,6),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5)],7)
[[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => [6,7,1,3,4,2,5] => ([(0,4),(1,3),(1,5),(2,6),(3,6),(5,2)],7)
[[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => [6,1,7,2,4,3,5] => ([(0,6),(1,4),(1,6),(2,5),(3,5),(4,2),(4,3)],7)
[[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => [6,1,2,7,3,4,5] => ([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)
[[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => [6,1,2,3,7,5,4] => ([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7)
[[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => [2,3,5,1,4,6,7] => ([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)
[[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => [2,4,1,5,3,6,7] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)
[[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => [3,1,4,5,2,6,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)
[[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => [2,3,6,1,4,5,7] => ([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7)
[[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => [2,4,1,6,3,5,7] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
[[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => [3,1,4,6,2,5,7] => ([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7)
[[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => [2,5,1,3,6,4,7] => ([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7)
[[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => [3,1,5,2,6,4,7] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
[[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => [4,1,2,5,6,3,7] => ([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7)
[[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [2,3,7,1,4,5,6] => ([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => [2,4,1,7,3,5,6] => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)
[[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => [3,1,4,7,2,5,6] => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)
[[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [2,5,1,3,7,4,6] => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)
[[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => [3,1,5,2,7,4,6] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [4,1,2,5,7,3,6] => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)
[[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => [2,6,1,3,4,7,5] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)
[[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => [3,1,6,2,4,7,5] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)
[[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => [4,1,2,6,3,7,5] => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)
[[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [5,1,2,3,6,7,4] => ([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [7,3,2,1,5,4,6] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [7,4,1,2,5,3,6] => ([(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7)
[[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [7,1,4,3,5,2,6] => ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [7,5,1,2,4,3,6] => ([(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => [7,1,5,3,4,2,6] => ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [7,3,2,1,4,6,5] => ([(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [7,4,1,2,3,6,5] => ([(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => [7,1,4,3,2,6,5] => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [7,5,1,3,2,6,4] => ([(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => [7,1,5,2,3,6,4] => ([(1,3),(1,4),(3,6),(4,5),(5,2),(5,6)],7)
[[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => [7,1,2,5,4,6,3] => ([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7)
[[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => [7,1,6,3,2,4,5] => ([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [7,6,1,3,2,5,4] => ([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => [7,1,6,2,3,5,4] => ([(1,4),(1,5),(5,6),(6,2),(6,3)],7)
[[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => [7,1,2,6,4,5,3] => ([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [6,7,1,2,3,4,5] => ([(0,6),(1,3),(4,5),(5,2),(6,4)],7)
[[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => [6,1,7,3,2,4,5] => ([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7)
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [6,7,1,3,2,5,4] => ([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6)],7)
[[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => [6,1,7,2,3,5,4] => ([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)
[[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [6,1,2,7,4,5,3] => ([(0,6),(1,5),(4,3),(5,2),(5,4),(5,6)],7)
[[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [5,6,3,1,2,4,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [5,6,1,4,2,3,7] => ([(0,4),(1,3),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => [5,1,6,4,3,2,7] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [4,6,1,2,5,3,7] => ([(0,4),(1,3),(1,5),(2,6),(3,6),(4,2),(4,5),(5,6)],7)
[[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => [4,1,6,3,5,2,7] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7)
[[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [5,7,3,1,2,4,6] => ([(0,6),(1,4),(2,3),(2,5),(4,6),(6,5)],7)
[[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [5,7,1,4,2,3,6] => ([(0,4),(0,6),(1,3),(1,5),(2,6),(3,6),(5,2)],7)
[[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [5,1,7,4,3,2,6] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7)
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [4,7,1,2,5,3,6] => ([(0,3),(0,6),(1,4),(2,5),(4,2),(4,6),(6,5)],7)
[[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => [4,1,7,3,5,2,6] => ([(0,2),(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(6,4)],7)
[[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [6,7,3,1,4,2,5] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7)
[[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [6,7,1,4,3,2,5] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6)],7)
[[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [6,1,7,4,2,3,5] => ([(0,6),(1,3),(1,4),(1,6),(2,5),(3,5),(4,2)],7)
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [6,7,1,3,5,2,4] => ([(0,4),(1,3),(1,5),(3,6),(5,2),(5,6)],7)
[[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => [6,1,7,2,5,3,4] => ([(0,6),(1,5),(1,6),(4,3),(5,2),(5,4)],7)
[[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => [6,1,2,7,5,4,3] => ([(0,6),(1,5),(5,2),(5,3),(5,4),(5,6)],7)
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [4,7,1,2,3,6,5] => ([(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(4,2)],7)
[[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => [4,1,7,3,2,6,5] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7)
[[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [5,7,1,3,2,6,4] => ([(0,4),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6)],7)
[[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => [5,1,7,2,3,6,4] => ([(0,5),(0,6),(1,3),(1,6),(3,4),(4,2),(4,5)],7)
[[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => [5,1,2,7,4,6,3] => ([(0,5),(0,6),(1,4),(3,5),(4,2),(4,3),(4,6)],7)
[[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [6,3,5,1,2,4,7] => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)
[[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [6,4,1,5,2,3,7] => ([(0,6),(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
[[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => [6,1,4,5,3,2,7] => ([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [5,3,6,1,2,4,7] => ([(0,4),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7)
[[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [5,4,1,6,2,3,7] => ([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7)
[[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => [5,1,4,6,3,2,7] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7)
[[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [4,5,1,2,6,3,7] => ([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7)
[[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => [4,1,5,3,6,2,7] => ([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(5,4),(6,5)],7)
[[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [7,3,4,2,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [7,3,5,1,2,4,6] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)
[[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [7,4,1,5,2,3,6] => ([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
[[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [7,1,4,5,3,2,6] => ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [7,3,6,1,4,2,5] => ([(1,3),(1,5),(2,4),(2,5),(4,6),(5,6)],7)
[[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [7,4,1,6,3,2,5] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
[[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [7,1,4,6,2,3,5] => ([(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)
[[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [7,5,1,3,6,2,4] => ([(1,5),(2,3),(2,4),(3,6),(4,5),(4,6)],7)
[[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [7,1,5,2,6,3,4] => ([(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7)
[[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => [7,1,2,5,6,4,3] => ([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [5,3,7,1,2,4,6] => ([(0,4),(0,6),(1,4),(1,5),(2,3),(3,6),(6,5)],7)
[[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [5,4,1,7,2,3,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)
[[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => [5,1,4,7,3,2,6] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(4,6)],7)
[[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [4,5,1,2,7,3,6] => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7)
[[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => [4,1,5,3,7,2,6] => ([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [6,3,7,1,4,2,5] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(5,6)],7)
[[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [6,4,1,7,3,2,5] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
[[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [6,1,4,7,2,3,5] => ([(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2)],7)
[[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [6,5,1,3,7,2,4] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7)
[[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => [6,1,5,2,7,3,4] => ([(0,6),(1,3),(1,5),(3,6),(4,2),(5,4),(5,6)],7)
[[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => [6,1,2,5,7,4,3] => ([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7)
[[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [4,6,1,2,3,7,5] => ([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)
[[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => [4,1,6,3,2,7,5] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
[[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => [5,6,1,3,2,7,4] => ([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
[[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => [5,1,6,2,3,7,4] => ([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
[[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => [5,1,2,6,4,7,3] => ([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7)
[[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [2,3,4,6,1,5,7] => ([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)
[[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => [2,3,5,1,6,4,7] => ([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7)
[[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => [2,4,1,5,6,3,7] => ([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7)
[[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [3,1,4,5,6,2,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)
[[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [2,3,4,7,1,5,6] => ([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)
[[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [2,3,5,1,7,4,6] => ([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)
[[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => [2,4,1,5,7,3,6] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)
[[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [3,1,4,5,7,2,6] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)
[[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [2,3,6,1,4,7,5] => ([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)
[[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => [2,4,1,6,3,7,5] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
[[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [3,1,4,6,2,7,5] => ([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)
[[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [2,5,1,3,6,7,4] => ([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)
[[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [3,1,5,2,6,7,4] => ([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)
[[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [4,1,2,5,6,7,3] => ([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)
[[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [6,7,4,3,1,2,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7)
[[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [6,7,5,1,3,2,4] => ([(1,3),(2,4),(2,5),(4,6),(5,6)],7)
[[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [6,7,1,5,4,2,3] => ([(0,5),(1,3),(1,4),(1,6),(6,2)],7)
[[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [6,1,7,5,4,3,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [5,7,6,1,2,3,4] => ([(0,6),(1,3),(1,4),(5,2),(6,5)],7)
[[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [5,7,1,6,2,4,3] => ([(0,4),(0,6),(1,5),(1,6),(5,2),(5,3)],7)
[[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [5,1,7,6,3,4,2] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(4,2)],7)
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [4,7,1,2,6,5,3] => ([(0,4),(1,3),(1,5),(1,6),(4,2),(4,5),(4,6)],7)
[[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => [4,1,7,3,6,5,2] => ([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5)],7)
[[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [5,6,7,1,2,3,4] => ([(0,5),(1,6),(4,3),(5,4),(6,2)],7)
[[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [5,6,1,7,2,4,3] => ([(0,4),(1,5),(1,6),(4,6),(5,2),(5,3)],7)
[[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => [5,1,6,7,3,4,2] => ([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7)
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [4,6,1,2,7,5,3] => ([(0,3),(0,6),(1,4),(3,5),(4,2),(4,5),(4,6)],7)
[[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [4,1,6,3,7,5,2] => ([(0,2),(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(6,4)],7)
[[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [7,3,4,5,2,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [7,3,4,6,1,2,5] => ([(1,3),(2,4),(3,6),(4,5),(4,6)],7)
[[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [7,3,5,1,6,2,4] => ([(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)
[[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [7,4,1,5,6,2,3] => ([(1,6),(2,3),(2,6),(3,5),(6,4)],7)
[[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [7,1,4,5,6,3,2] => ([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [6,3,4,7,1,2,5] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(4,6)],7)
[[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [6,3,5,1,7,2,4] => ([(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)
[[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [6,4,1,5,7,2,3] => ([(0,6),(1,5),(2,3),(2,5),(3,4),(5,6)],7)
[[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [6,1,4,5,7,3,2] => ([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7)
[[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [5,3,6,1,2,7,4] => ([(0,4),(1,4),(1,5),(2,3),(3,5),(3,6),(4,6)],7)
[[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [5,4,1,6,2,7,3] => ([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7)
[[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => [5,1,4,6,3,7,2] => ([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7)
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [4,5,1,2,6,7,3] => ([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)
[[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [4,1,5,3,6,7,2] => ([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7)
[[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [2,3,4,5,7,1,6] => ([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)
[[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [2,3,4,6,1,7,5] => ([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)
[[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [2,3,5,1,6,7,4] => ([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)
[[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [2,4,1,5,6,7,3] => ([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)
[[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [3,1,4,5,6,7,2] => ([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[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)
[[1,3,4,5,6,7,8],[2]] => [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)
[[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => [3,1,2,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => [4,1,2,3,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[1,3,5,6,7,8],[2,4]] => [2,4,1,3,5,6,7,8] => [4,2,1,3,5,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[[1,2,5,6,7,8],[3,4]] => [3,4,1,2,5,6,7,8] => [4,1,3,2,5,6,7,8] => ([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[1,3,4,6,7,8],[2,5]] => [2,5,1,3,4,6,7,8] => [5,2,1,3,4,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => [5,1,3,2,4,6,7,8] => ([(0,7),(1,3),(1,4),(3,6),(4,6),(5,2),(6,7),(7,5)],8)
[[1,2,3,6,7,8],[4,5]] => [4,5,1,2,3,6,7,8] => [5,1,2,4,3,6,7,8] => ([(0,7),(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => [6,1,2,4,3,5,7,8] => ([(0,7),(1,5),(3,6),(4,6),(5,3),(5,4),(6,7),(7,2)],8)
[[1,2,3,4,7,8],[5,6]] => [5,6,1,2,3,4,7,8] => [6,1,2,3,5,4,7,8] => ([(0,7),(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[1,3,4,5,6,8],[2,7]] => [2,7,1,3,4,5,6,8] => [7,2,1,3,4,5,6,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => [7,1,3,2,4,5,6,8] => ([(0,7),(1,3),(1,4),(2,7),(3,6),(4,6),(5,2),(6,5)],8)
[[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => [7,1,2,4,3,5,6,8] => ([(0,6),(1,5),(2,7),(3,7),(4,6),(5,2),(5,3),(7,4)],8)
[[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => [7,1,2,3,5,4,6,8] => ([(0,7),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
[[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => [7,1,2,3,4,6,5,8] => ([(0,7),(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[[1,3,4,5,6,7],[2,8]] => [2,8,1,3,4,5,6,7] => [8,2,1,3,4,5,6,7] => ([(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => [8,1,3,2,4,5,6,7] => ([(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => [8,1,2,4,3,5,6,7] => ([(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => [8,1,2,3,5,4,6,7] => ([(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => [8,1,2,3,4,6,5,7] => ([(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,7,6] => ([(1,6),(4,5),(5,7),(6,4),(7,2),(7,3)],8)
[[1,4,5,6,7,8],[2],[3]] => [3,2,1,4,5,6,7,8] => [2,3,1,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[1,3,5,6,7,8],[2],[4]] => [4,2,1,3,5,6,7,8] => [2,4,1,3,5,6,7,8] => ([(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,6)],8)
[[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => [3,1,4,2,5,6,7,8] => ([(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,6)],8)
[[1,3,4,6,7,8],[2],[5]] => [5,2,1,3,4,6,7,8] => [2,5,1,3,4,6,7,8] => ([(0,7),(1,4),(1,7),(3,6),(4,6),(5,2),(6,5),(7,3)],8)
[[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => [4,1,2,5,3,6,7,8] => ([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5),(7,6)],8)
[[1,3,4,5,7,8],[2],[6]] => [6,2,1,3,4,5,7,8] => [2,6,1,3,4,5,7,8] => ([(0,6),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5),(7,2)],8)
[[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => [3,1,6,2,4,5,7,8] => ([(0,5),(0,7),(1,2),(1,5),(2,7),(3,6),(5,6),(6,4),(7,3)],8)
[[1,2,3,4,7,8],[5],[6]] => [6,5,1,2,3,4,7,8] => [5,1,2,3,6,4,7,8] => ([(0,6),(1,4),(2,7),(4,5),(5,2),(5,6),(6,7),(7,3)],8)
[[1,3,4,5,6,8],[2],[7]] => [7,2,1,3,4,5,6,8] => [2,7,1,3,4,5,6,8] => ([(0,7),(1,3),(1,7),(2,6),(3,6),(4,5),(5,2),(7,4)],8)
[[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => [3,1,7,2,4,5,6,8] => ([(0,6),(0,7),(1,3),(1,7),(2,5),(3,6),(4,2),(6,4),(7,5)],8)
[[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => [4,1,2,7,3,5,6,8] => ([(0,6),(0,7),(1,4),(2,7),(3,5),(4,2),(4,6),(6,5),(7,3)],8)
[[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => [6,1,2,3,4,7,5,8] => ([(0,7),(1,5),(2,6),(3,4),(4,2),(4,7),(5,3),(7,6)],8)
[[1,3,4,5,6,7],[2],[8]] => [8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,7] => ([(0,7),(1,3),(1,7),(4,5),(5,2),(6,4),(7,6)],8)
[[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [3,1,8,2,4,5,6,7] => ([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5)],8)
[[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => [4,1,2,8,3,5,6,7] => ([(0,6),(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5)],8)
[[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => [5,1,2,3,8,4,6,7] => ([(0,6),(0,7),(1,4),(2,7),(4,5),(5,2),(5,6),(7,3)],8)
[[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => [6,1,2,3,4,8,5,7] => ([(0,6),(0,7),(1,4),(2,7),(3,5),(4,3),(5,2),(5,6)],8)
[[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,6] => ([(0,7),(1,5),(3,4),(4,6),(5,3),(6,2),(6,7)],8)
[[1,3,5,7,8],[2,4,6]] => [2,4,6,1,3,5,7,8] => [6,2,1,4,3,5,7,8] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(4,3),(5,4),(6,5),(7,5)],8)
[[1,2,5,7,8],[3,4,6]] => [3,4,6,1,2,5,7,8] => [6,1,3,4,2,5,7,8] => ([(0,7),(1,4),(1,5),(3,6),(4,6),(5,3),(6,7),(7,2)],8)
[[1,3,5,6,8],[2,4,7]] => [2,4,7,1,3,5,6,8] => [7,2,1,4,3,5,6,8] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,5),(4,3),(6,4),(7,4)],8)
[[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => [7,1,3,2,5,4,6,8] => ([(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[1,2,3,4,8],[5,6,7]] => [5,6,7,1,2,3,4,8] => [7,1,2,3,5,6,4,8] => ([(0,7),(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[[1,2,4,6,7],[3,5,8]] => [3,5,8,1,2,4,6,7] => [8,1,3,2,5,4,6,7] => ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[[1,2,3,6,7],[4,5,8]] => [4,5,8,1,2,3,6,7] => [8,1,2,4,5,3,6,7] => ([(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[[1,3,4,5,7],[2,6,8]] => [2,6,8,1,3,4,5,7] => [8,2,1,3,4,6,5,7] => ([(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(6,3)],8)
[[1,2,4,5,7],[3,6,8]] => [3,6,8,1,2,4,5,7] => [8,1,3,2,4,6,5,7] => ([(1,2),(1,3),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => [8,1,2,4,3,6,5,7] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7)],8)
[[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => [8,1,2,3,5,6,4,7] => ([(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[[1,3,4,5,6],[2,7,8]] => [2,7,8,1,3,4,5,6] => [8,2,1,3,4,5,7,6] => ([(1,7),(2,7),(5,6),(6,3),(6,4),(7,5)],8)
[[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => [8,1,3,2,4,5,7,6] => ([(1,4),(1,5),(4,7),(5,7),(6,2),(6,3),(7,6)],8)
[[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => [8,1,2,4,3,5,7,6] => ([(1,6),(2,7),(3,7),(6,2),(6,3),(7,4),(7,5)],8)
[[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => [8,1,2,3,5,4,7,6] => ([(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3)],8)
[[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => [8,1,2,3,4,6,7,5] => ([(1,6),(4,7),(5,2),(6,4),(7,3),(7,5)],8)
[[1,4,6,7,8],[2,5],[3]] => [3,2,5,1,4,6,7,8] => [5,3,2,1,4,6,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[[1,3,6,7,8],[2,5],[4]] => [4,2,5,1,3,6,7,8] => [5,4,1,2,3,6,7,8] => ([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[1,2,6,7,8],[3,5],[4]] => [4,3,5,1,2,6,7,8] => [5,1,4,3,2,6,7,8] => ([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[1,3,6,7,8],[2,4],[5]] => [5,2,4,1,3,6,7,8] => [4,5,1,2,3,6,7,8] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[[1,3,5,7,8],[2,6],[4]] => [4,2,6,1,3,5,7,8] => [6,4,1,2,3,5,7,8] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[[1,2,4,7,8],[3,6],[5]] => [5,3,6,1,2,4,7,8] => [6,1,5,2,3,4,7,8] => ([(0,7),(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[[1,3,5,7,8],[2,4],[6]] => [6,2,4,1,3,5,7,8] => [4,6,1,2,3,5,7,8] => ([(0,5),(1,4),(1,6),(3,6),(4,7),(5,3),(6,7),(7,2)],8)
[[1,2,5,7,8],[3,4],[6]] => [6,3,4,1,2,5,7,8] => [4,1,6,3,2,5,7,8] => ([(0,5),(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,6),(6,2),(7,6)],8)
[[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => [5,1,6,2,3,4,7,8] => ([(0,6),(1,5),(1,6),(3,7),(4,3),(5,4),(6,7),(7,2)],8)
[[1,4,5,6,8],[2,7],[3]] => [3,2,7,1,4,5,6,8] => [7,3,2,1,4,5,6,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[[1,3,5,6,8],[2,7],[4]] => [4,2,7,1,3,5,6,8] => [7,4,1,2,3,5,6,8] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[[1,3,4,6,8],[2,7],[5]] => [5,2,7,1,3,4,6,8] => [7,5,1,3,2,4,6,8] => ([(0,6),(1,5),(2,3),(2,4),(3,7),(4,7),(5,6),(7,5)],8)
[[1,3,4,5,8],[2,7],[6]] => [6,2,7,1,3,4,5,8] => [7,6,1,3,4,2,5,8] => ([(0,7),(1,7),(2,3),(2,4),(3,5),(4,6),(5,6),(6,7)],8)
[[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => [7,1,2,6,3,4,5,8] => ([(0,7),(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => [7,1,2,3,6,5,4,8] => ([(0,7),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[1,2,5,6,8],[3,4],[7]] => [7,3,4,1,2,5,6,8] => [4,1,7,3,2,5,6,8] => ([(0,6),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(4,5),(6,5),(7,4)],8)
[[1,3,4,6,8],[2,5],[7]] => [7,2,5,1,3,4,6,8] => [5,7,1,3,2,4,6,8] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(4,6),(5,7),(7,6)],8)
[[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => [5,1,7,2,3,4,6,8] => ([(0,6),(0,7),(1,4),(1,7),(2,6),(3,2),(4,3),(6,5),(7,5)],8)
[[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => [6,1,2,7,3,4,5,8] => ([(0,7),(1,5),(2,6),(3,4),(4,2),(5,3),(5,7),(7,6)],8)
[[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => [6,1,2,3,7,5,4,8] => ([(0,6),(1,4),(2,7),(3,7),(4,5),(5,2),(5,3),(5,6),(6,7)],8)
[[1,4,5,6,7],[2,8],[3]] => [3,2,8,1,4,5,6,7] => [8,3,2,1,4,5,6,7] => ([(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[1,3,5,6,7],[2,8],[4]] => [4,2,8,1,3,5,6,7] => [8,4,1,2,3,5,6,7] => ([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[1,2,5,6,7],[3,8],[4]] => [4,3,8,1,2,5,6,7] => [8,1,4,3,2,5,6,7] => ([(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[1,3,4,6,7],[2,8],[5]] => [5,2,8,1,3,4,6,7] => [8,5,1,3,2,4,6,7] => ([(1,6),(2,3),(2,4),(3,7),(4,7),(6,5),(7,6)],8)
[[1,2,4,6,7],[3,8],[5]] => [5,3,8,1,2,4,6,7] => [8,1,5,2,3,4,6,7] => ([(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => [8,1,2,5,4,3,6,7] => ([(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[[1,3,4,5,7],[2,8],[6]] => [6,2,8,1,3,4,5,7] => [8,6,1,3,4,2,5,7] => ([(1,6),(2,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => [8,1,6,2,4,3,5,7] => ([(1,2),(1,5),(2,7),(3,6),(4,6),(5,3),(5,4),(6,7)],8)
[[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => [8,1,2,6,3,4,5,7] => ([(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => [8,1,2,3,6,5,4,7] => ([(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[1,3,4,5,6],[2,8],[7]] => [7,2,8,1,3,4,5,6] => [8,7,1,3,4,5,2,6] => ([(2,4),(2,6),(3,7),(4,7),(5,3),(6,5)],8)
[[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => [8,1,7,2,4,5,3,6] => ([(1,2),(1,6),(3,7),(4,7),(5,4),(6,3),(6,5)],8)
[[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => [8,1,2,7,3,5,4,6] => ([(1,6),(3,7),(4,7),(5,3),(5,4),(6,2),(6,5)],8)
[[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => [8,1,2,3,7,4,5,6] => ([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => [8,1,2,3,4,7,6,5] => ([(1,6),(5,7),(6,5),(7,2),(7,3),(7,4)],8)
[[1,3,5,6,7],[2,4],[8]] => [8,2,4,1,3,5,6,7] => [4,8,1,2,3,5,6,7] => ([(0,6),(1,4),(1,7),(3,7),(5,2),(6,3),(7,5)],8)
[[1,2,5,6,7],[3,4],[8]] => [8,3,4,1,2,5,6,7] => [4,1,8,3,2,5,6,7] => ([(0,6),(0,7),(1,3),(1,4),(1,6),(3,7),(4,7),(5,2),(7,5)],8)
[[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => [5,1,8,2,3,4,6,7] => ([(0,6),(0,7),(1,5),(1,6),(3,7),(4,3),(5,4),(7,2)],8)
[[1,3,4,5,7],[2,6],[8]] => [8,2,6,1,3,4,5,7] => [6,8,1,3,4,2,5,7] => ([(0,4),(0,7),(1,3),(1,5),(2,6),(3,6),(5,2),(6,7)],8)
[[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => [6,1,8,2,4,3,5,7] => ([(0,6),(0,7),(1,4),(1,7),(2,5),(3,5),(4,2),(4,3),(5,6)],8)
[[1,2,3,5,7],[4,6],[8]] => [8,4,6,1,2,3,5,7] => [6,1,2,8,3,4,5,7] => ([(0,6),(0,7),(1,5),(2,7),(3,4),(4,2),(5,3),(5,6)],8)
[[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => [6,1,2,3,8,5,4,7] => ([(0,6),(0,7),(1,4),(2,7),(3,7),(4,5),(5,2),(5,3),(5,6)],8)
[[1,3,4,5,6],[2,7],[8]] => [8,2,7,1,3,4,5,6] => [7,8,1,3,4,5,2,6] => ([(0,4),(1,3),(1,6),(2,7),(3,7),(5,2),(6,5)],8)
[[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => [7,1,8,2,4,5,3,6] => ([(0,7),(1,5),(1,7),(2,6),(3,6),(4,3),(5,2),(5,4)],8)
[[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => [7,1,2,8,3,5,4,6] => ([(0,7),(1,4),(2,6),(3,6),(4,5),(4,7),(5,2),(5,3)],8)
[[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => [7,1,2,3,8,4,5,6] => ([(0,7),(1,5),(3,4),(4,2),(5,6),(6,3),(6,7)],8)
[[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => [7,1,2,3,4,8,6,5] => ([(0,7),(1,5),(4,6),(5,4),(6,2),(6,3),(6,7)],8)
[[1,5,6,7,8],[2],[3],[4]] => [4,3,2,1,5,6,7,8] => [2,3,4,1,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[1,4,6,7,8],[2],[3],[5]] => [5,3,2,1,4,6,7,8] => [2,3,5,1,4,6,7,8] => ([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5),(7,6)],8)
[[1,3,6,7,8],[2],[4],[5]] => [5,4,2,1,3,6,7,8] => [2,4,1,5,3,6,7,8] => ([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5),(7,5)],8)
[[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => [3,1,4,5,2,6,7,8] => ([(0,7),(1,4),(1,7),(3,6),(4,6),(5,2),(6,5),(7,3)],8)
[[1,4,5,7,8],[2],[3],[6]] => [6,3,2,1,4,5,7,8] => [2,3,6,1,4,5,7,8] => ([(0,7),(1,5),(2,6),(3,6),(5,3),(5,7),(6,4),(7,2)],8)
[[1,3,5,7,8],[2],[4],[6]] => [6,4,2,1,3,5,7,8] => [2,4,1,6,3,5,7,8] => ([(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(4,2),(5,4),(6,4),(7,5)],8)
[[1,3,4,7,8],[2],[5],[6]] => [6,5,2,1,3,4,7,8] => [2,5,1,3,6,4,7,8] => ([(0,7),(1,2),(1,7),(2,5),(3,6),(5,6),(6,4),(7,3),(7,5)],8)
[[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => [4,1,2,5,6,3,7,8] => ([(0,7),(1,5),(2,6),(3,6),(5,3),(5,7),(6,4),(7,2)],8)
[[1,4,5,6,8],[2],[3],[7]] => [7,3,2,1,4,5,6,8] => [2,3,7,1,4,5,6,8] => ([(0,7),(1,5),(2,6),(3,6),(4,3),(5,2),(5,7),(7,4)],8)
[[1,3,4,6,8],[2],[5],[7]] => [7,5,2,1,3,4,6,8] => [2,5,1,3,7,4,6,8] => ([(0,7),(1,3),(1,7),(2,6),(3,5),(3,6),(5,4),(6,4),(7,2),(7,5)],8)
[[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [3,1,5,2,7,4,6,8] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(4,3),(5,3),(6,4),(7,4),(7,5)],8)
[[1,2,3,6,8],[4],[5],[7]] => [7,5,4,1,2,3,6,8] => [4,1,2,5,7,3,6,8] => ([(0,7),(1,4),(2,6),(3,5),(4,3),(4,7),(5,6),(7,2),(7,5)],8)
[[1,2,4,5,8],[3],[6],[7]] => [7,6,3,1,2,4,5,8] => [3,1,6,2,4,7,5,8] => ([(0,3),(0,7),(1,6),(1,7),(2,4),(3,6),(5,4),(6,2),(6,5),(7,5)],8)
[[1,2,3,5,8],[4],[6],[7]] => [7,6,4,1,2,3,5,8] => [4,1,2,6,3,7,5,8] => ([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8)
[[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => [5,1,2,3,6,7,4,8] => ([(0,7),(1,5),(2,6),(3,6),(4,3),(4,7),(5,4),(7,2)],8)
[[1,4,5,6,7],[2],[3],[8]] => [8,3,2,1,4,5,6,7] => [2,3,8,1,4,5,6,7] => ([(0,7),(1,5),(4,2),(5,3),(5,7),(6,4),(7,6)],8)
[[1,3,5,6,7],[2],[4],[8]] => [8,4,2,1,3,5,6,7] => [2,4,1,8,3,5,6,7] => ([(0,6),(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(5,4),(7,5)],8)
[[1,2,5,6,7],[3],[4],[8]] => [8,4,3,1,2,5,6,7] => [3,1,4,8,2,5,6,7] => ([(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2),(7,6)],8)
[[1,3,4,6,7],[2],[5],[8]] => [8,5,2,1,3,4,6,7] => [2,5,1,3,8,4,6,7] => ([(0,7),(1,3),(1,7),(2,6),(3,5),(3,6),(6,4),(7,2),(7,5)],8)
[[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => [3,1,5,2,8,4,6,7] => ([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],8)
[[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => [4,1,2,5,8,3,6,7] => ([(0,7),(1,5),(3,6),(5,3),(5,7),(6,4),(7,2),(7,6)],8)
[[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => [4,1,2,6,3,8,5,7] => ([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => [5,1,2,3,6,8,4,7] => ([(0,7),(1,5),(3,6),(4,3),(4,7),(5,4),(7,2),(7,6)],8)
[[1,3,4,5,6],[2],[7],[8]] => [8,7,2,1,3,4,5,6] => [2,7,1,3,4,5,8,6] => ([(0,7),(1,3),(1,7),(3,6),(4,5),(5,2),(5,6),(7,4)],8)
[[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => [4,1,2,7,3,5,8,6] => ([(0,6),(0,7),(1,4),(3,7),(4,3),(4,6),(6,5),(7,2),(7,5)],8)
[[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => [5,1,2,3,7,4,8,6] => ([(0,6),(0,7),(1,3),(2,5),(2,7),(3,4),(4,2),(4,6),(6,5)],8)
[[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,5] => ([(0,7),(1,5),(4,6),(5,4),(6,2),(6,7),(7,3)],8)
[[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => [8,2,1,4,3,6,5,7] => ([(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => [8,1,3,4,2,6,5,7] => ([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(5,7),(6,7)],8)
[[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => [8,1,3,2,5,6,4,7] => ([(1,3),(1,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(7,2)],8)
[[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => [8,1,2,4,5,6,3,7] => ([(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => [8,2,1,4,3,5,7,6] => ([(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => [8,1,3,2,5,4,7,6] => ([(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => [8,1,2,4,5,3,7,6] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4)],8)
[[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => [8,1,3,2,4,6,7,5] => ([(1,3),(1,4),(3,7),(4,7),(6,2),(7,5),(7,6)],8)
[[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => ([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[[1,4,6,8],[2,5,7],[3]] => [3,2,5,7,1,4,6,8] => [7,3,2,1,5,4,6,8] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,4),(7,4)],8)
[[1,3,6,8],[2,4,7],[5]] => [5,2,4,7,1,3,6,8] => [7,5,1,2,4,3,6,8] => ([(0,3),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[1,4,5,8],[2,6,7],[3]] => [3,2,6,7,1,4,5,8] => [7,3,2,1,4,6,5,8] => ([(0,7),(1,6),(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[1,3,4,8],[2,6,7],[5]] => [5,2,6,7,1,3,4,8] => [7,5,1,3,2,6,4,8] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(3,7),(4,5),(4,7),(5,6),(7,6)],8)
[[1,2,4,8],[3,6,7],[5]] => [5,3,6,7,1,2,4,8] => [7,1,5,2,3,6,4,8] => ([(0,7),(1,3),(1,4),(2,7),(3,6),(4,5),(5,2),(5,6),(6,7)],8)
[[1,2,3,8],[4,6,7],[5]] => [5,4,6,7,1,2,3,8] => [7,1,2,5,4,6,3,8] => ([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[1,3,5,8],[2,4,7],[6]] => [6,2,4,7,1,3,5,8] => [7,6,1,2,3,4,5,8] => ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[1,2,3,8],[4,5,7],[6]] => [6,4,5,7,1,2,3,8] => [7,1,2,6,4,5,3,8] => ([(0,7),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[1,3,5,8],[2,4,6],[7]] => [7,2,4,6,1,3,5,8] => [6,7,1,2,3,4,5,8] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[1,2,5,8],[3,4,6],[7]] => [7,3,4,6,1,2,5,8] => [6,1,7,3,2,4,5,8] => ([(0,6),(1,2),(1,3),(1,6),(2,7),(3,7),(4,5),(6,5),(7,4)],8)
[[1,3,4,8],[2,5,6],[7]] => [7,2,5,6,1,3,4,8] => [6,7,1,3,2,5,4,8] => ([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[1,4,6,7],[2,5,8],[3]] => [3,2,5,8,1,4,6,7] => [8,3,2,1,5,4,6,7] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[1,3,6,7],[2,5,8],[4]] => [4,2,5,8,1,3,6,7] => [8,4,1,2,5,3,6,7] => ([(1,7),(2,3),(3,5),(3,7),(5,6),(6,4),(7,6)],8)
[[1,2,6,7],[3,5,8],[4]] => [4,3,5,8,1,2,6,7] => [8,1,4,3,5,2,6,7] => ([(1,3),(1,4),(1,5),(3,7),(4,6),(5,6),(6,7),(7,2)],8)
[[1,3,6,7],[2,4,8],[5]] => [5,2,4,8,1,3,6,7] => [8,5,1,2,4,3,6,7] => ([(1,7),(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[[1,2,6,7],[3,4,8],[5]] => [5,3,4,8,1,2,6,7] => [8,1,5,3,4,2,6,7] => ([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[1,4,5,7],[2,6,8],[3]] => [3,2,6,8,1,4,5,7] => [8,3,2,1,4,6,5,7] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[1,2,5,7],[3,6,8],[4]] => [4,3,6,8,1,2,5,7] => [8,1,4,3,2,6,5,7] => ([(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[1,2,3,7],[4,6,8],[5]] => [5,4,6,8,1,2,3,7] => [8,1,2,5,4,6,3,7] => ([(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[1,3,5,7],[2,4,8],[6]] => [6,2,4,8,1,3,5,7] => [8,6,1,2,3,4,5,7] => ([(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => [8,1,6,2,3,5,4,7] => ([(1,4),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3)],8)
[[1,2,3,7],[4,5,8],[6]] => [6,4,5,8,1,2,3,7] => [8,1,2,6,4,5,3,7] => ([(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[1,4,5,6],[2,7,8],[3]] => [3,2,7,8,1,4,5,6] => [8,3,2,1,4,5,7,6] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[1,2,5,6],[3,7,8],[4]] => [4,3,7,8,1,2,5,6] => [8,1,4,3,2,5,7,6] => ([(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[1,3,4,6],[2,7,8],[5]] => [5,2,7,8,1,3,4,6] => [8,5,1,3,2,4,7,6] => ([(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[1,2,4,5],[3,7,8],[6]] => [6,3,7,8,1,2,4,5] => [8,1,6,2,4,3,7,5] => ([(1,2),(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4)],8)
[[1,2,3,4],[5,7,8],[6]] => [6,5,7,8,1,2,3,4] => [8,1,2,3,6,5,7,4] => ([(1,5),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[1,2,5,6],[3,4,8],[7]] => [7,3,4,8,1,2,5,6] => [8,1,7,3,2,5,4,6] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,3,4,6],[2,5,8],[7]] => [7,2,5,8,1,3,4,6] => [8,7,1,3,2,4,5,6] => ([(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[[1,2,4,6],[3,5,8],[7]] => [7,3,5,8,1,2,4,6] => [8,1,7,2,3,4,5,6] => ([(1,3),(1,7),(4,6),(5,4),(6,2),(7,5)],8)
[[1,3,4,5],[2,6,8],[7]] => [7,2,6,8,1,3,4,5] => [8,7,1,3,4,2,6,5] => ([(2,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,4,5],[3,6,8],[7]] => [7,3,6,8,1,2,4,5] => [8,1,7,2,4,3,6,5] => ([(1,2),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4)],8)
[[1,2,3,5],[4,6,8],[7]] => [7,4,6,8,1,2,3,5] => [8,1,2,7,3,4,6,5] => ([(1,7),(5,6),(6,3),(6,4),(7,2),(7,5)],8)
[[1,2,3,4],[5,6,8],[7]] => [7,5,6,8,1,2,3,4] => [8,1,2,3,7,5,6,4] => ([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[[1,3,5,7],[2,4,6],[8]] => [8,2,4,6,1,3,5,7] => [6,8,1,2,3,4,5,7] => ([(0,6),(1,3),(1,7),(2,7),(4,5),(5,2),(6,4)],8)
[[1,3,4,7],[2,5,6],[8]] => [8,2,5,6,1,3,4,7] => [6,8,1,3,2,5,4,7] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7)],8)
[[1,3,5,6],[2,4,7],[8]] => [8,2,4,7,1,3,5,6] => [7,8,1,2,3,5,4,6] => ([(0,4),(1,5),(2,7),(3,7),(5,6),(6,2),(6,3)],8)
[[1,2,5,6],[3,4,7],[8]] => [8,3,4,7,1,2,5,6] => [7,1,8,3,2,5,4,6] => ([(0,5),(1,2),(1,3),(1,5),(2,6),(2,7),(3,6),(3,7),(6,4),(7,4)],8)
[[1,3,4,6],[2,5,7],[8]] => [8,2,5,7,1,3,4,6] => [7,8,1,3,2,4,5,6] => ([(0,5),(1,3),(1,4),(3,7),(4,7),(6,2),(7,6)],8)
[[1,2,4,6],[3,5,7],[8]] => [8,3,5,7,1,2,4,6] => [7,1,8,2,3,4,5,6] => ([(0,7),(1,6),(1,7),(3,5),(4,3),(5,2),(6,4)],8)
[[1,3,4,5],[2,6,7],[8]] => [8,2,6,7,1,3,4,5] => [7,8,1,3,4,2,6,5] => ([(0,4),(1,3),(1,5),(2,6),(2,7),(3,6),(3,7),(5,2)],8)
[[1,2,4,5],[3,6,7],[8]] => [8,3,6,7,1,2,4,5] => [7,1,8,2,4,3,6,5] => ([(0,7),(1,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],8)
[[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => [7,1,2,3,8,5,6,4] => ([(0,7),(1,5),(4,3),(5,6),(6,2),(6,4),(6,7)],8)
[[1,3,7,8],[2,5],[4,6]] => [4,6,2,5,1,3,7,8] => [5,6,1,4,2,3,7,8] => ([(0,5),(1,3),(1,6),(2,7),(3,7),(5,7),(6,2),(7,4)],8)
[[1,2,7,8],[3,5],[4,6]] => [4,6,3,5,1,2,7,8] => [5,1,6,4,3,2,7,8] => ([(0,6),(1,2),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,7),(7,5)],8)
[[1,3,7,8],[2,4],[5,6]] => [5,6,2,4,1,3,7,8] => [4,6,1,2,5,3,7,8] => ([(0,5),(1,4),(1,6),(2,7),(4,7),(5,2),(5,6),(6,7),(7,3)],8)
[[1,2,7,8],[3,4],[5,6]] => [5,6,3,4,1,2,7,8] => [4,1,6,3,5,2,7,8] => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,7),(4,5),(5,7),(6,7),(7,3)],8)
[[1,4,6,8],[2,5],[3,7]] => [3,7,2,5,1,4,6,8] => [5,7,3,1,2,4,6,8] => ([(0,6),(1,3),(2,4),(2,5),(3,6),(4,7),(5,7),(6,5)],8)
[[1,3,6,8],[2,5],[4,7]] => [4,7,2,5,1,3,6,8] => [5,7,1,4,2,3,6,8] => ([(0,4),(0,7),(1,3),(1,5),(2,7),(3,7),(4,6),(5,2),(7,6)],8)
[[1,3,6,8],[2,4],[5,7]] => [5,7,2,4,1,3,6,8] => [4,7,1,2,5,3,6,8] => ([(0,3),(0,7),(1,4),(2,5),(3,6),(4,2),(4,7),(5,6),(7,5)],8)
[[1,4,5,8],[2,6],[3,7]] => [3,7,2,6,1,4,5,8] => [6,7,3,1,4,2,5,8] => ([(0,5),(1,3),(2,4),(2,5),(3,7),(4,6),(5,6),(6,7)],8)
[[1,3,5,8],[2,6],[4,7]] => [4,7,2,6,1,3,5,8] => [6,7,1,4,3,2,5,8] => ([(0,5),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => [6,1,7,4,2,3,5,8] => ([(0,7),(1,3),(1,4),(1,7),(2,5),(3,5),(4,2),(5,6),(7,6)],8)
[[1,2,4,8],[3,6],[5,7]] => [5,7,3,6,1,2,4,8] => [6,1,7,2,5,3,4,8] => ([(0,6),(1,5),(1,6),(2,7),(3,7),(4,3),(5,2),(5,4),(6,7)],8)
[[1,2,3,8],[4,6],[5,7]] => [5,7,4,6,1,2,3,8] => [6,1,2,7,5,4,3,8] => ([(0,6),(1,5),(2,7),(3,7),(4,7),(5,2),(5,3),(5,4),(5,6),(6,7)],8)
[[1,2,5,8],[3,4],[6,7]] => [6,7,3,4,1,2,5,8] => [4,1,7,3,2,6,5,8] => ([(0,2),(0,3),(0,4),(1,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[[1,3,4,8],[2,5],[6,7]] => [6,7,2,5,1,3,4,8] => [5,7,1,3,2,6,4,8] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(7,6)],8)
[[1,4,6,7],[2,5],[3,8]] => [3,8,2,5,1,4,6,7] => [5,8,3,1,2,4,6,7] => ([(0,7),(1,4),(2,3),(2,6),(4,7),(6,5),(7,6)],8)
[[1,3,6,7],[2,5],[4,8]] => [4,8,2,5,1,3,6,7] => [5,8,1,4,2,3,6,7] => ([(0,5),(0,7),(1,3),(1,6),(2,7),(3,7),(6,2),(7,4)],8)
[[1,2,6,7],[3,5],[4,8]] => [4,8,3,5,1,2,6,7] => [5,1,8,4,3,2,6,7] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(7,5)],8)
[[1,3,6,7],[2,4],[5,8]] => [5,8,2,4,1,3,6,7] => [4,8,1,2,5,3,6,7] => ([(0,5),(1,4),(1,6),(3,7),(5,3),(5,6),(6,7),(7,2)],8)
[[1,2,6,7],[3,4],[5,8]] => [5,8,3,4,1,2,6,7] => [4,1,8,3,5,2,6,7] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(3,7),(4,5),(5,7),(7,2)],8)
[[1,4,5,7],[2,6],[3,8]] => [3,8,2,6,1,4,5,7] => [6,8,3,1,4,2,5,7] => ([(0,5),(1,4),(1,5),(2,3),(2,6),(4,7),(5,7),(7,6)],8)
[[1,2,4,7],[3,6],[5,8]] => [5,8,3,6,1,2,4,7] => [6,1,8,2,5,3,4,7] => ([(0,6),(0,7),(1,5),(1,6),(2,7),(3,7),(4,3),(5,2),(5,4)],8)
[[1,3,5,7],[2,4],[6,8]] => [6,8,2,4,1,3,5,7] => [4,8,1,2,3,6,5,7] => ([(0,4),(1,3),(1,6),(1,7),(2,6),(2,7),(4,2),(6,5),(7,5)],8)
[[1,3,4,7],[2,5],[6,8]] => [6,8,2,5,1,3,4,7] => [5,8,1,3,2,6,4,7] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(2,7),(3,5),(3,7),(5,6),(7,6)],8)
[[1,3,5,6],[2,7],[4,8]] => [4,8,2,7,1,3,5,6] => [7,8,1,4,3,5,2,6] => ([(0,5),(1,2),(1,3),(1,4),(2,7),(3,6),(4,6),(6,7)],8)
[[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => [7,1,8,4,2,5,3,6] => ([(0,7),(1,3),(1,4),(1,7),(2,6),(3,5),(4,2),(4,5),(5,6)],8)
[[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => [7,1,8,2,5,4,3,6] => ([(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(5,2),(5,3),(5,4)],8)
[[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => [7,1,2,8,5,3,4,6] => ([(0,7),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4),(5,7)],8)
[[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => [7,1,8,2,4,6,3,5] => ([(0,7),(1,5),(1,7),(3,6),(4,2),(4,6),(5,3),(5,4)],8)
[[1,2,3,5],[4,7],[6,8]] => [6,8,4,7,1,2,3,5] => [7,1,2,8,3,6,4,5] => ([(0,7),(1,5),(4,3),(5,6),(5,7),(6,2),(6,4)],8)
[[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => [7,1,2,3,8,6,5,4] => ([(0,7),(1,5),(5,6),(6,2),(6,3),(6,4),(6,7)],8)
[[1,3,5,6],[2,4],[7,8]] => [7,8,2,4,1,3,5,6] => [4,8,1,2,3,5,7,6] => ([(0,6),(1,5),(1,7),(2,7),(6,2),(7,3),(7,4)],8)
[[1,3,4,6],[2,5],[7,8]] => [7,8,2,5,1,3,4,6] => [5,8,1,3,2,4,7,6] => ([(0,4),(0,6),(0,7),(1,2),(1,3),(2,5),(3,5),(5,6),(5,7)],8)
[[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => [5,1,8,2,3,4,7,6] => ([(0,5),(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(3,2),(4,3)],8)
[[1,2,3,6],[4,5],[7,8]] => [7,8,4,5,1,2,3,6] => [5,1,2,8,4,3,7,6] => ([(0,5),(0,6),(0,7),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(4,5)],8)
[[1,3,4,5],[2,6],[7,8]] => [7,8,2,6,1,3,4,5] => [6,8,1,3,4,2,7,5] => ([(0,4),(0,7),(1,3),(1,5),(2,6),(2,7),(3,6),(3,7),(5,2)],8)
[[1,2,4,5],[3,6],[7,8]] => [7,8,3,6,1,2,4,5] => [6,1,8,2,4,3,7,5] => ([(0,6),(0,7),(1,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(4,3)],8)
[[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => [6,1,2,8,3,4,7,5] => ([(0,6),(0,7),(1,5),(3,4),(4,2),(4,6),(5,3),(5,7)],8)
[[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [6,1,2,3,8,5,7,4] => ([(0,6),(0,7),(1,4),(3,6),(4,5),(5,2),(5,3),(5,7)],8)
[[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => [6,3,4,2,1,5,7,8] => ([(0,7),(1,7),(2,6),(3,4),(4,7),(6,5),(7,6)],8)
[[1,4,7,8],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8] => [6,3,5,1,2,4,7,8] => ([(0,7),(1,5),(2,3),(2,6),(3,7),(5,6),(6,7),(7,4)],8)
[[1,3,7,8],[2,6],[4],[5]] => [5,4,2,6,1,3,7,8] => [6,4,1,5,2,3,7,8] => ([(0,7),(1,6),(2,3),(2,6),(3,5),(5,7),(6,7),(7,4)],8)
[[1,2,7,8],[3,6],[4],[5]] => [5,4,3,6,1,2,7,8] => [6,1,4,5,3,2,7,8] => ([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[1,4,7,8],[2,5],[3],[6]] => [6,3,2,5,1,4,7,8] => [5,3,6,1,2,4,7,8] => ([(0,5),(1,5),(1,7),(2,4),(4,7),(5,6),(6,3),(7,6)],8)
[[1,3,7,8],[2,5],[4],[6]] => [6,4,2,5,1,3,7,8] => [5,4,1,6,2,3,7,8] => ([(0,7),(1,7),(2,3),(2,7),(3,5),(5,6),(6,4),(7,6)],8)
[[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => [7,3,5,1,2,4,6,8] => ([(0,5),(1,4),(2,3),(2,6),(3,7),(4,6),(6,7),(7,5)],8)
[[1,3,6,8],[2,7],[4],[5]] => [5,4,2,7,1,3,6,8] => [7,4,1,5,2,3,6,8] => ([(0,5),(1,6),(2,3),(2,5),(3,4),(4,7),(5,7),(7,6)],8)
[[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => [7,1,4,5,3,2,6,8] => ([(0,6),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,2),(7,6)],8)
[[1,3,4,8],[2,7],[5],[6]] => [6,5,2,7,1,3,4,8] => [7,5,1,3,6,2,4,8] => ([(0,7),(1,5),(2,3),(2,4),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => [7,1,5,2,6,3,4,8] => ([(0,7),(1,3),(1,5),(2,7),(3,6),(4,2),(5,4),(5,6),(6,7)],8)
[[1,4,6,8],[2,5],[3],[7]] => [7,3,2,5,1,4,6,8] => [5,3,7,1,2,4,6,8] => ([(0,3),(1,5),(1,7),(2,6),(2,7),(3,6),(5,4),(6,5),(7,4)],8)
[[1,3,6,8],[2,4],[5],[7]] => [7,5,2,4,1,3,6,8] => [4,5,1,2,7,3,6,8] => ([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6),(5,7),(6,7)],8)
[[1,2,4,8],[3,6],[5],[7]] => [7,5,3,6,1,2,4,8] => [6,1,5,2,7,3,4,8] => ([(0,7),(1,2),(1,5),(2,7),(3,6),(4,3),(5,4),(5,7),(7,6)],8)
[[1,2,5,8],[3,4],[6],[7]] => [7,6,3,4,1,2,5,8] => [4,1,6,3,2,7,5,8] => ([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,7),(6,5),(7,5)],8)
[[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => [5,1,6,2,3,7,4,8] => ([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(5,6),(7,5)],8)
[[1,5,6,7],[2,8],[3],[4]] => [4,3,2,8,1,5,6,7] => [8,3,4,2,1,5,6,7] => ([(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[1,4,6,7],[2,8],[3],[5]] => [5,3,2,8,1,4,6,7] => [8,3,5,1,2,4,6,7] => ([(1,5),(2,3),(2,6),(3,7),(5,6),(6,7),(7,4)],8)
[[1,3,6,7],[2,8],[4],[5]] => [5,4,2,8,1,3,6,7] => [8,4,1,5,2,3,6,7] => ([(1,6),(2,4),(2,6),(4,5),(5,7),(6,7),(7,3)],8)
[[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => [8,1,4,5,3,2,6,7] => ([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => [8,4,1,6,3,2,5,7] => ([(1,5),(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => [8,1,4,6,2,3,5,7] => ([(1,4),(1,5),(2,7),(3,6),(4,3),(5,2),(5,6),(6,7)],8)
[[1,3,4,7],[2,8],[5],[6]] => [6,5,2,8,1,3,4,7] => [8,5,1,3,6,2,4,7] => ([(1,6),(2,3),(2,4),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => [8,1,5,2,6,3,4,7] => ([(1,3),(1,5),(2,7),(3,6),(4,2),(5,4),(5,6),(6,7)],8)
[[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => [8,1,2,5,6,4,3,7] => ([(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[1,3,5,6],[2,8],[4],[7]] => [7,4,2,8,1,3,5,6] => [8,4,1,7,3,5,2,6] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,7),(4,6),(6,7)],8)
[[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => [8,1,4,7,2,5,3,6] => ([(1,4),(1,5),(3,7),(4,2),(4,6),(5,3),(5,6),(6,7)],8)
[[1,3,4,6],[2,8],[5],[7]] => [7,5,2,8,1,3,4,6] => [8,5,1,3,7,4,2,6] => ([(1,6),(1,7),(2,3),(2,4),(3,7),(4,5),(4,6),(5,7)],8)
[[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [8,1,5,2,7,4,3,6] => ([(1,4),(1,5),(2,7),(3,7),(4,6),(4,7),(5,2),(5,3),(5,6)],8)
[[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => [8,1,2,5,7,3,4,6] => ([(1,6),(3,7),(4,3),(5,2),(5,7),(6,4),(6,5)],8)
[[1,2,3,5],[4,8],[6],[7]] => [7,6,4,8,1,2,3,5] => [8,1,2,6,3,7,4,5] => ([(1,6),(3,7),(4,2),(5,4),(5,7),(6,3),(6,5)],8)
[[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => [8,1,2,3,6,7,5,4] => ([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[[1,3,6,7],[2,5],[4],[8]] => [8,4,2,5,1,3,6,7] => [5,4,1,8,2,3,6,7] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,6),(4,5),(5,7),(7,3)],8)
[[1,2,6,7],[3,5],[4],[8]] => [8,4,3,5,1,2,6,7] => [5,1,4,8,3,2,6,7] => ([(0,6),(0,7),(1,2),(1,3),(1,5),(2,7),(3,7),(5,6),(5,7),(7,4)],8)
[[1,3,6,7],[2,4],[5],[8]] => [8,5,2,4,1,3,6,7] => [4,5,1,2,8,3,6,7] => ([(0,4),(1,5),(3,7),(4,6),(4,7),(5,3),(5,6),(7,2)],8)
[[1,2,6,7],[3,4],[5],[8]] => [8,5,3,4,1,2,6,7] => [4,1,5,3,8,2,6,7] => ([(0,6),(1,2),(1,4),(1,6),(2,7),(4,5),(4,7),(6,5),(6,7),(7,3)],8)
[[1,4,5,7],[2,6],[3],[8]] => [8,3,2,6,1,4,5,7] => [6,3,8,1,4,2,5,7] => ([(0,3),(0,7),(1,4),(1,5),(2,5),(2,7),(3,6),(6,4),(7,6)],8)
[[1,3,5,7],[2,6],[4],[8]] => [8,4,2,6,1,3,5,7] => [6,4,1,8,3,2,5,7] => ([(0,6),(0,7),(1,5),(1,6),(2,3),(2,4),(2,6),(3,7),(4,7),(7,5)],8)
[[1,2,4,7],[3,6],[5],[8]] => [8,5,3,6,1,2,4,7] => [6,1,5,2,8,3,4,7] => ([(0,6),(0,7),(1,3),(1,5),(2,6),(3,6),(3,7),(4,2),(5,4),(5,7)],8)
[[1,3,5,7],[2,4],[6],[8]] => [8,6,2,4,1,3,5,7] => [4,6,1,2,3,8,5,7] => ([(0,3),(0,7),(1,4),(2,5),(2,7),(3,5),(3,6),(4,2),(7,6)],8)
[[1,2,4,7],[3,5],[6],[8]] => [8,6,3,5,1,2,4,7] => [5,1,6,2,3,8,4,7] => ([(0,7),(1,3),(1,7),(2,6),(3,4),(4,2),(4,5),(7,5),(7,6)],8)
[[1,2,3,7],[4,5],[6],[8]] => [8,6,4,5,1,2,3,7] => [5,1,2,6,4,8,3,7] => ([(0,6),(1,4),(2,7),(3,5),(3,7),(4,2),(4,3),(4,6),(6,5),(6,7)],8)
[[1,4,5,6],[2,7],[3],[8]] => [8,3,2,7,1,4,5,6] => [7,3,8,1,4,5,2,6] => ([(0,5),(1,5),(1,6),(2,4),(2,6),(3,7),(4,7),(6,3)],8)
[[1,3,5,6],[2,7],[4],[8]] => [8,4,2,7,1,3,5,6] => [7,4,1,8,3,5,2,6] => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(4,5),(5,6)],8)
[[1,3,4,6],[2,7],[5],[8]] => [8,5,2,7,1,3,4,6] => [7,5,1,3,8,4,2,6] => ([(0,6),(1,6),(1,7),(2,3),(2,4),(3,7),(4,5),(4,6),(5,7)],8)
[[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => [7,1,2,5,8,3,4,6] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(4,3),(5,2),(5,4)],8)
[[1,3,4,5],[2,7],[6],[8]] => [8,6,2,7,1,3,4,5] => [7,6,1,3,4,8,2,5] => ([(0,7),(1,7),(2,3),(2,4),(3,5),(4,6),(5,6),(5,7)],8)
[[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => [7,1,6,2,4,8,3,5] => ([(0,7),(1,2),(1,5),(2,7),(3,6),(4,6),(4,7),(5,3),(5,4)],8)
[[1,2,3,5],[4,7],[6],[8]] => [8,6,4,7,1,2,3,5] => [7,1,2,6,3,8,4,5] => ([(0,7),(1,6),(3,7),(4,2),(5,4),(5,7),(6,3),(6,5)],8)
[[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => [7,1,2,3,6,8,5,4] => ([(0,7),(1,5),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[1,3,5,6],[2,4],[7],[8]] => [8,7,2,4,1,3,5,6] => [4,7,1,2,3,5,8,6] => ([(0,4),(0,7),(1,5),(3,7),(4,6),(5,3),(7,2),(7,6)],8)
[[1,2,5,6],[3,4],[7],[8]] => [8,7,3,4,1,2,5,6] => [4,1,7,3,2,5,8,6] => ([(0,6),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(6,5),(7,4),(7,5)],8)
[[1,3,4,6],[2,5],[7],[8]] => [8,7,2,5,1,3,4,6] => [5,7,1,3,2,4,8,6] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(3,5),(4,6),(5,6),(5,7)],8)
[[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => [5,1,7,2,3,4,8,6] => ([(0,6),(0,7),(1,4),(1,7),(2,5),(2,6),(3,2),(4,3),(7,5)],8)
[[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => [6,1,7,2,4,3,8,5] => ([(0,6),(1,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(4,3),(6,7)],8)
[[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => [6,1,2,7,3,4,8,5] => ([(0,7),(1,4),(3,5),(4,3),(4,7),(5,2),(5,6),(7,6)],8)
[[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => [6,1,2,3,7,5,8,4] => ([(0,7),(1,4),(3,6),(4,5),(5,2),(5,3),(5,7),(7,6)],8)
[[1,6,7,8],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8] => [2,3,4,5,1,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[1,5,7,8],[2],[3],[4],[6]] => [6,4,3,2,1,5,7,8] => [2,3,4,6,1,5,7,8] => ([(0,6),(1,4),(2,7),(4,5),(5,2),(5,6),(6,7),(7,3)],8)
[[1,4,7,8],[2],[3],[5],[6]] => [6,5,3,2,1,4,7,8] => [2,3,5,1,6,4,7,8] => ([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(5,7),(6,7),(7,2)],8)
[[1,3,7,8],[2],[4],[5],[6]] => [6,5,4,2,1,3,7,8] => [2,4,1,5,6,3,7,8] => ([(0,5),(0,7),(1,2),(1,5),(2,7),(3,6),(5,6),(6,4),(7,3)],8)
[[1,5,6,8],[2],[3],[4],[7]] => [7,4,3,2,1,5,6,8] => [2,3,4,7,1,5,6,8] => ([(0,7),(1,5),(2,6),(3,6),(4,3),(4,7),(5,4),(7,2)],8)
[[1,4,5,8],[2],[3],[6],[7]] => [7,6,3,2,1,4,5,8] => [2,3,6,1,4,7,5,8] => ([(0,7),(1,4),(2,6),(3,5),(4,3),(4,7),(5,6),(7,2),(7,5)],8)
[[1,3,5,8],[2],[4],[6],[7]] => [7,6,4,2,1,3,5,8] => [2,4,1,6,3,7,5,8] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(4,3),(5,3),(6,4),(7,4),(7,5)],8)
[[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [4,1,2,5,6,7,3,8] => ([(0,7),(1,5),(2,6),(3,6),(4,3),(5,2),(5,7),(7,4)],8)
[[1,5,6,7],[2],[3],[4],[8]] => [8,4,3,2,1,5,6,7] => [2,3,4,8,1,5,6,7] => ([(0,7),(1,4),(4,5),(5,2),(5,7),(6,3),(7,6)],8)
[[1,4,6,7],[2],[3],[5],[8]] => [8,5,3,2,1,4,6,7] => [2,3,5,1,8,4,6,7] => ([(0,5),(0,6),(1,4),(3,5),(3,7),(4,3),(4,6),(6,7),(7,2)],8)
[[1,3,6,7],[2],[4],[5],[8]] => [8,5,4,2,1,3,6,7] => [2,4,1,5,8,3,6,7] => ([(0,5),(0,7),(1,3),(1,5),(3,7),(5,6),(6,4),(7,2),(7,6)],8)
[[1,2,6,7],[3],[4],[5],[8]] => [8,5,4,3,1,2,6,7] => [3,1,4,5,8,2,6,7] => ([(0,6),(1,4),(1,6),(4,7),(5,3),(5,7),(6,5),(7,2)],8)
[[1,4,5,7],[2],[3],[6],[8]] => [8,6,3,2,1,4,5,7] => [2,3,6,1,4,8,5,7] => ([(0,7),(1,4),(2,5),(3,5),(3,6),(4,3),(4,7),(7,2),(7,6)],8)
[[1,3,5,7],[2],[4],[6],[8]] => [8,6,4,2,1,3,5,7] => [2,4,1,6,3,8,5,7] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)
[[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => [3,1,4,6,2,8,5,7] => ([(0,7),(1,3),(1,7),(2,4),(2,5),(3,4),(3,6),(6,5),(7,2),(7,6)],8)
[[1,3,4,7],[2],[5],[6],[8]] => [8,6,5,2,1,3,4,7] => [2,5,1,3,6,8,4,7] => ([(0,7),(1,3),(1,7),(2,5),(3,6),(6,4),(6,5),(7,2),(7,6)],8)
[[1,2,4,7],[3],[5],[6],[8]] => [8,6,5,3,1,2,4,7] => [3,1,5,2,6,8,4,7] => ([(0,3),(0,7),(1,5),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,6)],8)
[[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => [4,1,2,5,6,8,3,7] => ([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(5,6),(7,5)],8)
[[1,4,5,6],[2],[3],[7],[8]] => [8,7,3,2,1,4,5,6] => [2,3,7,1,4,5,8,6] => ([(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(5,6),(7,5)],8)
[[1,3,5,6],[2],[4],[7],[8]] => [8,7,4,2,1,3,5,6] => [2,4,1,7,3,5,8,6] => ([(0,3),(0,7),(1,5),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,6)],8)
[[1,2,5,6],[3],[4],[7],[8]] => [8,7,4,3,1,2,5,6] => [3,1,4,7,2,5,8,6] => ([(0,7),(1,3),(1,7),(2,5),(3,6),(6,4),(6,5),(7,2),(7,6)],8)
[[1,3,4,6],[2],[5],[7],[8]] => [8,7,5,2,1,3,4,6] => [2,5,1,3,7,4,8,6] => ([(0,7),(1,3),(1,7),(2,4),(2,5),(3,4),(3,6),(6,5),(7,2),(7,6)],8)
[[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => [3,1,5,2,7,4,8,6] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8)
[[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => [4,1,2,5,7,3,8,6] => ([(0,7),(1,4),(2,5),(3,5),(3,6),(4,3),(4,7),(7,2),(7,6)],8)
[[1,3,4,5],[2],[6],[7],[8]] => [8,7,6,2,1,3,4,5] => [2,6,1,3,4,7,8,5] => ([(0,6),(1,4),(1,6),(4,7),(5,3),(5,7),(6,5),(7,2)],8)
[[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => [3,1,6,2,4,7,8,5] => ([(0,5),(0,7),(1,3),(1,5),(3,7),(5,6),(6,4),(7,2),(7,6)],8)
[[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => [4,1,2,6,3,7,8,5] => ([(0,5),(0,6),(1,4),(3,5),(3,7),(4,3),(4,6),(6,7),(7,2)],8)
[[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,4] => ([(0,7),(1,4),(4,5),(5,2),(5,7),(6,3),(7,6)],8)
[[1,4,7],[2,5,8],[3,6]] => [3,6,2,5,8,1,4,7] => [8,6,3,1,2,5,4,7] => ([(1,7),(2,5),(2,6),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[[1,3,7],[2,5,8],[4,6]] => [4,6,2,5,8,1,3,7] => [8,6,1,4,2,5,3,7] => ([(1,7),(2,3),(2,4),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,7],[3,5,8],[4,6]] => [4,6,3,5,8,1,2,7] => [8,1,6,4,3,5,2,7] => ([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[1,3,7],[2,4,8],[5,6]] => [5,6,2,4,8,1,3,7] => [8,6,1,2,5,4,3,7] => ([(1,7),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[1,3,6],[2,5,8],[4,7]] => [4,7,2,5,8,1,3,6] => [8,7,1,4,2,3,5,6] => ([(2,4),(2,6),(3,7),(4,7),(6,3),(7,5)],8)
[[1,3,6],[2,4,8],[5,7]] => [5,7,2,4,8,1,3,6] => [8,7,1,2,5,3,4,6] => ([(2,6),(3,7),(4,7),(5,4),(6,3),(6,5)],8)
[[1,2,6],[3,4,8],[5,7]] => [5,7,3,4,8,1,2,6] => [8,1,7,3,5,2,4,6] => ([(1,3),(1,4),(1,5),(2,7),(4,6),(5,2),(5,6),(6,7)],8)
[[1,4,5],[2,6,8],[3,7]] => [3,7,2,6,8,1,4,5] => [8,7,3,1,4,2,6,5] => ([(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,5],[2,6,8],[4,7]] => [4,7,2,6,8,1,3,5] => [8,7,1,4,3,2,6,5] => ([(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,5],[3,6,8],[4,7]] => [4,7,3,6,8,1,2,5] => [8,1,7,4,2,3,6,5] => ([(1,2),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3)],8)
[[1,3,4],[2,6,8],[5,7]] => [5,7,2,6,8,1,3,4] => [8,7,1,3,5,2,6,4] => ([(2,3),(2,4),(3,5),(3,7),(4,6),(4,7),(5,6)],8)
[[1,2,4],[3,6,8],[5,7]] => [5,7,3,6,8,1,2,4] => [8,1,7,2,5,3,6,4] => ([(1,3),(1,6),(4,7),(5,2),(5,7),(6,4),(6,5)],8)
[[1,3,5],[2,4,8],[6,7]] => [6,7,2,4,8,1,3,5] => [8,7,1,2,3,6,4,5] => ([(2,6),(5,4),(6,7),(7,3),(7,5)],8)
[[1,2,4],[3,5,8],[6,7]] => [6,7,3,5,8,1,2,4] => [8,1,7,2,3,6,5,4] => ([(1,5),(1,6),(6,7),(7,2),(7,3),(7,4)],8)
[[1,2,3],[4,5,8],[6,7]] => [6,7,4,5,8,1,2,3] => [8,1,2,7,4,6,5,3] => ([(1,7),(6,4),(6,5),(7,2),(7,3),(7,6)],8)
[[1,4,6],[2,5,7],[3,8]] => [3,8,2,5,7,1,4,6] => [7,8,3,1,2,4,5,6] => ([(0,7),(1,4),(2,5),(5,7),(6,3),(7,6)],8)
[[1,3,6],[2,5,7],[4,8]] => [4,8,2,5,7,1,3,6] => [7,8,1,4,2,3,5,6] => ([(0,5),(1,3),(1,6),(2,7),(3,7),(6,2),(7,4)],8)
[[1,3,6],[2,4,7],[5,8]] => [5,8,2,4,7,1,3,6] => [7,8,1,2,5,3,4,6] => ([(0,4),(1,6),(2,7),(3,7),(5,3),(6,2),(6,5)],8)
[[1,4,5],[2,6,7],[3,8]] => [3,8,2,6,7,1,4,5] => [7,8,3,1,4,2,6,5] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,5],[3,6,7],[4,8]] => [4,8,3,6,7,1,2,5] => [7,1,8,4,2,3,6,5] => ([(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,2)],8)
[[1,3,4],[2,6,7],[5,8]] => [5,8,2,6,7,1,3,4] => [7,8,1,3,5,2,6,4] => ([(0,4),(1,3),(1,5),(2,6),(3,6),(3,7),(5,2),(5,7)],8)
[[1,2,4],[3,6,7],[5,8]] => [5,8,3,6,7,1,2,4] => [7,1,8,2,5,3,6,4] => ([(0,7),(1,5),(1,7),(3,6),(4,2),(4,6),(5,3),(5,4)],8)
[[1,3,5],[2,4,7],[6,8]] => [6,8,2,4,7,1,3,5] => [7,8,1,2,3,6,4,5] => ([(0,6),(1,4),(5,3),(6,7),(7,2),(7,5)],8)
[[1,3,4],[2,5,7],[6,8]] => [6,8,2,5,7,1,3,4] => [7,8,1,3,2,6,5,4] => ([(0,4),(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7)],8)
[[1,2,4],[3,5,7],[6,8]] => [6,8,3,5,7,1,2,4] => [7,1,8,2,3,6,5,4] => ([(0,7),(1,5),(1,7),(5,6),(6,2),(6,3),(6,4)],8)
[[1,2,3],[4,5,7],[6,8]] => [6,8,4,5,7,1,2,3] => [7,1,2,8,4,6,5,3] => ([(0,7),(1,6),(5,3),(5,4),(6,2),(6,5),(6,7)],8)
[[1,3,5],[2,4,6],[7,8]] => [7,8,2,4,6,1,3,5] => [6,8,1,2,3,4,7,5] => ([(0,6),(1,3),(1,7),(4,5),(5,2),(5,7),(6,4)],8)
[[1,2,5],[3,4,6],[7,8]] => [7,8,3,4,6,1,2,5] => [6,1,8,3,2,4,7,5] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(3,7),(4,7),(7,2),(7,5)],8)
[[1,3,4],[2,5,6],[7,8]] => [7,8,2,5,6,1,3,4] => [6,8,1,3,2,5,7,4] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(6,7)],8)
[[1,2,4],[3,5,6],[7,8]] => [7,8,3,5,6,1,2,4] => [6,1,8,2,3,5,7,4] => ([(0,6),(0,7),(1,4),(1,7),(3,6),(4,5),(5,2),(5,3)],8)
[[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => [6,1,2,8,4,5,7,3] => ([(0,6),(0,7),(1,5),(3,6),(4,3),(5,2),(5,4),(5,7)],8)
[[1,5,7],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7] => [8,3,4,2,1,6,5,7] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[1,4,7],[2,6,8],[3],[5]] => [5,3,2,6,8,1,4,7] => [8,3,5,1,2,6,4,7] => ([(1,4),(2,3),(2,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[1,3,7],[2,6,8],[4],[5]] => [5,4,2,6,8,1,3,7] => [8,4,1,5,2,6,3,7] => ([(1,5),(2,3),(2,5),(3,4),(3,7),(4,6),(5,7),(7,6)],8)
[[1,2,7],[3,6,8],[4],[5]] => [5,4,3,6,8,1,2,7] => [8,1,4,5,3,6,2,7] => ([(1,2),(1,4),(1,5),(2,7),(3,6),(4,6),(5,3),(6,7)],8)
[[1,3,7],[2,5,8],[4],[6]] => [6,4,2,5,8,1,3,7] => [8,4,1,6,2,5,3,7] => ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,7),(5,7),(6,7)],8)
[[1,2,7],[3,5,8],[4],[6]] => [6,4,3,5,8,1,2,7] => [8,1,4,6,3,5,2,7] => ([(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,2),(5,6),(6,7)],8)
[[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => [8,5,1,2,6,4,3,7] => ([(1,3),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[1,4,6],[2,7,8],[3],[5]] => [5,3,2,7,8,1,4,6] => [8,3,5,1,2,4,7,6] => ([(1,3),(2,4),(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,6],[2,7,8],[4],[5]] => [5,4,2,7,8,1,3,6] => [8,4,1,5,2,3,7,6] => ([(1,5),(2,3),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,6],[3,7,8],[4],[5]] => [5,4,3,7,8,1,2,6] => [8,1,4,5,3,2,7,6] => ([(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[[1,4,5],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5] => [8,3,6,1,4,2,7,5] => ([(1,3),(1,5),(2,4),(2,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,4],[3,7,8],[5],[6]] => [6,5,3,7,8,1,2,4] => [8,1,5,2,6,3,7,4] => ([(1,3),(1,5),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7)],8)
[[1,4,6],[2,5,8],[3],[7]] => [7,3,2,5,8,1,4,6] => [8,3,7,1,2,4,5,6] => ([(1,5),(2,4),(2,7),(5,7),(6,3),(7,6)],8)
[[1,3,6],[2,5,8],[4],[7]] => [7,4,2,5,8,1,3,6] => [8,4,1,7,2,3,5,6] => ([(1,6),(1,7),(2,4),(2,6),(4,5),(5,7),(7,3)],8)
[[1,2,6],[3,5,8],[4],[7]] => [7,4,3,5,8,1,2,6] => [8,1,4,7,3,2,5,6] => ([(1,3),(1,4),(1,6),(3,7),(4,7),(6,2),(6,7),(7,5)],8)
[[1,3,6],[2,4,8],[5],[7]] => [7,5,2,4,8,1,3,6] => [8,5,1,2,7,3,4,6] => ([(1,3),(2,6),(2,7),(3,5),(3,6),(4,7),(5,4)],8)
[[1,2,6],[3,4,8],[5],[7]] => [7,5,3,4,8,1,2,6] => [8,1,5,3,7,2,4,6] => ([(1,2),(1,3),(1,4),(2,6),(3,5),(3,7),(4,5),(4,6),(6,7)],8)
[[1,4,5],[2,6,8],[3],[7]] => [7,3,2,6,8,1,4,5] => [8,3,7,1,4,2,6,5] => ([(1,3),(1,5),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,5],[2,6,8],[4],[7]] => [7,4,2,6,8,1,3,5] => [8,4,1,7,3,2,6,5] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7)],8)
[[1,2,5],[3,6,8],[4],[7]] => [7,4,3,6,8,1,2,5] => [8,1,4,7,2,3,6,5] => ([(1,4),(1,5),(3,6),(3,7),(4,3),(5,2),(5,6),(5,7)],8)
[[1,3,4],[2,6,8],[5],[7]] => [7,5,2,6,8,1,3,4] => [8,5,1,3,7,2,6,4] => ([(1,5),(1,7),(2,3),(2,4),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => [8,1,5,2,7,3,6,4] => ([(1,3),(1,5),(3,6),(3,7),(4,2),(4,7),(5,4),(5,6)],8)
[[1,2,3],[4,6,8],[5],[7]] => [7,5,4,6,8,1,2,3] => [8,1,2,5,7,4,6,3] => ([(1,6),(4,7),(5,3),(5,7),(6,2),(6,4),(6,5)],8)
[[1,3,5],[2,4,8],[6],[7]] => [7,6,2,4,8,1,3,5] => [8,6,1,2,3,7,4,5] => ([(1,7),(2,5),(4,3),(5,6),(6,4),(6,7)],8)
[[1,2,5],[3,4,8],[6],[7]] => [7,6,3,4,8,1,2,5] => [8,1,6,3,2,7,4,5] => ([(1,2),(1,3),(1,4),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5)],8)
[[1,2,4],[3,5,8],[6],[7]] => [7,6,3,5,8,1,2,4] => [8,1,6,2,3,7,5,4] => ([(1,4),(1,5),(4,7),(5,6),(6,2),(6,3),(6,7)],8)
[[1,2,3],[4,5,8],[6],[7]] => [7,6,4,5,8,1,2,3] => [8,1,2,6,4,7,5,3] => ([(1,6),(4,7),(5,3),(5,7),(6,2),(6,4),(6,5)],8)
[[1,4,6],[2,5,7],[3],[8]] => [8,3,2,5,7,1,4,6] => [7,3,8,1,2,4,5,6] => ([(0,6),(1,6),(1,7),(2,3),(3,7),(4,5),(7,4)],8)
[[1,3,6],[2,5,7],[4],[8]] => [8,4,2,5,7,1,3,6] => [7,4,1,8,2,3,5,6] => ([(0,7),(1,6),(1,7),(2,3),(2,7),(3,5),(5,6),(6,4)],8)
[[1,3,6],[2,4,7],[5],[8]] => [8,5,2,4,7,1,3,6] => [7,5,1,2,8,3,4,6] => ([(0,3),(1,7),(2,6),(2,7),(3,5),(3,7),(4,6),(5,4)],8)
[[1,4,5],[2,6,7],[3],[8]] => [8,3,2,6,7,1,4,5] => [7,3,8,1,4,2,6,5] => ([(0,6),(1,3),(1,7),(2,6),(2,7),(3,4),(3,5),(7,4),(7,5)],8)
[[1,3,5],[2,6,7],[4],[8]] => [8,4,2,6,7,1,3,5] => [7,4,1,8,3,2,6,5] => ([(0,5),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7)],8)
[[1,2,5],[3,6,7],[4],[8]] => [8,4,3,6,7,1,2,5] => [7,1,4,8,2,3,6,5] => ([(0,7),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,2)],8)
[[1,3,4],[2,6,7],[5],[8]] => [8,5,2,6,7,1,3,4] => [7,5,1,3,8,2,6,4] => ([(0,6),(1,6),(1,7),(2,3),(2,4),(3,5),(3,7),(4,5),(4,6),(4,7)],8)
[[1,2,4],[3,6,7],[5],[8]] => [8,5,3,6,7,1,2,4] => [7,1,5,2,8,3,6,4] => ([(0,7),(1,3),(1,4),(3,6),(3,7),(4,5),(4,7),(5,2),(5,6)],8)
[[1,2,3],[4,6,7],[5],[8]] => [8,5,4,6,7,1,2,3] => [7,1,2,5,8,4,6,3] => ([(0,7),(1,5),(3,6),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[1,3,5],[2,4,7],[6],[8]] => [8,6,2,4,7,1,3,5] => [7,6,1,2,3,8,4,5] => ([(0,7),(1,7),(2,5),(4,3),(5,6),(6,4),(6,7)],8)
[[1,2,5],[3,4,7],[6],[8]] => [8,6,3,4,7,1,2,5] => [7,1,6,3,2,8,4,5] => ([(0,7),(1,2),(1,3),(1,4),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5)],8)
[[1,2,4],[3,5,7],[6],[8]] => [8,6,3,5,7,1,2,4] => [7,1,6,2,3,8,5,4] => ([(0,7),(1,4),(1,5),(4,7),(5,6),(6,2),(6,3),(6,7)],8)
[[1,3,5],[2,4,6],[7],[8]] => [8,7,2,4,6,1,3,5] => [6,7,1,2,3,4,8,5] => ([(0,6),(1,3),(3,7),(4,5),(5,2),(5,7),(6,4)],8)
[[1,3,4],[2,5,6],[7],[8]] => [8,7,2,5,6,1,3,4] => [6,7,1,3,2,5,8,4] => ([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,7),(6,7)],8)
[[1,2,4],[3,5,6],[7],[8]] => [8,7,3,5,6,1,2,4] => [6,1,7,2,3,5,8,4] => ([(0,7),(1,4),(1,7),(3,6),(4,5),(5,2),(5,3),(7,6)],8)
[[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => [6,1,2,7,4,5,8,3] => ([(0,7),(1,5),(3,6),(4,3),(5,2),(5,4),(5,7),(7,6)],8)
[[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => [6,7,5,1,3,2,4,8] => ([(0,7),(1,3),(2,4),(2,5),(3,7),(4,6),(5,6),(6,7)],8)
[[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => [5,7,6,1,2,3,4,8] => ([(0,6),(1,3),(1,4),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => [5,7,1,6,2,4,3,8] => ([(0,4),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(5,2),(5,3),(6,7)],8)
[[1,2,8],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2,8] => [4,1,7,3,6,5,2,8] => ([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => [5,6,7,1,2,3,4,8] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[[1,3,8],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3,8] => [5,6,1,7,2,4,3,8] => ([(0,4),(1,5),(1,6),(2,7),(3,7),(4,6),(5,2),(5,3),(6,7)],8)
[[1,2,8],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2,8] => [5,1,6,7,3,4,2,8] => ([(0,6),(1,3),(1,5),(1,6),(2,7),(3,7),(4,7),(5,2),(6,4)],8)
[[1,3,8],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3,8] => [4,6,1,2,7,5,3,8] => ([(0,3),(0,6),(1,4),(2,7),(3,5),(4,2),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,8],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2,8] => [4,1,6,3,7,5,2,8] => ([(0,2),(0,3),(0,6),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7),(6,4)],8)
[[1,4,7],[2,5],[3,8],[6]] => [6,3,8,2,5,1,4,7] => [5,8,6,1,2,3,4,7] => ([(0,6),(1,2),(1,4),(3,7),(4,7),(5,3),(6,5)],8)
[[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => [5,8,1,6,2,4,3,7] => ([(0,4),(0,6),(1,5),(1,6),(2,7),(3,7),(5,2),(5,3),(6,7)],8)
[[1,2,7],[3,5],[4,8],[6]] => [6,4,8,3,5,1,2,7] => [5,1,8,6,3,4,2,7] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,2),(6,7)],8)
[[1,3,7],[2,4],[5,8],[6]] => [6,5,8,2,4,1,3,7] => [4,8,1,2,6,5,3,7] => ([(0,4),(1,3),(1,5),(1,6),(2,7),(4,2),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,7],[3,4],[5,8],[6]] => [6,5,8,3,4,1,2,7] => [4,1,8,3,6,5,2,7] => ([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8)
[[1,5,6],[2,7],[3,8],[4]] => [4,3,8,2,7,1,5,6] => [7,8,4,3,1,5,2,6] => ([(0,7),(1,7),(2,4),(3,5),(3,7),(5,6),(7,6)],8)
[[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => [7,1,8,5,4,2,3,6] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,2)],8)
[[1,4,5],[2,7],[3,8],[6]] => [6,3,8,2,7,1,4,5] => [7,8,6,1,4,3,2,5] => ([(1,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => [7,8,1,6,3,4,2,5] => ([(0,5),(1,2),(1,4),(1,6),(3,7),(4,7),(6,3)],8)
[[1,2,5],[3,7],[4,8],[6]] => [6,4,8,3,7,1,2,5] => [7,1,8,6,2,4,3,5] => ([(0,7),(1,2),(1,5),(1,7),(3,6),(4,6),(5,3),(5,4)],8)
[[1,3,4],[2,7],[5,8],[6]] => [6,5,8,2,7,1,3,4] => [7,8,1,3,6,5,2,4] => ([(0,5),(1,4),(1,6),(4,7),(6,2),(6,3),(6,7)],8)
[[1,2,3],[4,7],[5,8],[6]] => [6,5,8,4,7,1,2,3] => [7,1,2,8,6,5,4,3] => ([(0,7),(1,6),(6,2),(6,3),(6,4),(6,5),(6,7)],8)
[[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => [5,8,7,1,2,4,3,6] => ([(0,6),(1,2),(1,3),(1,7),(4,7),(5,7),(6,4),(6,5)],8)
[[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => [4,8,1,2,7,3,5,6] => ([(0,5),(1,4),(1,6),(1,7),(3,7),(5,3),(5,6),(7,2)],8)
[[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => [6,8,1,7,3,2,4,5] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(3,7),(4,7),(7,2)],8)
[[1,2,5],[3,6],[4,8],[7]] => [7,4,8,3,6,1,2,5] => [6,1,8,7,2,3,4,5] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(5,3)],8)
[[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => [6,8,1,3,7,2,5,4] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(3,7)],8)
[[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => [6,1,8,2,7,3,5,4] => ([(0,6),(0,7),(1,4),(1,7),(4,5),(4,6),(5,2),(5,3)],8)
[[1,2,3],[4,6],[5,8],[7]] => [7,5,8,4,6,1,2,3] => [6,1,2,8,7,4,5,3] => ([(0,6),(0,7),(1,5),(4,3),(5,2),(5,4),(5,6),(5,7)],8)
[[1,3,5],[2,4],[6,8],[7]] => [7,6,8,2,4,1,3,5] => [4,8,1,2,3,7,6,5] => ([(0,4),(1,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,2)],8)
[[1,2,5],[3,4],[6,8],[7]] => [7,6,8,3,4,1,2,5] => [4,1,8,3,2,7,6,5] => ([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7)],8)
[[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => [5,6,8,1,2,3,4,7] => ([(0,5),(1,6),(3,7),(4,3),(5,4),(6,2),(6,7)],8)
[[1,2,7],[3,5],[4,6],[8]] => [8,4,6,3,5,1,2,7] => [5,1,6,8,3,4,2,7] => ([(0,6),(1,3),(1,5),(1,6),(2,7),(3,7),(5,2),(6,4),(6,7)],8)
[[1,3,7],[2,4],[5,6],[8]] => [8,5,6,2,4,1,3,7] => [4,6,1,2,8,5,3,7] => ([(0,3),(0,6),(1,4),(2,7),(3,5),(3,7),(4,2),(4,5),(4,6),(6,7)],8)
[[1,2,7],[3,4],[5,6],[8]] => [8,5,6,3,4,1,2,7] => [4,1,6,3,8,5,2,7] => ([(0,2),(0,3),(0,6),(1,5),(1,6),(2,7),(3,4),(3,5),(5,7),(6,4),(6,7)],8)
[[1,4,6],[2,5],[3,7],[8]] => [8,3,7,2,5,1,4,6] => [5,7,8,1,2,4,3,6] => ([(0,6),(1,5),(1,7),(3,7),(4,7),(5,2),(6,3),(6,4)],8)
[[1,2,6],[3,5],[4,7],[8]] => [8,4,7,3,5,1,2,6] => [5,1,7,8,3,2,4,6] => ([(0,6),(0,7),(1,3),(1,4),(1,7),(3,5),(4,5),(5,6),(7,2)],8)
[[1,3,6],[2,4],[5,7],[8]] => [8,5,7,2,4,1,3,6] => [4,7,1,2,8,3,5,6] => ([(0,4),(0,7),(1,5),(3,7),(4,6),(5,3),(5,6),(7,2)],8)
[[1,2,6],[3,4],[5,7],[8]] => [8,5,7,3,4,1,2,6] => [4,1,7,3,8,2,5,6] => ([(0,6),(0,7),(1,2),(1,4),(1,6),(2,7),(4,5),(4,7),(6,5),(7,3)],8)
[[1,4,5],[2,6],[3,7],[8]] => [8,3,7,2,6,1,4,5] => [6,7,8,1,4,2,3,5] => ([(0,6),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2)],8)
[[1,3,5],[2,6],[4,7],[8]] => [8,4,7,2,6,1,3,5] => [6,7,1,8,3,2,4,5] => ([(0,5),(1,3),(1,4),(1,6),(3,7),(4,7),(5,6),(7,2)],8)
[[1,2,5],[3,6],[4,7],[8]] => [8,4,7,3,6,1,2,5] => [6,1,7,8,2,3,4,5] => ([(0,7),(1,6),(1,7),(4,5),(5,2),(6,4),(7,3)],8)
[[1,3,5],[2,4],[6,7],[8]] => [8,6,7,2,4,1,3,5] => [4,7,1,2,3,8,6,5] => ([(0,4),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(4,2)],8)
[[1,2,5],[3,4],[6,7],[8]] => [8,6,7,3,4,1,2,5] => [4,1,7,3,2,8,6,5] => ([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7)],8)
[[1,3,4],[2,5],[6,7],[8]] => [8,6,7,2,5,1,3,4] => [5,7,1,3,2,8,6,4] => ([(0,4),(0,7),(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6)],8)
[[1,2,4],[3,5],[6,7],[8]] => [8,6,7,3,5,1,2,4] => [5,1,7,2,3,8,6,4] => ([(0,6),(0,7),(1,3),(1,7),(3,4),(4,2),(4,5),(4,6),(7,5)],8)
[[1,6,8],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6,8] => [7,3,4,5,2,1,6,8] => ([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[[1,4,8],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4,8] => [7,3,5,1,6,2,4,8] => ([(0,7),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5),(5,7),(6,7)],8)
[[1,3,8],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3,8] => [7,4,1,5,6,2,3,8] => ([(0,7),(1,6),(2,3),(2,6),(3,5),(4,7),(5,7),(6,4)],8)
[[1,4,8],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4,8] => [6,3,5,1,7,2,4,8] => ([(0,7),(1,4),(1,6),(2,3),(2,7),(3,6),(4,7),(6,5),(7,5)],8)
[[1,3,8],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3,8] => [6,4,1,5,7,2,3,8] => ([(0,5),(1,7),(2,3),(2,5),(3,4),(4,6),(5,7),(7,6)],8)
[[1,4,8],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4,8] => [5,3,6,1,2,7,4,8] => ([(0,3),(1,5),(2,5),(2,7),(3,6),(3,7),(5,6),(6,4),(7,4)],8)
[[1,3,8],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3,8] => [5,4,1,6,2,7,3,8] => ([(0,7),(1,7),(2,3),(2,7),(3,4),(3,6),(4,5),(6,5),(7,6)],8)
[[1,3,8],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3,8] => [4,5,1,2,6,7,3,8] => ([(0,4),(1,5),(2,6),(3,6),(4,7),(5,3),(5,7),(7,2)],8)
[[1,6,7],[2,8],[3],[4],[5]] => [5,4,3,2,8,1,6,7] => [8,3,4,5,2,1,6,7] => ([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[1,4,7],[2,8],[3],[5],[6]] => [6,5,3,2,8,1,4,7] => [8,3,5,1,6,2,4,7] => ([(1,4),(1,7),(2,3),(2,6),(3,7),(4,6),(6,5),(7,5)],8)
[[1,3,7],[2,8],[4],[5],[6]] => [6,5,4,2,8,1,3,7] => [8,4,1,5,6,2,3,7] => ([(1,6),(2,3),(2,6),(3,5),(4,7),(5,7),(6,4)],8)
[[1,2,7],[3,8],[4],[5],[6]] => [6,5,4,3,8,1,2,7] => [8,1,4,5,6,3,2,7] => ([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[[1,4,6],[2,8],[3],[5],[7]] => [7,5,3,2,8,1,4,6] => [8,3,5,1,7,4,2,6] => ([(1,4),(1,5),(2,3),(2,5),(2,6),(3,7),(4,6),(4,7),(5,7)],8)
[[1,3,6],[2,8],[4],[5],[7]] => [7,5,4,2,8,1,3,6] => [8,4,1,5,7,3,2,6] => ([(1,6),(2,3),(2,4),(2,6),(3,7),(4,7),(6,5),(6,7)],8)
[[1,2,6],[3,8],[4],[5],[7]] => [7,5,4,3,8,1,2,6] => [8,1,4,5,7,2,3,6] => ([(1,4),(1,5),(3,7),(4,6),(5,3),(6,2),(6,7)],8)
[[1,4,5],[2,8],[3],[6],[7]] => [7,6,3,2,8,1,4,5] => [8,3,6,1,4,7,2,5] => ([(1,4),(1,5),(2,3),(2,5),(3,6),(4,7),(5,6),(5,7)],8)
[[1,2,5],[3,8],[4],[6],[7]] => [7,6,4,3,8,1,2,5] => [8,1,4,6,2,7,3,5] => ([(1,4),(1,5),(2,7),(3,6),(4,3),(4,7),(5,2),(5,6)],8)
[[1,3,4],[2,8],[5],[6],[7]] => [7,6,5,2,8,1,3,4] => [8,5,1,3,6,7,2,4] => ([(1,6),(2,3),(2,4),(3,7),(4,6),(4,7),(6,5)],8)
[[1,2,4],[3,8],[5],[6],[7]] => [7,6,5,3,8,1,2,4] => [8,1,5,2,6,7,3,4] => ([(1,3),(1,6),(3,7),(5,2),(6,5),(6,7),(7,4)],8)
[[1,2,3],[4,8],[5],[6],[7]] => [7,6,5,4,8,1,2,3] => [8,1,2,5,6,7,4,3] => ([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[[1,4,7],[2,6],[3],[5],[8]] => [8,5,3,2,6,1,4,7] => [6,3,5,1,8,2,4,7] => ([(0,6),(0,7),(1,4),(1,6),(2,3),(2,5),(3,6),(3,7),(4,5),(5,7)],8)
[[1,2,7],[3,6],[4],[5],[8]] => [8,5,4,3,6,1,2,7] => [6,1,4,5,8,3,2,7] => ([(0,6),(0,7),(1,2),(1,3),(1,5),(2,7),(3,7),(4,6),(4,7),(5,4)],8)
[[1,4,7],[2,5],[3],[6],[8]] => [8,6,3,2,5,1,4,7] => [5,3,6,1,2,8,4,7] => ([(0,3),(1,7),(2,6),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[[1,3,7],[2,5],[4],[6],[8]] => [8,6,4,2,5,1,3,7] => [5,4,1,6,2,8,3,7] => ([(0,7),(1,7),(2,3),(2,7),(3,4),(3,6),(4,5),(7,5),(7,6)],8)
[[1,3,7],[2,4],[5],[6],[8]] => [8,6,5,2,4,1,3,7] => [4,5,1,2,6,8,3,7] => ([(0,4),(1,5),(3,6),(4,7),(5,3),(5,7),(7,2),(7,6)],8)
[[1,2,7],[3,4],[5],[6],[8]] => [8,6,5,3,4,1,2,7] => [4,1,5,3,6,8,2,7] => ([(0,6),(1,3),(1,4),(1,6),(3,7),(4,5),(6,7),(7,2),(7,5)],8)
[[1,4,6],[2,7],[3],[5],[8]] => [8,5,3,2,7,1,4,6] => [7,3,5,1,8,4,2,6] => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,7),(4,6),(4,7),(5,7)],8)
[[1,3,6],[2,7],[4],[5],[8]] => [8,5,4,2,7,1,3,6] => [7,4,1,5,8,3,2,6] => ([(0,6),(1,5),(2,3),(2,4),(2,5),(3,7),(4,7),(5,6),(5,7)],8)
[[1,4,5],[2,7],[3],[6],[8]] => [8,6,3,2,7,1,4,5] => [7,3,6,1,4,8,2,5] => ([(0,7),(1,3),(1,5),(2,4),(2,5),(3,6),(4,7),(5,6),(5,7)],8)
[[1,3,5],[2,7],[4],[6],[8]] => [8,6,4,2,7,1,3,5] => [7,4,1,6,3,8,2,5] => ([(0,6),(1,5),(1,7),(2,3),(2,4),(2,5),(3,7),(4,6),(4,7),(5,6)],8)
[[1,2,4],[3,7],[5],[6],[8]] => [8,6,5,3,7,1,2,4] => [7,1,5,2,6,8,3,4] => ([(0,7),(1,3),(1,5),(3,6),(4,2),(5,4),(5,6),(6,7)],8)
[[1,2,6],[3,5],[4],[7],[8]] => [8,7,4,3,5,1,2,6] => [5,1,4,7,3,2,8,6] => ([(0,5),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
[[1,3,6],[2,4],[5],[7],[8]] => [8,7,5,2,4,1,3,6] => [4,5,1,2,7,3,8,6] => ([(0,3),(1,4),(2,5),(2,7),(3,5),(3,6),(4,2),(4,6),(6,7)],8)
[[1,2,6],[3,4],[5],[7],[8]] => [8,7,5,3,4,1,2,6] => [4,1,5,3,7,2,8,6] => ([(0,6),(1,2),(1,3),(1,6),(2,5),(2,7),(3,4),(3,7),(5,4),(6,5),(6,7)],8)
[[1,4,5],[2,6],[3],[7],[8]] => [8,7,3,2,6,1,4,5] => [6,3,7,1,4,2,8,5] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(3,7),(4,7),(5,6),(5,7)],8)
[[1,3,5],[2,6],[4],[7],[8]] => [8,7,4,2,6,1,3,5] => [6,4,1,7,3,2,8,5] => ([(0,5),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,7)],8)
[[1,2,5],[3,6],[4],[7],[8]] => [8,7,4,3,6,1,2,5] => [6,1,4,7,2,3,8,5] => ([(0,7),(1,2),(1,4),(2,5),(2,7),(3,5),(3,6),(4,3),(7,6)],8)
[[1,3,4],[2,6],[5],[7],[8]] => [8,7,5,2,6,1,3,4] => [6,5,1,3,7,2,8,4] => ([(0,7),(1,7),(2,3),(2,4),(3,6),(3,7),(4,5),(4,6),(7,5)],8)
[[1,2,4],[3,6],[5],[7],[8]] => [8,7,5,3,6,1,2,4] => [6,1,5,2,7,3,8,4] => ([(0,7),(1,3),(1,4),(3,7),(4,5),(4,7),(5,2),(5,6),(7,6)],8)
[[1,2,5],[3,4],[6],[7],[8]] => [8,7,6,3,4,1,2,5] => [4,1,6,3,2,7,8,5] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,7),(7,2)],8)
[[1,3,4],[2,5],[6],[7],[8]] => [8,7,6,2,5,1,3,4] => [5,6,1,3,2,7,8,4] => ([(0,5),(1,3),(1,4),(3,6),(3,7),(4,6),(4,7),(5,7),(7,2)],8)
[[1,2,4],[3,5],[6],[7],[8]] => [8,7,6,3,5,1,2,4] => [5,1,6,2,3,7,8,4] => ([(0,6),(1,5),(1,6),(4,3),(4,7),(5,4),(6,7),(7,2)],8)
[[1,7,8],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8] => [2,3,4,5,6,1,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[1,6,8],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6,8] => [2,3,4,5,7,1,6,8] => ([(0,7),(1,5),(2,6),(3,4),(4,2),(4,7),(5,3),(7,6)],8)
[[1,5,8],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5,8] => [2,3,4,6,1,7,5,8] => ([(0,6),(0,7),(1,3),(2,7),(3,4),(4,2),(4,6),(6,5),(7,5)],8)
[[1,3,8],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3,8] => [2,4,1,5,6,7,3,8] => ([(0,6),(0,7),(1,3),(1,7),(2,5),(3,6),(4,2),(6,4),(7,5)],8)
[[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [3,1,4,5,6,7,2,8] => ([(0,7),(1,3),(1,7),(2,6),(3,6),(4,5),(5,2),(7,4)],8)
[[1,6,7],[2],[3],[4],[5],[8]] => [8,5,4,3,2,1,6,7] => [2,3,4,5,8,1,6,7] => ([(0,7),(1,5),(4,6),(5,4),(6,2),(6,7),(7,3)],8)
[[1,5,7],[2],[3],[4],[6],[8]] => [8,6,4,3,2,1,5,7] => [2,3,4,6,1,8,5,7] => ([(0,6),(0,7),(1,3),(2,5),(2,7),(3,4),(4,2),(4,6),(6,5)],8)
[[1,4,7],[2],[3],[5],[6],[8]] => [8,6,5,3,2,1,4,7] => [2,3,5,1,6,8,4,7] => ([(0,6),(0,7),(1,4),(3,7),(4,3),(4,6),(6,5),(7,2),(7,5)],8)
[[1,3,7],[2],[4],[5],[6],[8]] => [8,6,5,4,2,1,3,7] => [2,4,1,5,6,8,3,7] => ([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(4,5),(6,4),(7,5)],8)
[[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => [3,1,4,5,6,8,2,7] => ([(0,7),(1,3),(1,7),(3,6),(4,5),(5,2),(5,6),(7,4)],8)
[[1,5,6],[2],[3],[4],[7],[8]] => [8,7,4,3,2,1,5,6] => [2,3,4,7,1,5,8,6] => ([(0,7),(1,5),(3,6),(4,3),(4,7),(5,4),(7,2),(7,6)],8)
[[1,4,6],[2],[3],[5],[7],[8]] => [8,7,5,3,2,1,4,6] => [2,3,5,1,7,4,8,6] => ([(0,2),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[[1,3,6],[2],[4],[5],[7],[8]] => [8,7,5,4,2,1,3,6] => [2,4,1,5,7,3,8,6] => ([(0,3),(0,7),(1,6),(1,7),(2,5),(3,6),(6,2),(6,4),(7,4),(7,5)],8)
[[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => [3,1,4,5,7,2,8,6] => ([(0,7),(1,3),(1,7),(2,5),(3,5),(3,6),(4,2),(4,6),(7,4)],8)
[[1,4,5],[2],[3],[6],[7],[8]] => [8,7,6,3,2,1,4,5] => [2,3,6,1,4,7,8,5] => ([(0,7),(1,5),(3,6),(5,3),(5,7),(6,4),(7,2),(7,6)],8)
[[1,3,5],[2],[4],[6],[7],[8]] => [8,7,6,4,2,1,3,5] => [2,4,1,6,3,7,8,5] => ([(0,3),(0,7),(1,6),(1,7),(3,4),(3,6),(5,2),(6,5),(7,4),(7,5)],8)
[[1,2,5],[3],[4],[6],[7],[8]] => [8,7,6,4,3,1,2,5] => [3,1,4,6,2,7,8,5] => ([(0,7),(1,3),(1,7),(2,6),(3,5),(3,6),(6,4),(7,2),(7,5)],8)
[[1,3,4],[2],[5],[6],[7],[8]] => [8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,4] => ([(0,7),(1,4),(1,7),(4,6),(5,3),(6,5),(7,2),(7,6)],8)
[[1,2,4],[3],[5],[6],[7],[8]] => [8,7,6,5,3,1,2,4] => [3,1,5,2,6,7,8,4] => ([(0,6),(0,7),(1,3),(1,7),(3,5),(3,6),(4,2),(5,4),(7,5)],8)
[[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,3] => ([(0,7),(1,5),(4,2),(5,3),(5,7),(6,4),(7,6)],8)
[[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => [6,7,8,4,1,2,3,5] => ([(0,7),(1,5),(2,6),(4,7),(5,3),(6,4)],8)
[[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => [6,7,8,1,5,2,3,4] => ([(0,7),(1,4),(1,6),(5,3),(6,5),(7,2)],8)
[[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => [6,7,1,8,5,2,4,3] => ([(0,5),(1,4),(1,6),(1,7),(5,7),(6,2),(6,3)],8)
[[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => [6,1,7,8,5,3,4,2] => ([(0,7),(1,3),(1,4),(1,6),(1,7),(6,2),(7,5)],8)
[[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => [5,7,8,1,2,6,3,4] => ([(0,6),(1,5),(1,7),(4,3),(5,2),(6,4),(6,7)],8)
[[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => [5,1,7,8,3,6,4,2] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(5,3),(5,6),(7,2)],8)
[[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => [4,7,1,2,8,6,5,3] => ([(0,4),(1,3),(1,6),(1,7),(3,5),(4,2),(4,5),(4,6),(4,7)],8)
[[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => [5,6,8,1,2,3,7,4] => ([(0,5),(1,6),(4,3),(4,7),(5,4),(6,2),(6,7)],8)
[[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => [5,1,6,8,3,4,7,2] => ([(0,7),(1,3),(1,5),(1,7),(4,6),(5,4),(7,2),(7,6)],8)
[[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => [4,6,1,2,8,5,7,3] => ([(0,3),(0,7),(1,4),(3,5),(3,6),(4,2),(4,6),(4,7),(7,5)],8)
[[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => ([(0,2),(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8)
[[1,5],[2,7],[3,8],[4],[6]] => [6,4,3,8,2,7,1,5] => [7,8,4,6,1,3,2,5] => ([(0,5),(1,6),(1,7),(2,3),(2,4),(3,7),(4,7)],8)
[[1,4],[2,7],[3,8],[5],[6]] => [6,5,3,8,2,7,1,4] => [7,8,5,1,6,3,2,4] => ([(0,6),(1,3),(2,4),(2,5),(2,6),(4,7),(5,7)],8)
[[1,3],[2,7],[4,8],[5],[6]] => [6,5,4,8,2,7,1,3] => [7,8,1,5,6,4,2,3] => ([(0,5),(1,4),(1,6),(1,7),(6,3),(7,2)],8)
[[1,4],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4] => [6,8,5,1,7,2,3,4] => ([(0,7),(1,6),(1,7),(2,4),(2,7),(5,3),(6,5)],8)
[[1,2],[3,5],[4,8],[6],[7]] => [7,6,4,8,3,5,1,2] => [5,1,8,6,3,7,4,2] => ([(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(4,2),(4,5),(7,5)],8)
[[1,3],[2,4],[5,8],[6],[7]] => [7,6,5,8,2,4,1,3] => [4,8,1,2,6,7,5,3] => ([(0,5),(1,4),(1,6),(1,7),(5,3),(5,6),(5,7),(7,2)],8)
[[1,2],[3,4],[5,8],[6],[7]] => [7,6,5,8,3,4,1,2] => [4,1,8,3,6,7,5,2] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(4,5),(4,7),(7,2)],8)
[[1,5],[2,6],[3,7],[4],[8]] => [8,4,3,7,2,6,1,5] => [6,7,4,8,1,2,3,5] => ([(0,6),(0,7),(1,3),(2,4),(3,7),(4,5),(5,6)],8)
[[1,4],[2,6],[3,7],[5],[8]] => [8,5,3,7,2,6,1,4] => [6,7,5,1,8,2,3,4] => ([(0,7),(1,4),(2,6),(2,7),(4,7),(5,3),(6,5)],8)
[[1,3],[2,6],[4,7],[5],[8]] => [8,5,4,7,2,6,1,3] => [6,7,1,5,8,2,4,3] => ([(0,5),(1,4),(1,6),(4,7),(5,7),(6,2),(6,3)],8)
[[1,2],[3,6],[4,7],[5],[8]] => [8,5,4,7,3,6,1,2] => [6,1,7,5,8,3,4,2] => ([(0,7),(1,3),(1,4),(1,5),(1,7),(4,6),(5,2),(7,6)],8)
[[1,4],[2,5],[3,7],[6],[8]] => [8,6,3,7,2,5,1,4] => [5,7,6,1,2,8,3,4] => ([(0,6),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(6,7)],8)
[[1,3],[2,5],[4,7],[6],[8]] => [8,6,4,7,2,5,1,3] => [5,7,1,6,2,8,4,3] => ([(0,4),(0,6),(1,5),(1,6),(4,7),(5,2),(5,3),(5,7),(6,7)],8)
[[1,2],[3,4],[5,7],[6],[8]] => [8,6,5,7,3,4,1,2] => [4,1,7,3,6,8,5,2] => ([(0,2),(0,3),(0,7),(1,5),(1,6),(1,7),(3,5),(3,6),(6,4),(7,4)],8)
[[1,4],[2,5],[3,6],[7],[8]] => [8,7,3,6,2,5,1,4] => [5,6,7,1,2,3,8,4] => ([(0,5),(1,6),(3,7),(4,2),(4,7),(5,3),(6,4)],8)
[[1,3],[2,5],[4,6],[7],[8]] => [8,7,4,6,2,5,1,3] => [5,6,1,7,2,4,8,3] => ([(0,4),(1,5),(1,7),(3,6),(4,7),(5,2),(5,3),(7,6)],8)
[[1,2],[3,5],[4,6],[7],[8]] => [8,7,4,6,3,5,1,2] => [5,1,6,7,3,4,8,2] => ([(0,7),(1,2),(1,5),(1,7),(3,6),(4,6),(5,4),(7,3)],8)
[[1,3],[2,4],[5,6],[7],[8]] => [8,7,5,6,2,4,1,3] => [4,6,1,2,7,5,8,3] => ([(0,3),(0,7),(1,4),(3,5),(4,2),(4,5),(4,7),(5,6),(7,6)],8)
[[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => [4,1,6,3,7,5,8,2] => ([(0,2),(0,3),(0,7),(1,6),(1,7),(3,5),(3,6),(5,4),(6,4),(7,5)],8)
[[1,7],[2,8],[3],[4],[5],[6]] => [6,5,4,3,2,8,1,7] => [8,3,4,5,6,2,1,7] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[1,6],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6] => [8,3,4,5,7,1,2,6] => ([(1,6),(2,4),(4,7),(5,3),(5,7),(6,5)],8)
[[1,5],[2,8],[3],[4],[6],[7]] => [7,6,4,3,2,8,1,5] => [8,3,4,6,1,7,2,5] => ([(1,4),(2,3),(2,6),(3,7),(4,5),(4,7),(5,6)],8)
[[1,4],[2,8],[3],[5],[6],[7]] => [7,6,5,3,2,8,1,4] => [8,3,5,1,6,7,2,4] => ([(1,5),(1,7),(2,3),(2,6),(3,7),(5,6),(7,4)],8)
[[1,3],[2,8],[4],[5],[6],[7]] => [7,6,5,4,2,8,1,3] => [8,4,1,5,6,7,2,3] => ([(1,7),(2,5),(2,7),(5,4),(6,3),(7,6)],8)
[[1,2],[3,8],[4],[5],[6],[7]] => [7,6,5,4,3,8,1,2] => [8,1,4,5,6,7,3,2] => ([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[[1,6],[2,7],[3],[4],[5],[8]] => [8,5,4,3,2,7,1,6] => [7,3,4,5,8,1,2,6] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(5,7)],8)
[[1,4],[2,7],[3],[5],[6],[8]] => [8,6,5,3,2,7,1,4] => [7,3,5,1,6,8,2,4] => ([(0,5),(1,4),(1,6),(2,3),(2,7),(3,6),(4,7),(7,5)],8)
[[1,3],[2,7],[4],[5],[6],[8]] => [8,6,5,4,2,7,1,3] => [7,4,1,5,6,8,2,3] => ([(0,7),(1,6),(2,3),(2,6),(3,5),(4,7),(6,4)],8)
[[1,2],[3,7],[4],[5],[6],[8]] => [8,6,5,4,3,7,1,2] => [7,1,4,5,6,8,3,2] => ([(0,7),(1,2),(1,3),(1,6),(4,7),(5,4),(6,5)],8)
[[1,4],[2,6],[3],[5],[7],[8]] => [8,7,5,3,2,6,1,4] => [6,3,5,1,7,2,8,4] => ([(0,7),(1,4),(1,7),(2,3),(2,5),(3,7),(4,5),(4,6),(7,6)],8)
[[1,3],[2,6],[4],[5],[7],[8]] => [8,7,5,4,2,6,1,3] => [6,4,1,5,7,2,8,3] => ([(0,6),(1,5),(2,3),(2,5),(3,4),(3,7),(5,6),(6,7)],8)
[[1,4],[2,5],[3],[6],[7],[8]] => [8,7,6,3,2,5,1,4] => [5,3,6,1,2,7,8,4] => ([(0,5),(1,5),(1,6),(2,4),(4,6),(4,7),(5,7),(7,3)],8)
[[1,3],[2,5],[4],[6],[7],[8]] => [8,7,6,4,2,5,1,3] => [5,4,1,6,2,7,8,3] => ([(0,7),(1,7),(2,3),(2,7),(3,5),(3,6),(6,4),(7,6)],8)
[[1,3],[2,4],[5],[6],[7],[8]] => [8,7,6,5,2,4,1,3] => [4,5,1,2,6,7,8,3] => ([(0,6),(1,4),(4,7),(5,3),(6,2),(6,7),(7,5)],8)
[[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => [4,1,5,3,6,7,8,2] => ([(0,7),(1,3),(1,4),(1,7),(4,6),(5,2),(6,5),(7,6)],8)
[[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,1,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[1,7],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7] => [2,3,4,5,6,8,1,7] => ([(0,7),(1,5),(3,4),(4,6),(5,3),(6,2),(6,7)],8)
[[1,6],[2],[3],[4],[5],[7],[8]] => [8,7,5,4,3,2,1,6] => [2,3,4,5,7,1,8,6] => ([(0,6),(0,7),(1,4),(2,7),(3,5),(4,3),(5,2),(5,6)],8)
[[1,5],[2],[3],[4],[6],[7],[8]] => [8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,5] => ([(0,6),(0,7),(1,4),(2,7),(4,5),(5,2),(5,6),(7,3)],8)
[[1,4],[2],[3],[5],[6],[7],[8]] => [8,7,6,5,3,2,1,4] => [2,3,5,1,6,7,8,4] => ([(0,6),(0,7),(1,4),(3,6),(4,3),(4,7),(5,2),(6,5)],8)
[[1,3],[2],[4],[5],[6],[7],[8]] => [8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,3] => ([(0,6),(0,7),(1,3),(1,7),(3,6),(4,2),(5,4),(6,5)],8)
[[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,2] => ([(0,7),(1,3),(1,7),(4,5),(5,2),(6,4),(7,6)],8)
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[1,2,4,6,8],[3,5,7,9,10]] => [3,5,7,9,10,1,2,4,6,8] => [10,1,3,2,5,4,7,6,9,8] => ([(1,2),(1,3),(2,8),(2,9),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
[[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => ([(1,8),(4,7),(5,9),(6,4),(7,2),(8,5),(9,3),(9,6)],10)
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [3,5,7,9,11,12,1,2,4,6,8,10] => [12,1,3,2,5,4,7,6,9,8,11,10] => ([(1,2),(1,3),(2,10),(2,11),(3,10),(3,11),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,1,2,3,4,5,7,8,9,10,11,6] => ([(1,10),(4,5),(5,9),(6,7),(7,11),(8,4),(9,2),(10,6),(11,3),(11,8)],12)
[[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => ([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)
[[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,8,7] => ([(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3)],9)
[[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,9,7] => ([(0,8),(1,6),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],9)
[[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => [9,1,2,3,4,5,7,8,6] => ([(1,7),(4,5),(5,8),(6,2),(7,4),(8,3),(8,6)],9)
[[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,9,6] => ([(0,8),(1,6),(4,5),(5,7),(6,4),(7,2),(7,8),(8,3)],9)
[[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,9,5] => ([(0,8),(1,5),(4,6),(5,4),(6,2),(6,8),(7,3),(8,7)],9)
[[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,9,4] => ([(0,8),(1,5),(4,2),(5,6),(6,3),(6,8),(7,4),(8,7)],9)
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,9,3] => ([(0,8),(1,6),(4,5),(5,2),(6,3),(6,8),(7,4),(8,7)],9)
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,2] => ([(0,8),(1,3),(1,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,1] => ([(1,8),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],9)
[[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => ([(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],10)
[[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => [10,1,2,3,4,5,6,7,9,8] => ([(1,8),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(9,3)],10)
[[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,10,8] => ([(0,9),(1,7),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(8,9)],10)
[[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,9,10,7] => ([(0,9),(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,9),(9,3)],10)
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,9,10,6] => ([(0,9),(1,6),(4,5),(5,7),(6,4),(7,2),(7,9),(8,3),(9,8)],10)
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,9,10,5] => ([(0,9),(1,6),(4,7),(5,2),(6,4),(7,3),(7,9),(8,5),(9,8)],10)
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,9,10,4] => ([(0,9),(1,6),(4,5),(5,2),(6,7),(7,3),(7,9),(8,4),(9,8)],10)
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,9,10,3] => ([(0,9),(1,7),(4,6),(5,4),(6,2),(7,3),(7,9),(8,5),(9,8)],10)
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => [3,1,4,5,6,7,8,9,10,2] => ([(0,9),(1,3),(1,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => ([(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],10)
[[1,2,3,4,5,6,7,8,9,10,11,12]] => [1,2,3,4,5,6,7,8,9,10,11,12] => [1,2,3,4,5,6,7,8,9,10,11,12] => ([(0,11),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,10),(9,7),(10,1),(11,9)],12)
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1] => ([(1,11),(3,4),(4,6),(5,3),(6,8),(7,5),(8,10),(9,7),(10,2),(11,9)],12)
[[1,3,4,5,6,7,8,9],[2]] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[[1,4,5,6,7,8,9],[2],[3]] => [3,2,1,4,5,6,7,8,9] => [2,3,1,4,5,6,7,8,9] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[[1,5,6,7,8,9],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9] => [2,3,4,1,5,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[[1,6,7,8,9],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9] => [2,3,4,5,1,6,7,8,9] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[[1,7,8,9],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,1,7,8,9] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,1,8,9] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7] => [9,3,4,5,6,8,1,2,7] => ([(1,7),(2,4),(4,8),(5,6),(6,3),(6,8),(7,5)],9)
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,1,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[[1,3,4,5,6,7,8,9,10],[2]] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[1,4,5,6,7,8,9,10],[2],[3]] => [3,2,1,4,5,6,7,8,9,10] => [2,3,1,4,5,6,7,8,9,10] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[1,5,6,7,8,9,10],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9,10] => [2,3,4,1,5,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9,10] => [2,3,4,5,1,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9,10] => [2,3,4,5,6,1,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9,10] => [2,3,4,5,6,7,1,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9,10] => [2,3,4,5,6,7,8,1,9,10] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,10,1,8] => [10,3,4,5,6,7,9,1,2,8] => ([(1,8),(2,4),(4,9),(5,7),(6,5),(7,3),(7,9),(8,6)],10)
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => [2,3,4,5,6,7,8,9,1,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[[1,8],[2,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,9,1,8] => [9,3,4,5,6,7,2,1,8] => ([(1,4),(2,8),(3,8),(4,7),(5,8),(6,5),(7,6)],9)
[[1,3,5,7,9],[2,4,6,8]] => [2,4,6,8,1,3,5,7,9] => [8,2,1,4,3,6,5,7,9] => ([(0,3),(1,7),(1,8),(2,7),(2,8),(4,6),(5,6),(6,3),(7,4),(7,5),(8,4),(8,5)],9)
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,10,1,9] => [10,3,4,5,6,7,8,2,1,9] => ([(1,9),(2,9),(3,8),(4,9),(5,7),(6,5),(7,4),(8,6)],10)
[[1,3],[2,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,4,1,3] => [4,5,1,2,6,7,8,9,3] => ([(0,7),(1,4),(4,8),(5,3),(6,5),(7,2),(7,8),(8,6)],9)
[[1,5],[2,6],[3,7],[4,8],[9]] => [9,4,8,3,7,2,6,1,5] => [6,7,8,9,1,2,3,4,5] => ([(0,7),(1,8),(4,5),(5,2),(6,3),(7,6),(8,4)],9)
[[1,3,5],[2,4,6],[7],[8],[9]] => [9,8,7,2,4,6,1,3,5] => [6,7,1,2,3,4,8,9,5] => ([(0,7),(1,4),(4,8),(5,6),(6,2),(6,8),(7,5),(8,3)],9)
[[1,2,4,6],[3,5,7],[8],[9]] => [9,8,3,5,7,1,2,4,6] => [7,1,8,2,3,4,5,9,6] => ([(0,8),(1,5),(1,8),(3,4),(4,6),(5,3),(6,2),(6,7),(8,7)],9)
[[1,3,5,7],[2,4,6,8],[9]] => [9,2,4,6,8,1,3,5,7] => [8,9,1,2,3,4,5,6,7] => ([(0,8),(1,3),(4,5),(5,7),(6,4),(7,2),(8,6)],9)
[[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => [8,1,2,9,3,4,5,6,7] => ([(0,8),(1,7),(3,4),(4,6),(5,3),(6,2),(7,5),(7,8)],9)
[[1,2,3,4,5,7],[6,8],[9]] => [9,6,8,1,2,3,4,5,7] => [8,1,2,3,4,9,5,6,7] => ([(0,8),(1,6),(3,7),(4,5),(5,2),(6,3),(7,4),(7,8)],9)
[[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => [9,1,2,3,4,5,7,6,8] => ([(1,6),(2,8),(3,8),(4,5),(5,7),(6,4),(7,2),(7,3)],9)
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [10,5,9,4,8,3,7,1,2,6] => [7,1,8,9,10,2,3,4,5,6] => ([(0,9),(1,7),(1,9),(4,6),(5,4),(6,2),(7,5),(8,3),(9,8)],10)
[[1,4,7],[2,5,8],[3,6,9],[10]] => [10,3,6,9,2,5,8,1,4,7] => [8,9,10,1,2,3,4,5,6,7] => ([(0,9),(1,8),(4,5),(5,7),(6,4),(7,3),(8,6),(9,2)],10)
[[1,3,5,7],[2,4,6,8],[9],[10]] => [10,9,2,4,6,8,1,3,5,7] => [8,9,1,2,3,4,5,6,10,7] => ([(0,8),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(7,9),(8,6)],10)
[[1,2,4,6,8],[3,5,7,9],[10]] => [10,3,5,7,9,1,2,4,6,8] => [9,1,10,2,3,4,5,6,7,8] => ([(0,9),(1,8),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => [8,1,2,3,4,5,7,6,9] => ([(0,8),(1,6),(2,8),(3,8),(4,5),(5,7),(6,4),(7,2),(7,3)],9)
[[1,2,3,4,5,6,9],[7],[8]] => [8,7,1,2,3,4,5,6,9] => [7,1,2,3,4,5,8,6,9] => ([(0,8),(1,6),(2,7),(3,5),(4,3),(5,2),(5,8),(6,4),(8,7)],9)
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [3,1,4,5,6,7,8,2,9] => ([(0,8),(1,3),(1,8),(2,7),(3,7),(4,6),(5,4),(6,2),(8,5)],9)
[[1,3],[2,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,2,9,1,3] => [9,4,1,5,6,7,8,2,3] => ([(1,8),(2,6),(2,8),(5,3),(6,4),(7,5),(8,7)],9)
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[[1,2,3,4,5,6,7,10],[8,9]] => [8,9,1,2,3,4,5,6,7,10] => [9,1,2,3,4,5,6,8,7,10] => ([(0,9),(1,7),(2,9),(3,9),(4,6),(5,4),(6,8),(7,5),(8,2),(8,3)],10)
[[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,10,1,3] => [10,4,1,5,6,7,8,9,2,3] => ([(1,9),(2,7),(2,9),(5,6),(6,3),(7,4),(8,5),(9,8)],10)
[] => [] => [] => ([],0)
[[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => [3,1,2,4,5,6,7,8,9] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[[1,3,5,6,7,8,9],[2],[4]] => [4,2,1,3,5,6,7,8,9] => [2,4,1,3,5,6,7,8,9] => ([(0,7),(1,3),(1,7),(3,8),(4,6),(5,4),(6,2),(7,8),(8,5)],9)
[[1,4,6,7,8,9],[2],[3],[5]] => [5,3,2,1,4,6,7,8,9] => [2,3,5,1,4,6,7,8,9] => ([(0,7),(1,6),(3,8),(4,5),(5,2),(6,3),(6,7),(7,8),(8,4)],9)
[[1,5,7,8,9],[2],[3],[4],[6]] => [6,4,3,2,1,5,7,8,9] => [2,3,4,6,1,5,7,8,9] => ([(0,7),(1,5),(3,8),(4,2),(5,6),(6,3),(6,7),(7,8),(8,4)],9)
[[1,6,8,9],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6,8,9] => [2,3,4,5,7,1,6,8,9] => ([(0,8),(1,6),(2,7),(4,5),(5,2),(5,8),(6,4),(7,3),(8,7)],9)
[[1,7,9],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7,9] => [2,3,4,5,6,8,1,7,9] => ([(0,8),(1,6),(2,7),(3,5),(4,3),(5,2),(5,8),(6,4),(8,7)],9)
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,9,1,8] => ([(0,8),(1,6),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],9)
[[1,2,4,5,6,7,8,9,10],[3]] => [3,1,2,4,5,6,7,8,9,10] => [3,1,2,4,5,6,7,8,9,10] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[1,3,5,6,7,8,9,10],[2],[4]] => [4,2,1,3,5,6,7,8,9,10] => [2,4,1,3,5,6,7,8,9,10] => ([(0,8),(1,3),(1,8),(3,9),(4,5),(5,7),(6,4),(7,2),(8,9),(9,6)],10)
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [10,8,7,6,5,4,3,2,1,9] => [2,3,4,5,6,7,8,10,1,9] => ([(0,9),(1,7),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(8,9)],10)
[[1,3,4,5,6,7,8],[2,9]] => [2,9,1,3,4,5,6,7,8] => [9,2,1,3,4,5,6,7,8] => ([(1,8),(2,8),(4,6),(5,4),(6,3),(7,5),(8,7)],9)
[[1,3,4,5,6,7,8],[2],[9]] => [9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,8] => ([(0,8),(1,3),(1,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[[1,3,4,5,6,7],[2],[8],[9]] => [9,8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,9,7] => ([(0,8),(1,3),(1,8),(3,7),(4,6),(5,4),(6,2),(6,7),(8,5)],9)
[[1,3,4,5,6],[2],[7],[8],[9]] => [9,8,7,2,1,3,4,5,6] => [2,7,1,3,4,5,8,9,6] => ([(0,7),(1,4),(1,7),(4,8),(5,3),(5,8),(6,5),(7,6),(8,2)],9)
[[1,3,4],[2],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,9,4] => ([(0,8),(1,4),(1,8),(4,7),(5,3),(6,5),(7,6),(8,2),(8,7)],9)
[[1,3],[2],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,9,3] => ([(0,7),(0,8),(1,3),(1,7),(3,8),(4,6),(5,4),(6,2),(8,5)],9)
[[1,3,4,5,6,7,8,9],[2,10]] => [2,10,1,3,4,5,6,7,8,9] => [10,2,1,3,4,5,6,7,8,9] => ([(1,9),(2,9),(4,5),(5,7),(6,4),(7,3),(8,6),(9,8)],10)
[[1,3,4,5,6,7,8,9],[2],[10]] => [10,2,1,3,4,5,6,7,8,9] => [2,10,1,3,4,5,6,7,8,9] => ([(0,9),(1,3),(1,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[[1,3,4,5,6,7,8],[2,9,10]] => [2,9,10,1,3,4,5,6,7,8] => [10,2,1,3,4,5,6,7,9,8] => ([(1,9),(2,9),(5,6),(6,8),(7,5),(8,3),(8,4),(9,7)],10)
[[1,3,4,5,6,7,8],[2],[9],[10]] => [10,9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,10,8] => ([(0,9),(1,3),(1,9),(3,8),(4,5),(5,7),(6,4),(7,2),(7,8),(9,6)],10)
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,2,1,3,4] => [2,5,1,3,6,7,8,9,10,4] => ([(0,9),(1,4),(1,9),(4,8),(5,6),(6,3),(7,5),(8,7),(9,2),(9,8)],10)
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,2,1,3] => [2,4,1,5,6,7,8,9,10,3] => ([(0,8),(0,9),(1,3),(1,8),(3,9),(4,5),(5,7),(6,4),(7,2),(9,6)],10)
[[1,2,3,5,6,7,8,9,10],[4]] => [4,1,2,3,5,6,7,8,9,10] => [4,1,2,3,5,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[[1,2,3,4,6,7,8,9,10],[5]] => [5,1,2,3,4,6,7,8,9,10] => [5,1,2,3,4,6,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[[1,2,3,4,5,6,7,9,10],[8]] => [8,1,2,3,4,5,6,7,9,10] => [8,1,2,3,4,5,6,7,9,10] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[[1,2,3,4,5,6,8,9,10],[7]] => [7,1,2,3,4,5,6,8,9,10] => [7,1,2,3,4,5,6,8,9,10] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[[1,2,3,4,5,7,8,9,10],[6]] => [6,1,2,3,4,5,7,8,9,10] => [6,1,2,3,4,5,7,8,9,10] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[[1,2,4,5,6,7,8,9,10,11,12],[3]] => [3,1,2,4,5,6,7,8,9,10,11,12] => [3,1,2,4,5,6,7,8,9,10,11,12] => ([(0,11),(1,3),(3,11),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8),(11,10)],12)
[[1,4,5,6,7,8],[2],[3],[9]] => [9,3,2,1,4,5,6,7,8] => [2,3,9,1,4,5,6,7,8] => ([(0,8),(1,6),(4,5),(5,2),(6,3),(6,8),(7,4),(8,7)],9)
[[1,5,6,7,8],[2],[3],[4],[9]] => [9,4,3,2,1,5,6,7,8] => [2,3,4,9,1,5,6,7,8] => ([(0,8),(1,5),(4,2),(5,6),(6,3),(6,8),(7,4),(8,7)],9)
[[1,6,7,8],[2],[3],[4],[5],[9]] => [9,5,4,3,2,1,6,7,8] => [2,3,4,5,9,1,6,7,8] => ([(0,8),(1,5),(4,6),(5,4),(6,2),(6,8),(7,3),(8,7)],9)
[[1,7,8],[2],[3],[4],[5],[6],[9]] => [9,6,5,4,3,2,1,7,8] => [2,3,4,5,6,9,1,7,8] => ([(0,8),(1,6),(4,5),(5,7),(6,4),(7,2),(7,8),(8,3)],9)
[[1,4,5,6,7,8,9],[2],[3],[10]] => [10,3,2,1,4,5,6,7,8,9] => [2,3,10,1,4,5,6,7,8,9] => ([(0,9),(1,7),(4,6),(5,4),(6,2),(7,3),(7,9),(8,5),(9,8)],10)
[[1,5,6,7,8,9],[2],[3],[4],[10]] => [10,4,3,2,1,5,6,7,8,9] => [2,3,4,10,1,5,6,7,8,9] => ([(0,9),(1,6),(4,5),(5,2),(6,7),(7,3),(7,9),(8,4),(9,8)],10)
[[1,6,7,8,9],[2],[3],[4],[5],[10]] => [10,5,4,3,2,1,6,7,8,9] => [2,3,4,5,10,1,6,7,8,9] => ([(0,9),(1,6),(4,7),(5,2),(6,4),(7,3),(7,9),(8,5),(9,8)],10)
[[1,7,8,9],[2],[3],[4],[5],[6],[10]] => [10,6,5,4,3,2,1,7,8,9] => [2,3,4,5,6,10,1,7,8,9] => ([(0,9),(1,6),(4,5),(5,7),(6,4),(7,2),(7,9),(8,3),(9,8)],10)
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [10,7,6,5,4,3,2,1,8,9] => [2,3,4,5,6,7,10,1,8,9] => ([(0,9),(1,7),(4,6),(5,4),(6,8),(7,5),(8,2),(8,9),(9,3)],10)
[[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => [3,1,4,2,5,6,7,8,9] => ([(0,7),(1,3),(1,7),(3,8),(4,6),(5,4),(6,2),(7,8),(8,5)],9)
[[1,2,5,6,7,8,9,10],[3],[4]] => [4,3,1,2,5,6,7,8,9,10] => [3,1,4,2,5,6,7,8,9,10] => ([(0,8),(1,3),(1,8),(3,9),(4,5),(5,7),(6,4),(7,2),(8,9),(9,6)],10)
[[1,2,5,6,7,8],[3],[4],[9]] => [9,4,3,1,2,5,6,7,8] => [3,1,4,9,2,5,6,7,8] => ([(0,8),(1,4),(1,8),(4,7),(5,3),(6,5),(7,6),(8,2),(8,7)],9)
[[1,2,7,8],[3],[4],[5],[6],[9]] => [9,6,5,4,3,1,2,7,8] => [3,1,4,5,6,9,2,7,8] => ([(0,7),(1,4),(1,7),(4,8),(5,3),(5,8),(6,5),(7,6),(8,2)],9)
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,2,1,4] => [2,3,5,1,6,7,8,9,10,4] => ([(0,8),(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(7,8),(9,5)],10)
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,3,2,1,5] => [2,3,4,6,1,7,8,9,10,5] => ([(0,8),(0,9),(1,6),(3,9),(4,5),(5,2),(6,7),(7,3),(7,8),(9,4)],10)
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => [10,9,7,6,5,4,3,2,1,8] => [2,3,4,5,6,7,9,1,10,8] => ([(0,8),(0,9),(1,6),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(7,8)],10)
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => [10,9,8,6,5,4,3,2,1,7] => [2,3,4,5,6,8,1,9,10,7] => ([(0,8),(0,9),(1,6),(2,9),(4,5),(5,7),(6,4),(7,2),(7,8),(9,3)],10)
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => [10,9,8,7,5,4,3,2,1,6] => [2,3,4,5,7,1,8,9,10,6] => ([(0,8),(0,9),(1,6),(3,9),(4,7),(5,2),(6,4),(7,3),(7,8),(9,5)],10)
[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]] => [12,10,9,8,7,6,5,4,3,2,1,11] => [2,3,4,5,6,7,8,9,10,12,1,11] => ([(0,11),(1,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,10),(9,7),(10,2),(10,11)],12)
[[1,2,3,4,5,7],[6],[8],[9]] => [9,8,6,1,2,3,4,5,7] => [6,1,2,3,4,8,5,9,7] => ([(0,7),(0,8),(1,4),(2,6),(2,8),(3,5),(4,3),(5,2),(5,7),(7,6)],9)
[[1,2,3,4,5,6,8],[7],[9]] => [9,7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,9,6,8] => ([(0,7),(0,8),(1,5),(2,8),(3,4),(4,6),(5,3),(6,2),(6,7)],9)
[[1,2,3,4,5,7,9],[6,8]] => [6,8,1,2,3,4,5,7,9] => [8,1,2,3,4,6,5,7,9] => ([(0,8),(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3),(7,8)],9)
[[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => [9,1,3,2,4,5,6,7,8] => ([(1,3),(1,4),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9)
[[1,2,3,4,5,6],[7,9],[8]] => [8,7,9,1,2,3,4,5,6] => [9,1,2,3,4,5,8,7,6] => ([(1,7),(5,6),(6,8),(7,5),(8,2),(8,3),(8,4)],9)
[[1,2,3,4,5,6,7],[8,10],[9]] => [9,8,10,1,2,3,4,5,6,7] => [10,1,2,3,4,5,6,9,8,7] => ([(1,8),(5,7),(6,5),(7,9),(8,6),(9,2),(9,3),(9,4)],10)
[[1,3,4,5,6,7,9],[2,8]] => [2,8,1,3,4,5,6,7,9] => [8,2,1,3,4,5,6,7,9] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[[1,3,4,5,6,7,8,10],[2,9]] => [2,9,1,3,4,5,6,7,8,10] => [9,2,1,3,4,5,6,7,8,10] => ([(0,9),(1,9),(2,8),(3,8),(4,5),(5,7),(6,4),(7,3),(9,6)],10)
[[1,2,3,4,5,6,8],[7,10],[9]] => [9,7,10,1,2,3,4,5,6,8] => [10,1,2,3,4,5,9,6,7,8] => ([(1,8),(4,5),(5,9),(6,7),(7,2),(8,4),(9,3),(9,6)],10)
[[1,7,8],[2,9],[3],[4],[5],[6]] => [6,5,4,3,2,9,1,7,8] => [9,3,4,5,6,2,1,7,8] => ([(1,8),(2,8),(3,4),(4,6),(6,7),(7,8),(8,5)],9)
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
searching the database
Sorry, this map was not found in the database.