Identifier
Mp00112:
Set partitions
—complement⟶
Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Images
{{1}} => {{1}} => [1] => ([],1)
{{1,2}} => {{1,2}} => [2,1] => ([(0,1)],2)
{{1},{2}} => {{1},{2}} => [1,2] => ([],2)
{{1,2,3}} => {{1,2,3}} => [2,3,1] => ([(0,2),(1,2)],3)
{{1,2},{3}} => {{1},{2,3}} => [1,3,2] => ([(1,2)],3)
{{1,3},{2}} => {{1,3},{2}} => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
{{1},{2,3}} => {{1,2},{3}} => [2,1,3] => ([(1,2)],3)
{{1},{2},{3}} => {{1},{2},{3}} => [1,2,3] => ([],3)
{{1,2,3,4}} => {{1,2,3,4}} => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
{{1,2,3},{4}} => {{1},{2,3,4}} => [1,3,4,2] => ([(1,3),(2,3)],4)
{{1,2,4},{3}} => {{1,3,4},{2}} => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
{{1,2},{3,4}} => {{1,2},{3,4}} => [2,1,4,3] => ([(0,3),(1,2)],4)
{{1,2},{3},{4}} => {{1},{2},{3,4}} => [1,2,4,3] => ([(2,3)],4)
{{1,3,4},{2}} => {{1,2,4},{3}} => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
{{1,3},{2,4}} => {{1,3},{2,4}} => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
{{1,3},{2},{4}} => {{1},{2,4},{3}} => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
{{1,4},{2,3}} => {{1,4},{2,3}} => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
{{1},{2,3,4}} => {{1,2,3},{4}} => [2,3,1,4] => ([(1,3),(2,3)],4)
{{1},{2,3},{4}} => {{1},{2,3},{4}} => [1,3,2,4] => ([(2,3)],4)
{{1,4},{2},{3}} => {{1,4},{2},{3}} => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
{{1},{2,4},{3}} => {{1,3},{2},{4}} => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
{{1},{2},{3,4}} => {{1,2},{3},{4}} => [2,1,3,4] => ([(2,3)],4)
{{1},{2},{3},{4}} => {{1},{2},{3},{4}} => [1,2,3,4] => ([],4)
{{1,2,3,4,5}} => {{1,2,3,4,5}} => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
{{1,2,3,4},{5}} => {{1},{2,3,4,5}} => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
{{1,2,3,5},{4}} => {{1,3,4,5},{2}} => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
{{1,2,3},{4,5}} => {{1,2},{3,4,5}} => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
{{1,2,3},{4},{5}} => {{1},{2},{3,4,5}} => [1,2,4,5,3] => ([(2,4),(3,4)],5)
{{1,2,4,5},{3}} => {{1,2,4,5},{3}} => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
{{1,2,4},{3,5}} => {{1,3},{2,4,5}} => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
{{1,2,4},{3},{5}} => {{1},{2,4,5},{3}} => [1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
{{1,2,5},{3,4}} => {{1,4,5},{2,3}} => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1,2},{3,4,5}} => {{1,2,3},{4,5}} => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
{{1,2},{3,4},{5}} => {{1},{2,3},{4,5}} => [1,3,2,5,4] => ([(1,4),(2,3)],5)
{{1,2,5},{3},{4}} => {{1,4,5},{2},{3}} => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1,2},{3,5},{4}} => {{1,3},{2},{4,5}} => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
{{1,2},{3},{4,5}} => {{1,2},{3},{4,5}} => [2,1,3,5,4] => ([(1,4),(2,3)],5)
{{1,2},{3},{4},{5}} => {{1},{2},{3},{4,5}} => [1,2,3,5,4] => ([(3,4)],5)
{{1,3,4,5},{2}} => {{1,2,3,5},{4}} => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
{{1,3,4},{2,5}} => {{1,4},{2,3,5}} => [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
{{1,3,4},{2},{5}} => {{1},{2,3,5},{4}} => [1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
{{1,3,5},{2,4}} => {{1,3,5},{2,4}} => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1,3},{2,4,5}} => {{1,2,4},{3,5}} => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
{{1,3},{2,4},{5}} => {{1},{2,4},{3,5}} => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
{{1,3,5},{2},{4}} => {{1,3,5},{2},{4}} => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
{{1,3},{2,5},{4}} => {{1,4},{2},{3,5}} => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
{{1,3},{2},{4,5}} => {{1,2},{3,5},{4}} => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
{{1,3},{2},{4},{5}} => {{1},{2},{3,5},{4}} => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
{{1,4,5},{2,3}} => {{1,2,5},{3,4}} => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1,4},{2,3,5}} => {{1,3,4},{2,5}} => [3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
{{1,4},{2,3},{5}} => {{1},{2,5},{3,4}} => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1,5},{2,3,4}} => {{1,5},{2,3,4}} => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2,3,4,5}} => {{1,2,3,4},{5}} => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
{{1},{2,3,4},{5}} => {{1},{2,3,4},{5}} => [1,3,4,2,5] => ([(2,4),(3,4)],5)
{{1,5},{2,3},{4}} => {{1,5},{2},{3,4}} => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2,3,5},{4}} => {{1,3,4},{2},{5}} => [3,2,4,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2,3},{4,5}} => {{1,2},{3,4},{5}} => [2,1,4,3,5] => ([(1,4),(2,3)],5)
{{1},{2,3},{4},{5}} => {{1},{2},{3,4},{5}} => [1,2,4,3,5] => ([(3,4)],5)
{{1,4,5},{2},{3}} => {{1,2,5},{3},{4}} => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1,4},{2,5},{3}} => {{1,4},{2,5},{3}} => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
{{1,4},{2},{3,5}} => {{1,3},{2,5},{4}} => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
{{1,4},{2},{3},{5}} => {{1},{2,5},{3},{4}} => [1,5,3,4,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1,5},{2,4},{3}} => {{1,5},{2,4},{3}} => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2,4,5},{3}} => {{1,2,4},{3},{5}} => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2,4},{3,5}} => {{1,3},{2,4},{5}} => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
{{1},{2,4},{3},{5}} => {{1},{2,4},{3},{5}} => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
{{1,5},{2},{3,4}} => {{1,5},{2,3},{4}} => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2,5},{3,4}} => {{1,4},{2,3},{5}} => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2},{3,4,5}} => {{1,2,3},{4},{5}} => [2,3,1,4,5] => ([(2,4),(3,4)],5)
{{1},{2},{3,4},{5}} => {{1},{2,3},{4},{5}} => [1,3,2,4,5] => ([(3,4)],5)
{{1,5},{2},{3},{4}} => {{1,5},{2},{3},{4}} => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2,5},{3},{4}} => {{1,4},{2},{3},{5}} => [4,2,3,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
{{1},{2},{3,5},{4}} => {{1,3},{2},{4},{5}} => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
{{1},{2},{3},{4,5}} => {{1,2},{3},{4},{5}} => [2,1,3,4,5] => ([(3,4)],5)
{{1},{2},{3},{4},{5}} => {{1},{2},{3},{4},{5}} => [1,2,3,4,5] => ([],5)
{{1,2,3,4,5,6}} => {{1,2,3,4,5,6}} => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
{{1,2,3,4,5},{6}} => {{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
{{1,2,3,4,6},{5}} => {{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,3,4},{5,6}} => {{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6)
{{1,2,3,4},{5},{6}} => {{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6)
{{1,2,3,5,6},{4}} => {{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,3,5},{4,6}} => {{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
{{1,2,3,5},{4},{6}} => {{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,3,6},{4,5}} => {{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,3},{4,5,6}} => {{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6)
{{1,2,3},{4,5},{6}} => {{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6)
{{1,2,3,6},{4},{5}} => {{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,3},{4,6},{5}} => {{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
{{1,2,3},{4},{5,6}} => {{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6)
{{1,2,3},{4},{5},{6}} => {{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => ([(3,5),(4,5)],6)
{{1,2,4,5,6},{3}} => {{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,4,5},{3,6}} => {{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,2,4,5},{3},{6}} => {{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,4,6},{3,5}} => {{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,4},{3,5,6}} => {{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
{{1,2,4},{3,5},{6}} => {{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
{{1,2,4,6},{3},{5}} => {{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
{{1,2,4},{3,6},{5}} => {{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
{{1,2,4},{3},{5,6}} => {{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,4},{3},{5},{6}} => {{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,5,6},{3,4}} => {{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
>>> Load all 3161 entries. <<<
{{1,2,5},{3,4,6}} => {{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,2,5},{3,4},{6}} => {{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,6},{3,4,5}} => {{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3,4,5,6}} => {{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6)
{{1,2},{3,4,5},{6}} => {{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6)
{{1,2,6},{3,4},{5}} => {{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3,4,6},{5}} => {{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3,4},{5,6}} => {{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
{{1,2},{3,4},{5},{6}} => {{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => ([(2,5),(3,4)],6)
{{1,2,5,6},{3},{4}} => {{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,5},{3,6},{4}} => {{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,5},{3},{4,6}} => {{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
{{1,2,5},{3},{4},{6}} => {{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2,6},{3,5},{4}} => {{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3,5,6},{4}} => {{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3,5},{4,6}} => {{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
{{1,2},{3,5},{4},{6}} => {{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6)
{{1,2,6},{3},{4,5}} => {{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3,6},{4,5}} => {{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3},{4,5,6}} => {{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6)
{{1,2},{3},{4,5},{6}} => {{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => ([(2,5),(3,4)],6)
{{1,2,6},{3},{4},{5}} => {{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3,6},{4},{5}} => {{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,2},{3},{4,6},{5}} => {{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6)
{{1,2},{3},{4},{5,6}} => {{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => ([(2,5),(3,4)],6)
{{1,2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => ([(4,5)],6)
{{1,3,4,5,6},{2}} => {{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,4,5},{2,6}} => {{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,3,4,5},{2},{6}} => {{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,4,6},{2,5}} => {{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,4},{2,5,6}} => {{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,3,4},{2,5},{6}} => {{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,3,4,6},{2},{5}} => {{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
{{1,3,4},{2,6},{5}} => {{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,4},{2},{5,6}} => {{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,4},{2},{5},{6}} => {{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,5,6},{2,4}} => {{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,5},{2,4,6}} => {{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
{{1,3,5},{2,4},{6}} => {{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3,6},{2,4,5}} => {{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3},{2,4,5,6}} => {{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
{{1,3},{2,4,5},{6}} => {{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
{{1,3,6},{2,4},{5}} => {{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3},{2,4,6},{5}} => {{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
{{1,3},{2,4},{5,6}} => {{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
{{1,3},{2,4},{5},{6}} => {{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
{{1,3,5,6},{2},{4}} => {{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
{{1,3,5},{2,6},{4}} => {{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,3,5},{2},{4,6}} => {{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)
{{1,3,5},{2},{4},{6}} => {{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
{{1,3,6},{2,5},{4}} => {{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3},{2,5,6},{4}} => {{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
{{1,3},{2,5},{4,6}} => {{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
{{1,3},{2,5},{4},{6}} => {{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
{{1,3,6},{2},{4,5}} => {{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3},{2,6},{4,5}} => {{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3},{2},{4,5,6}} => {{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
{{1,3},{2},{4,5},{6}} => {{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6)
{{1,3,6},{2},{4},{5}} => {{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3},{2,6},{4},{5}} => {{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,3},{2},{4,6},{5}} => {{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
{{1,3},{2},{4},{5,6}} => {{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6)
{{1,3},{2},{4},{5},{6}} => {{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
{{1,4,5,6},{2,3}} => {{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4,5},{2,3,6}} => {{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
{{1,4,5},{2,3},{6}} => {{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4,6},{2,3,5}} => {{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2,3,5,6}} => {{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,4},{2,3,5},{6}} => {{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,4,6},{2,3},{5}} => {{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2,3,6},{5}} => {{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
{{1,4},{2,3},{5,6}} => {{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2,3},{5},{6}} => {{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5,6},{2,3,4}} => {{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2,3,4,6}} => {{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,5},{2,3,4},{6}} => {{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2,3,4,5}} => {{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3,4,5,6}} => {{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
{{1},{2,3,4,5},{6}} => {{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6)
{{1,6},{2,3,4},{5}} => {{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3,4,6},{5}} => {{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3,4},{5,6}} => {{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6)
{{1},{2,3,4},{5},{6}} => {{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => ([(3,5),(4,5)],6)
{{1,5,6},{2,3},{4}} => {{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2,3,6},{4}} => {{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,5},{2,3},{4,6}} => {{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2,3},{4},{6}} => {{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2,3,5},{4}} => {{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3,5,6},{4}} => {{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3,5},{4,6}} => {{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
{{1},{2,3,5},{4},{6}} => {{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2,3},{4,5}} => {{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3,6},{4,5}} => {{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3},{4,5,6}} => {{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6)
{{1},{2,3},{4,5},{6}} => {{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => ([(2,5),(3,4)],6)
{{1,6},{2,3},{4},{5}} => {{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3,6},{4},{5}} => {{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,3},{4,6},{5}} => {{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => ([(1,2),(3,4),(3,5),(4,5)],6)
{{1},{2,3},{4},{5,6}} => {{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => ([(2,5),(3,4)],6)
{{1},{2,3},{4},{5},{6}} => {{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => ([(4,5)],6)
{{1,4,5,6},{2},{3}} => {{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4,5},{2,6},{3}} => {{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,4,5},{2},{3,6}} => {{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
{{1,4,5},{2},{3},{6}} => {{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4,6},{2,5},{3}} => {{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2,5,6},{3}} => {{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => ([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2,5},{3,6}} => {{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
{{1,4},{2,5},{3},{6}} => {{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
{{1,4,6},{2},{3,5}} => {{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2,6},{3,5}} => {{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2},{3,5,6}} => {{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
{{1,4},{2},{3,5},{6}} => {{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
{{1,4,6},{2},{3},{5}} => {{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2,6},{3},{5}} => {{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
{{1,4},{2},{3,6},{5}} => {{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
{{1,4},{2},{3},{5,6}} => {{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,4},{2},{3},{5},{6}} => {{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5,6},{2,4},{3}} => {{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2,4,6},{3}} => {{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1,5},{2,4},{3,6}} => {{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2,4},{3},{6}} => {{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2,4,5},{3}} => {{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,4,5,6},{3}} => {{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,4,5},{3,6}} => {{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1},{2,4,5},{3},{6}} => {{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2,4},{3,5}} => {{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,4,6},{3,5}} => {{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,4},{3,5,6}} => {{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
{{1},{2,4},{3,5},{6}} => {{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
{{1,6},{2,4},{3},{5}} => {{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,4,6},{3},{5}} => {{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
{{1},{2,4},{3,6},{5}} => {{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
{{1},{2,4},{3},{5,6}} => {{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => ([(1,2),(3,4),(3,5),(4,5)],6)
{{1},{2,4},{3},{5},{6}} => {{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6)
{{1,5,6},{2},{3,4}} => {{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2,6},{3,4}} => {{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2},{3,4,6}} => {{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2},{3,4},{6}} => {{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2,5},{3,4}} => {{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,5,6},{3,4}} => {{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,5},{3,4,6}} => {{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
{{1},{2,5},{3,4},{6}} => {{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2},{3,4,5}} => {{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,6},{3,4,5}} => {{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3,4,5,6}} => {{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6)
{{1},{2},{3,4,5},{6}} => {{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => ([(3,5),(4,5)],6)
{{1,6},{2},{3,4},{5}} => {{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,6},{3,4},{5}} => {{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3,4,6},{5}} => {{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3,4},{5,6}} => {{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => ([(2,5),(3,4)],6)
{{1},{2},{3,4},{5},{6}} => {{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => ([(4,5)],6)
{{1,5,6},{2},{3},{4}} => {{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2,6},{3},{4}} => {{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
{{1,5},{2},{3,6},{4}} => {{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
{{1,5},{2},{3},{4,6}} => {{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,5},{2},{3},{4},{6}} => {{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2,5},{3},{4}} => {{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,5,6},{3},{4}} => {{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,5},{3,6},{4}} => {{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
{{1},{2,5},{3},{4,6}} => {{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
{{1},{2,5},{3},{4},{6}} => {{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1,6},{2},{3,5},{4}} => {{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,6},{3,5},{4}} => {{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3,5,6},{4}} => {{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => ([(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3,5},{4,6}} => {{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
{{1},{2},{3,5},{4},{6}} => {{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => ([(3,4),(3,5),(4,5)],6)
{{1,6},{2},{3},{4,5}} => {{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,6},{3},{4,5}} => {{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3,6},{4,5}} => {{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3},{4,5,6}} => {{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => ([(3,5),(4,5)],6)
{{1},{2},{3},{4,5},{6}} => {{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => ([(4,5)],6)
{{1,6},{2},{3},{4},{5}} => {{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2,6},{3},{4},{5}} => {{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3,6},{4},{5}} => {{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
{{1},{2},{3},{4,6},{5}} => {{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6)
{{1},{2},{3},{4},{5,6}} => {{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => ([(4,5)],6)
{{1},{2},{3},{4},{5},{6}} => {{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => ([],6)
{{1,2,3,4,5,6,7}} => {{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
{{1,2,3,4,5,6},{7}} => {{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
{{1,2,3,4,5,7},{6}} => {{1,3,4,5,6,7},{2}} => [3,2,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,4,5},{6,7}} => {{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
{{1,2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
{{1,2,3,4,6,7},{5}} => {{1,2,4,5,6,7},{3}} => [2,4,3,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,4,6},{5,7}} => {{1,3},{2,4,5,6,7}} => [3,4,1,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,3,4,6},{5},{7}} => {{1},{2,4,5,6,7},{3}} => [1,4,3,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,4,7},{5,6}} => {{1,4,5,6,7},{2,3}} => [4,3,2,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,4},{5,6,7}} => {{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
{{1,2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7)
{{1,2,3,4,7},{5},{6}} => {{1,4,5,6,7},{2},{3}} => [4,2,3,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6,7}} => [3,2,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1,2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7)
{{1,2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7)
{{1,2,3,5,6,7},{4}} => {{1,2,3,5,6,7},{4}} => [2,3,5,4,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,5,6},{4,7}} => {{1,4},{2,3,5,6,7}} => [4,3,5,1,6,7,2] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,3,5,6},{4},{7}} => {{1},{2,3,5,6,7},{4}} => [1,3,5,4,6,7,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,5,7},{4,6}} => {{1,3,5,6,7},{2,4}} => [3,4,5,2,6,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,5},{4,6,7}} => {{1,2,4},{3,5,6,7}} => [2,4,5,1,6,7,3] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6,7}} => [1,4,5,2,6,7,3] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,2,3,5,7},{4},{6}} => {{1,3,5,6,7},{2},{4}} => [3,2,5,4,6,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,2,3,5},{4,7},{6}} => {{1,4},{2},{3,5,6,7}} => [4,2,5,1,6,7,3] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)
{{1,2,3,5},{4},{6,7}} => {{1,2},{3,5,6,7},{4}} => [2,1,5,4,6,7,3] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,5},{4},{6},{7}} => {{1},{2},{3,5,6,7},{4}} => [1,2,5,4,6,7,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,6,7},{4,5}} => {{1,2,5,6,7},{3,4}} => [2,5,4,3,6,7,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,6},{4,5,7}} => {{1,3,4},{2,5,6,7}} => [3,5,4,1,6,7,2] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,3,6},{4,5},{7}} => {{1},{2,5,6,7},{3,4}} => [1,5,4,3,6,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,7},{4,5,6}} => {{1,5,6,7},{2,3,4}} => [5,3,4,2,6,7,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4,5,6,7}} => {{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
{{1,2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7)
{{1,2,3,7},{4,5},{6}} => {{1,5,6,7},{2},{3,4}} => [5,2,4,3,6,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4,5,7},{6}} => {{1,3,4},{2},{5,6,7}} => [3,2,4,1,6,7,5] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7)
{{1,2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7)
{{1,2,3,6,7},{4},{5}} => {{1,2,5,6,7},{3},{4}} => [2,5,3,4,6,7,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,6},{4,7},{5}} => {{1,4},{2,5,6,7},{3}} => [4,5,3,1,6,7,2] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,6},{4},{5,7}} => {{1,3},{2,5,6,7},{4}} => [3,5,1,4,6,7,2] => ([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,2,3,6},{4},{5},{7}} => {{1},{2,5,6,7},{3},{4}} => [1,5,3,4,6,7,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3,7},{4,6},{5}} => {{1,5,6,7},{2,4},{3}} => [5,4,3,2,6,7,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6,7}} => [2,4,3,1,6,7,5] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4,6},{5,7}} => {{1,3},{2,4},{5,6,7}} => [3,4,1,2,6,7,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
{{1,2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6,7}} => [1,4,3,2,6,7,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1,2,3,7},{4},{5,6}} => {{1,5,6,7},{2,3},{4}} => [5,3,2,4,6,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6,7}} => [4,3,2,1,6,7,5] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7)
{{1,2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7)
{{1,2,3,7},{4},{5},{6}} => {{1,5,6,7},{2},{3},{4}} => [5,2,3,4,6,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6,7}} => [4,2,3,1,6,7,5] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
{{1,2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6,7}} => [3,2,1,4,6,7,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1,2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7)
{{1,2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7)
{{1,2,4,5,6,7},{3}} => {{1,2,3,4,6,7},{5}} => [2,3,4,6,5,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,5,6},{3,7}} => {{1,5},{2,3,4,6,7}} => [5,3,4,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,5,6},{3},{7}} => {{1},{2,3,4,6,7},{5}} => [1,3,4,6,5,7,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,5,7},{3,6}} => {{1,3,4,6,7},{2,5}} => [3,5,4,6,2,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,5},{3,6,7}} => {{1,2,5},{3,4,6,7}} => [2,5,4,6,1,7,3] => ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,5},{3,6},{7}} => {{1},{2,5},{3,4,6,7}} => [1,5,4,6,2,7,3] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,5,7},{3},{6}} => {{1,3,4,6,7},{2},{5}} => [3,2,4,6,5,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,2,4,5},{3,7},{6}} => {{1,5},{2},{3,4,6,7}} => [5,2,4,6,1,7,3] => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,5},{3},{6,7}} => {{1,2},{3,4,6,7},{5}} => [2,1,4,6,5,7,3] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6,7},{5}} => [1,2,4,6,5,7,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,6,7},{3,5}} => {{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,6},{3,5,7}} => {{1,3,5},{2,4,6,7}} => [3,4,5,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,6},{3,5},{7}} => {{1},{2,4,6,7},{3,5}} => [1,4,5,6,3,7,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,7},{3,5,6}} => {{1,4,6,7},{2,3,5}} => [4,3,5,6,2,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3,5,6,7}} => {{1,2,3,5},{4,6,7}} => [2,3,5,6,1,7,4] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6,7}} => [1,3,5,6,2,7,4] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,7},{3,5},{6}} => {{1,4,6,7},{2},{3,5}} => [4,2,5,6,3,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3,5,7},{6}} => {{1,3,5},{2},{4,6,7}} => [3,2,5,6,1,7,4] => ([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4},{3,5},{6,7}} => {{1,2},{3,5},{4,6,7}} => [2,1,5,6,3,7,4] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4},{3,5},{6},{7}} => {{1},{2},{3,5},{4,6,7}} => [1,2,5,6,3,7,4] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,2,4,6,7},{3},{5}} => {{1,2,4,6,7},{3},{5}} => [2,4,3,6,5,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,2,4,6},{3,7},{5}} => {{1,5},{2,4,6,7},{3}} => [5,4,3,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,6},{3},{5,7}} => {{1,3},{2,4,6,7},{5}} => [3,4,1,6,5,7,2] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,2,4,6},{3},{5},{7}} => {{1},{2,4,6,7},{3},{5}} => [1,4,3,6,5,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,2,4,7},{3,6},{5}} => {{1,4,6,7},{2,5},{3}} => [4,5,3,6,2,7,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3,6,7},{5}} => {{1,2,5},{3},{4,6,7}} => [2,5,3,6,1,7,4] => ([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
{{1,2,4},{3,6},{5,7}} => {{1,3},{2,5},{4,6,7}} => [3,5,1,6,2,7,4] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
{{1,2,4},{3,6},{5},{7}} => {{1},{2,5},{3},{4,6,7}} => [1,5,3,6,2,7,4] => ([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,4,7},{3},{5,6}} => {{1,4,6,7},{2,3},{5}} => [4,3,2,6,5,7,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3,7},{5,6}} => {{1,5},{2,3},{4,6,7}} => [5,3,2,6,1,7,4] => ([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
{{1,2,4},{3},{5,6,7}} => {{1,2,3},{4,6,7},{5}} => [2,3,1,6,5,7,4] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6,7},{5}} => [1,3,2,6,5,7,4] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4,7},{3},{5},{6}} => {{1,4,6,7},{2},{3},{5}} => [4,2,3,6,5,7,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3,7},{5},{6}} => {{1,5},{2},{3},{4,6,7}} => [5,2,3,6,1,7,4] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6,7},{5}} => [3,2,1,6,5,7,4] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6,7},{5}} => [2,1,3,6,5,7,4] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6,7},{5}} => [1,2,3,6,5,7,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5,6,7},{3,4}} => {{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5,6},{3,4,7}} => {{1,4,5},{2,3,6,7}} => [4,3,6,5,1,7,2] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,5,6},{3,4},{7}} => {{1},{2,3,6,7},{4,5}} => [1,3,6,5,4,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5,7},{3,4,6}} => {{1,3,6,7},{2,4,5}} => [3,4,6,5,2,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5},{3,4,6,7}} => {{1,2,4,5},{3,6,7}} => [2,4,6,5,1,7,3] => ([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,5},{3,4,6},{7}} => {{1},{2,4,5},{3,6,7}} => [1,4,6,5,2,7,3] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,5,7},{3,4},{6}} => {{1,3,6,7},{2},{4,5}} => [3,2,6,5,4,7,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5},{3,4,7},{6}} => {{1,4,5},{2},{3,6,7}} => [4,2,6,5,1,7,3] => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,5},{3,4},{6,7}} => {{1,2},{3,6,7},{4,5}} => [2,1,6,5,4,7,3] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5},{3,4},{6},{7}} => {{1},{2},{3,6,7},{4,5}} => [1,2,6,5,4,7,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6,7},{3,4,5}} => {{1,2,6,7},{3,4,5}} => [2,6,4,5,3,7,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3,4,5,7}} => {{1,3,4,5},{2,6,7}} => [3,6,4,5,1,7,2] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,6},{3,4,5},{7}} => {{1},{2,6,7},{3,4,5}} => [1,6,4,5,3,7,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3,4,5,6}} => {{1,6,7},{2,3,4,5}} => [6,3,4,5,2,7,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4,5,6,7}} => {{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
{{1,2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7)
{{1,2,7},{3,4,5},{6}} => {{1,6,7},{2},{3,4,5}} => [6,2,4,5,3,7,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4,5,7},{6}} => {{1,3,4,5},{2},{6,7}} => [3,2,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7)
{{1,2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => ([(2,3),(4,6),(5,6)],7)
{{1,2,6,7},{3,4},{5}} => {{1,2,6,7},{3},{4,5}} => [2,6,3,5,4,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3,4,7},{5}} => {{1,4,5},{2,6,7},{3}} => [4,6,3,5,1,7,2] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,6},{3,4},{5,7}} => {{1,3},{2,6,7},{4,5}} => [3,6,1,5,4,7,2] => ([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3,4},{5},{7}} => {{1},{2,6,7},{3},{4,5}} => [1,6,3,5,4,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3,4,6},{5}} => {{1,6,7},{2,4,5},{3}} => [6,4,3,5,2,7,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4,6,7},{5}} => {{1,2,4,5},{3},{6,7}} => [2,4,3,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2},{3,4,6},{5},{7}} => {{1},{2,4,5},{3},{6,7}} => [1,4,3,5,2,7,6] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3,4},{5,6}} => {{1,6,7},{2,3},{4,5}} => [6,3,2,5,4,7,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4,7},{5,6}} => {{1,4,5},{2,3},{6,7}} => [4,3,2,5,1,7,6] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7)
{{1,2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7)
{{1,2,7},{3,4},{5},{6}} => {{1,6,7},{2},{3},{4,5}} => [6,2,3,5,4,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4,7},{5},{6}} => {{1,4,5},{2},{3},{6,7}} => [4,2,3,5,1,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
{{1,2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => ([(1,6),(2,5),(3,4)],7)
{{1,2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7)
{{1,2,5,6,7},{3},{4}} => {{1,2,3,6,7},{4},{5}} => [2,3,6,4,5,7,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5,6},{3,7},{4}} => {{1,5},{2,3,6,7},{4}} => [5,3,6,4,1,7,2] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,5,6},{3},{4,7}} => {{1,4},{2,3,6,7},{5}} => [4,3,6,1,5,7,2] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1,2,5,6},{3},{4},{7}} => {{1},{2,3,6,7},{4},{5}} => [1,3,6,4,5,7,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5,7},{3,6},{4}} => {{1,3,6,7},{2,5},{4}} => [3,5,6,4,2,7,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5},{3,6,7},{4}} => {{1,2,5},{3,6,7},{4}} => [2,5,6,4,1,7,3] => ([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,5},{3,6},{4,7}} => {{1,4},{2,5},{3,6,7}} => [4,5,6,1,2,7,3] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
{{1,2,5},{3,6},{4},{7}} => {{1},{2,5},{3,6,7},{4}} => [1,5,6,4,2,7,3] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5,7},{3},{4,6}} => {{1,3,6,7},{2,4},{5}} => [3,4,6,2,5,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5},{3,7},{4,6}} => {{1,5},{2,4},{3,6,7}} => [5,4,6,2,1,7,3] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
{{1,2,5},{3},{4,6,7}} => {{1,2,4},{3,6,7},{5}} => [2,4,6,1,5,7,3] => ([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
{{1,2,5},{3},{4,6},{7}} => {{1},{2,4},{3,6,7},{5}} => [1,4,6,2,5,7,3] => ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,2,5,7},{3},{4},{6}} => {{1,3,6,7},{2},{4},{5}} => [3,2,6,4,5,7,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5},{3,7},{4},{6}} => {{1,5},{2},{3,6,7},{4}} => [5,2,6,4,1,7,3] => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,5},{3},{4,7},{6}} => {{1,4},{2},{3,6,7},{5}} => [4,2,6,1,5,7,3] => ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,2,5},{3},{4},{6,7}} => {{1,2},{3,6,7},{4},{5}} => [2,1,6,4,5,7,3] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,5},{3},{4},{6},{7}} => {{1},{2},{3,6,7},{4},{5}} => [1,2,6,4,5,7,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6,7},{3,5},{4}} => {{1,2,6,7},{3,5},{4}} => [2,6,5,4,3,7,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3,5,7},{4}} => {{1,3,5},{2,6,7},{4}} => [3,6,5,4,1,7,2] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,6},{3,5},{4,7}} => {{1,4},{2,6,7},{3,5}} => [4,6,5,1,3,7,2] => ([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3,5},{4},{7}} => {{1},{2,6,7},{3,5},{4}} => [1,6,5,4,3,7,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3,5,6},{4}} => {{1,6,7},{2,3,5},{4}} => [6,3,5,4,2,7,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6,7}} => [2,3,5,4,1,7,6] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,5,6},{4,7}} => {{1,4},{2,3,5},{6,7}} => [4,3,5,1,2,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6,7}} => [1,3,5,4,2,7,6] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3,5},{4,6}} => {{1,6,7},{2,4},{3,5}} => [6,4,5,2,3,7,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,5,7},{4,6}} => {{1,3,5},{2,4},{6,7}} => [3,4,5,2,1,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6,7}} => [2,4,5,1,3,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2},{3,5},{4,6},{7}} => {{1},{2,4},{3,5},{6,7}} => [1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2,7},{3,5},{4},{6}} => {{1,6,7},{2},{3,5},{4}} => [6,2,5,4,3,7,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,5,7},{4},{6}} => {{1,3,5},{2},{4},{6,7}} => [3,2,5,4,1,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,2},{3,5},{4,7},{6}} => {{1,4},{2},{3,5},{6,7}} => [4,2,5,1,3,7,6] => ([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
{{1,2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6,7}} => [1,2,5,4,3,7,6] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,2,6,7},{3},{4,5}} => {{1,2,6,7},{3,4},{5}} => [2,6,4,3,5,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3,7},{4,5}} => {{1,5},{2,6,7},{3,4}} => [5,6,4,3,1,7,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3},{4,5,7}} => {{1,3,4},{2,6,7},{5}} => [3,6,4,1,5,7,2] => ([(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3},{4,5},{7}} => {{1},{2,6,7},{3,4},{5}} => [1,6,4,3,5,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3,6},{4,5}} => {{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6,7}} => [2,5,4,3,1,7,6] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,6},{4,5,7}} => {{1,3,4},{2,5},{6,7}} => [3,5,4,1,2,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3},{4,5,6}} => {{1,6,7},{2,3,4},{5}} => [6,3,4,2,5,7,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6,7}} => [5,3,4,2,1,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7)
{{1,2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => ([(2,3),(4,6),(5,6)],7)
{{1,2,7},{3},{4,5},{6}} => {{1,6,7},{2},{3,4},{5}} => [6,2,4,3,5,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6,7}} => [5,2,4,3,1,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4,5,7},{6}} => {{1,3,4},{2},{5},{6,7}} => [3,2,4,1,5,7,6] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => ([(1,6),(2,5),(3,4)],7)
{{1,2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7)
{{1,2,6,7},{3},{4},{5}} => {{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3,7},{4},{5}} => {{1,5},{2,6,7},{3},{4}} => [5,6,3,4,1,7,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,2,6},{3},{4,7},{5}} => {{1,4},{2,6,7},{3},{5}} => [4,6,3,1,5,7,2] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3},{4},{5,7}} => {{1,3},{2,6,7},{4},{5}} => [3,6,1,4,5,7,2] => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,6},{3},{4},{5},{7}} => {{1},{2,6,7},{3},{4},{5}} => [1,6,3,4,5,7,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3,6},{4},{5}} => {{1,6,7},{2,5},{3},{4}} => [6,5,3,4,2,7,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6,7}} => [2,5,3,4,1,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,6},{4,7},{5}} => {{1,4},{2,5},{3},{6,7}} => [4,5,3,1,2,7,6] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,2},{3,6},{4},{5,7}} => {{1,3},{2,5},{4},{6,7}} => [3,5,1,4,2,7,6] => ([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6,7}} => [1,5,3,4,2,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3},{4,6},{5}} => {{1,6,7},{2,4},{3},{5}} => [6,4,3,2,5,7,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6,7}} => [5,4,3,2,1,7,6] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6,7}} => [2,4,3,1,5,7,6] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4,6},{5,7}} => {{1,3},{2,4},{5},{6,7}} => [3,4,1,2,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
{{1,2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6,7}} => [1,4,3,2,5,7,6] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,2,7},{3},{4},{5,6}} => {{1,6,7},{2,3},{4},{5}} => [6,3,2,4,5,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6,7}} => [5,3,2,4,1,7,6] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => ([(2,3),(4,6),(5,6)],7)
{{1,2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7)
{{1,2,7},{3},{4},{5},{6}} => {{1,6,7},{2},{3},{4},{5}} => [6,2,3,4,5,7,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6,7}} => [5,2,3,4,1,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6,7}} => [4,2,3,1,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6,7}} => [3,2,1,4,5,7,6] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => ([(3,6),(4,5)],7)
{{1,2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => ([(5,6)],7)
{{1,3,4,5,6,7},{2}} => {{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,5,6},{2,7}} => {{1,6},{2,3,4,5,7}} => [6,3,4,5,7,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4,5,6},{2},{7}} => {{1},{2,3,4,5,7},{6}} => [1,3,4,5,7,6,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,5,7},{2,6}} => {{1,3,4,5,7},{2,6}} => [3,6,4,5,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,5},{2,6,7}} => {{1,2,6},{3,4,5,7}} => [2,6,4,5,7,1,3] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4,5},{2,6},{7}} => {{1},{2,6},{3,4,5,7}} => [1,6,4,5,7,2,3] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4,5,7},{2},{6}} => {{1,3,4,5,7},{2},{6}} => [3,2,4,5,7,6,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3,4,5},{2,7},{6}} => {{1,6},{2},{3,4,5,7}} => [6,2,4,5,7,1,3] => ([(0,5),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,3,4,5},{2},{6,7}} => {{1,2},{3,4,5,7},{6}} => [2,1,4,5,7,6,3] => ([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,5},{2},{6},{7}} => {{1},{2},{3,4,5,7},{6}} => [1,2,4,5,7,6,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,6,7},{2,5}} => {{1,2,4,5,7},{3,6}} => [2,4,6,5,7,3,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,6},{2,5,7}} => {{1,3,6},{2,4,5,7}} => [3,4,6,5,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4,6},{2,5},{7}} => {{1},{2,4,5,7},{3,6}} => [1,4,6,5,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,7},{2,5,6}} => {{1,4,5,7},{2,3,6}} => [4,3,6,5,7,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,5,6,7}} => {{1,2,3,6},{4,5,7}} => [2,3,6,5,7,1,4] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4},{2,5,6},{7}} => {{1},{2,3,6},{4,5,7}} => [1,3,6,5,7,2,4] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4,7},{2,5},{6}} => {{1,4,5,7},{2},{3,6}} => [4,2,6,5,7,3,1] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,5,7},{6}} => {{1,3,6},{2},{4,5,7}} => [3,2,6,5,7,1,4] => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,5},{6,7}} => {{1,2},{3,6},{4,5,7}} => [2,1,6,5,7,3,4] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4},{2,5},{6},{7}} => {{1},{2},{3,6},{4,5,7}} => [1,2,6,5,7,3,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4,6,7},{2},{5}} => {{1,2,4,5,7},{3},{6}} => [2,4,3,5,7,6,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3,4,6},{2,7},{5}} => {{1,6},{2,4,5,7},{3}} => [6,4,3,5,7,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,4,6},{2},{5,7}} => {{1,3},{2,4,5,7},{6}} => [3,4,1,5,7,6,2] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,3,4,6},{2},{5},{7}} => {{1},{2,4,5,7},{3},{6}} => [1,4,3,5,7,6,2] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3,4,7},{2,6},{5}} => {{1,4,5,7},{2,6},{3}} => [4,6,3,5,7,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,6,7},{5}} => {{1,2,6},{3},{4,5,7}} => [2,6,3,5,7,1,4] => ([(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,6},{5,7}} => {{1,3},{2,6},{4,5,7}} => [3,6,1,5,7,2,4] => ([(0,1),(0,6),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,6},{5},{7}} => {{1},{2,6},{3},{4,5,7}} => [1,6,3,5,7,2,4] => ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,7},{2},{5,6}} => {{1,4,5,7},{2,3},{6}} => [4,3,2,5,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,7},{5,6}} => {{1,6},{2,3},{4,5,7}} => [6,3,2,5,7,1,4] => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,3,4},{2},{5,6,7}} => {{1,2,3},{4,5,7},{6}} => [2,3,1,5,7,6,4] => ([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2},{5,6},{7}} => {{1},{2,3},{4,5,7},{6}} => [1,3,2,5,7,6,4] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4,7},{2},{5},{6}} => {{1,4,5,7},{2},{3},{6}} => [4,2,3,5,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2,7},{5},{6}} => {{1,6},{2},{3},{4,5,7}} => [6,2,3,5,7,1,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2},{5,7},{6}} => {{1,3},{2},{4,5,7},{6}} => [3,2,1,5,7,6,4] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2},{5},{6,7}} => {{1,2},{3},{4,5,7},{6}} => [2,1,3,5,7,6,4] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,4},{2},{5},{6},{7}} => {{1},{2},{3},{4,5,7},{6}} => [1,2,3,5,7,6,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5,6,7},{2,4}} => {{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5,6},{2,4,7}} => {{1,4,6},{2,3,5,7}} => [4,3,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5,6},{2,4},{7}} => {{1},{2,3,5,7},{4,6}} => [1,3,5,6,7,4,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5,7},{2,4,6}} => {{1,3,5,7},{2,4,6}} => [3,4,5,6,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5},{2,4,6,7}} => {{1,2,4,6},{3,5,7}} => [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5},{2,4,6},{7}} => {{1},{2,4,6},{3,5,7}} => [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5,7},{2,4},{6}} => {{1,3,5,7},{2},{4,6}} => [3,2,5,6,7,4,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5},{2,4,7},{6}} => {{1,4,6},{2},{3,5,7}} => [4,2,5,6,7,1,3] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)
{{1,3,5},{2,4},{6,7}} => {{1,2},{3,5,7},{4,6}} => [2,1,5,6,7,4,3] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5},{2,4},{6},{7}} => {{1},{2},{3,5,7},{4,6}} => [1,2,5,6,7,4,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6,7},{2,4,5}} => {{1,2,5,7},{3,4,6}} => [2,5,4,6,7,3,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2,4,5,7}} => {{1,3,4,6},{2,5,7}} => [3,5,4,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,6},{2,4,5},{7}} => {{1},{2,5,7},{3,4,6}} => [1,5,4,6,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2,4,5,6}} => {{1,5,7},{2,3,4,6}} => [5,3,4,6,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,4,5,6,7}} => {{1,2,3,4,6},{5,7}} => [2,3,4,6,7,1,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3},{2,4,5,6},{7}} => {{1},{2,3,4,6},{5,7}} => [1,3,4,6,7,2,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,3,7},{2,4,5},{6}} => {{1,5,7},{2},{3,4,6}} => [5,2,4,6,7,3,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,4,5,7},{6}} => {{1,3,4,6},{2},{5,7}} => [3,2,4,6,7,1,5] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,3},{2,4,5},{6,7}} => {{1,2},{3,4,6},{5,7}} => [2,1,4,6,7,3,5] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3},{2,4,5},{6},{7}} => {{1},{2},{3,4,6},{5,7}} => [1,2,4,6,7,3,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,3,6,7},{2,4},{5}} => {{1,2,5,7},{3},{4,6}} => [2,5,3,6,7,4,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2,4,7},{5}} => {{1,4,6},{2,5,7},{3}} => [4,5,3,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,6},{2,4},{5,7}} => {{1,3},{2,5,7},{4,6}} => [3,5,1,6,7,4,2] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2,4},{5},{7}} => {{1},{2,5,7},{3},{4,6}} => [1,5,3,6,7,4,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2,4,6},{5}} => {{1,5,7},{2,4,6},{3}} => [5,4,3,6,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,4,6,7},{5}} => {{1,2,4,6},{3},{5,7}} => [2,4,3,6,7,1,5] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,3},{2,4,6},{5,7}} => {{1,3},{2,4,6},{5,7}} => [3,4,1,6,7,2,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,3},{2,4,6},{5},{7}} => {{1},{2,4,6},{3},{5,7}} => [1,4,3,6,7,2,5] => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,3,7},{2,4},{5,6}} => {{1,5,7},{2,3},{4,6}} => [5,3,2,6,7,4,1] => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,4,7},{5,6}} => {{1,4,6},{2,3},{5,7}} => [4,3,2,6,7,1,5] => ([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,4},{5,6,7}} => {{1,2,3},{4,6},{5,7}} => [2,3,1,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)
{{1,3},{2,4},{5,6},{7}} => {{1},{2,3},{4,6},{5,7}} => [1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,7},{2,4},{5},{6}} => {{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,4,7},{5},{6}} => {{1,4,6},{2},{3},{5,7}} => [4,2,3,6,7,1,5] => ([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,4},{5,7},{6}} => {{1,3},{2},{4,6},{5,7}} => [3,2,1,6,7,4,5] => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
{{1,3},{2,4},{5},{6,7}} => {{1,2},{3},{4,6},{5,7}} => [2,1,3,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3},{2,4},{5},{6},{7}} => {{1},{2},{3},{4,6},{5,7}} => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5,6,7},{2},{4}} => {{1,2,3,5,7},{4},{6}} => [2,3,5,4,7,6,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3,5,6},{2,7},{4}} => {{1,6},{2,3,5,7},{4}} => [6,3,5,4,7,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5,6},{2},{4,7}} => {{1,4},{2,3,5,7},{6}} => [4,3,5,1,7,6,2] => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3,5,6},{2},{4},{7}} => {{1},{2,3,5,7},{4},{6}} => [1,3,5,4,7,6,2] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3,5,7},{2,6},{4}} => {{1,3,5,7},{2,6},{4}} => [3,6,5,4,7,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5},{2,6,7},{4}} => {{1,2,6},{3,5,7},{4}} => [2,6,5,4,7,1,3] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5},{2,6},{4,7}} => {{1,4},{2,6},{3,5,7}} => [4,6,5,1,7,2,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5},{2,6},{4},{7}} => {{1},{2,6},{3,5,7},{4}} => [1,6,5,4,7,2,3] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5,7},{2},{4,6}} => {{1,3,5,7},{2,4},{6}} => [3,4,5,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,5},{2,7},{4,6}} => {{1,6},{2,4},{3,5,7}} => [6,4,5,2,7,1,3] => ([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,3,5},{2},{4,6,7}} => {{1,2,4},{3,5,7},{6}} => [2,4,5,1,7,6,3] => ([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,5},{2},{4,6},{7}} => {{1},{2,4},{3,5,7},{6}} => [1,4,5,2,7,6,3] => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,3,5,7},{2},{4},{6}} => {{1,3,5,7},{2},{4},{6}} => [3,2,5,4,7,6,1] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1,3,5},{2,7},{4},{6}} => {{1,6},{2},{3,5,7},{4}} => [6,2,5,4,7,1,3] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,3,5},{2},{4,7},{6}} => {{1,4},{2},{3,5,7},{6}} => [4,2,5,1,7,6,3] => ([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
{{1,3,5},{2},{4},{6,7}} => {{1,2},{3,5,7},{4},{6}} => [2,1,5,4,7,6,3] => ([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3,5},{2},{4},{6},{7}} => {{1},{2},{3,5,7},{4},{6}} => [1,2,5,4,7,6,3] => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3,6,7},{2,5},{4}} => {{1,2,5,7},{3,6},{4}} => [2,5,6,4,7,3,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2,5,7},{4}} => {{1,3,6},{2,5,7},{4}} => [3,5,6,4,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,6},{2,5},{4,7}} => {{1,4},{2,5,7},{3,6}} => [4,5,6,1,7,3,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2,5},{4},{7}} => {{1},{2,5,7},{3,6},{4}} => [1,5,6,4,7,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2,5,6},{4}} => {{1,5,7},{2,3,6},{4}} => [5,3,6,4,7,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,5,6,7},{4}} => {{1,2,3,6},{4},{5,7}} => [2,3,6,4,7,1,5] => ([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3},{2,5,6},{4,7}} => {{1,4},{2,3,6},{5,7}} => [4,3,6,1,7,2,5] => ([(0,1),(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1,3},{2,5,6},{4},{7}} => {{1},{2,3,6},{4},{5,7}} => [1,3,6,4,7,2,5] => ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2,5},{4,6}} => {{1,5,7},{2,4},{3,6}} => [5,4,6,2,7,3,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,3},{2,5,7},{4,6}} => {{1,3,6},{2,4},{5,7}} => [3,4,6,2,7,1,5] => ([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)
{{1,3},{2,5},{4,6,7}} => {{1,2,4},{3,6},{5,7}} => [2,4,6,1,7,3,5] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
{{1,3},{2,5},{4,6},{7}} => {{1},{2,4},{3,6},{5,7}} => [1,4,6,2,7,3,5] => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
{{1,3,7},{2,5},{4},{6}} => {{1,5,7},{2},{3,6},{4}} => [5,2,6,4,7,3,1] => ([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,5,7},{4},{6}} => {{1,3,6},{2},{4},{5,7}} => [3,2,6,4,7,1,5] => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3},{2,5},{4,7},{6}} => {{1,4},{2},{3,6},{5,7}} => [4,2,6,1,7,3,5] => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
{{1,3},{2,5},{4},{6,7}} => {{1,2},{3,6},{4},{5,7}} => [2,1,6,4,7,3,5] => ([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3},{2,5},{4},{6},{7}} => {{1},{2},{3,6},{4},{5,7}} => [1,2,6,4,7,3,5] => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3,6,7},{2},{4,5}} => {{1,2,5,7},{3,4},{6}} => [2,5,4,3,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2,7},{4,5}} => {{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,6},{2},{4,5,7}} => {{1,3,4},{2,5,7},{6}} => [3,5,4,1,7,6,2] => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2},{4,5},{7}} => {{1},{2,5,7},{3,4},{6}} => [1,5,4,3,7,6,2] => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2,6},{4,5}} => {{1,5,7},{2,6},{3,4}} => [5,6,4,3,7,2,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,6,7},{4,5}} => {{1,2,6},{3,4},{5,7}} => [2,6,4,3,7,1,5] => ([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,6},{4,5,7}} => {{1,3,4},{2,6},{5,7}} => [3,6,4,1,7,2,5] => ([(0,1),(0,6),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,6},{4,5},{7}} => {{1},{2,6},{3,4},{5,7}} => [1,6,4,3,7,2,5] => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2},{4,5,6}} => {{1,5,7},{2,3,4},{6}} => [5,3,4,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,7},{4,5,6}} => {{1,6},{2,3,4},{5,7}} => [6,3,4,2,7,1,5] => ([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,5,6,7}} => {{1,2,3,4},{5,7},{6}} => [2,3,4,1,7,6,5] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1,3},{2},{4,5,6},{7}} => {{1},{2,3,4},{5,7},{6}} => [1,3,4,2,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1,3,7},{2},{4,5},{6}} => {{1,5,7},{2},{3,4},{6}} => [5,2,4,3,7,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,7},{4,5},{6}} => {{1,6},{2},{3,4},{5,7}} => [6,2,4,3,7,1,5] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,5,7},{6}} => {{1,3,4},{2},{5,7},{6}} => [3,2,4,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,5},{6,7}} => {{1,2},{3,4},{5,7},{6}} => [2,1,4,3,7,6,5] => ([(0,3),(1,2),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,5},{6},{7}} => {{1},{2},{3,4},{5,7},{6}} => [1,2,4,3,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,3,6,7},{2},{4},{5}} => {{1,2,5,7},{3},{4},{6}} => [2,5,3,4,7,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2,7},{4},{5}} => {{1,6},{2,5,7},{3},{4}} => [6,5,3,4,7,1,2] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,3,6},{2},{4,7},{5}} => {{1,4},{2,5,7},{3},{6}} => [4,5,3,1,7,6,2] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2},{4},{5,7}} => {{1,3},{2,5,7},{4},{6}} => [3,5,1,4,7,6,2] => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3,6},{2},{4},{5},{7}} => {{1},{2,5,7},{3},{4},{6}} => [1,5,3,4,7,6,2] => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2,6},{4},{5}} => {{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,6,7},{4},{5}} => {{1,2,6},{3},{4},{5,7}} => [2,6,3,4,7,1,5] => ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,6},{4,7},{5}} => {{1,4},{2,6},{3},{5,7}} => [4,6,3,1,7,2,5] => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,6},{4},{5,7}} => {{1,3},{2,6},{4},{5,7}} => [3,6,1,4,7,2,5] => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
{{1,3},{2,6},{4},{5},{7}} => {{1},{2,6},{3},{4},{5,7}} => [1,6,3,4,7,2,5] => ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2},{4,6},{5}} => {{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,7},{4,6},{5}} => {{1,6},{2,4},{3},{5,7}} => [6,4,3,2,7,1,5] => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,6,7},{5}} => {{1,2,4},{3},{5,7},{6}} => [2,4,3,1,7,6,5] => ([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,6},{5,7}} => {{1,3},{2,4},{5,7},{6}} => [3,4,1,2,7,6,5] => ([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)
{{1,3},{2},{4,6},{5},{7}} => {{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
{{1,3,7},{2},{4},{5,6}} => {{1,5,7},{2,3},{4},{6}} => [5,3,2,4,7,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,7},{4},{5,6}} => {{1,6},{2,3},{4},{5,7}} => [6,3,2,4,7,1,5] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,7},{5,6}} => {{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4},{5,6,7}} => {{1,2,3},{4},{5,7},{6}} => [2,3,1,4,7,6,5] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1,3},{2},{4},{5,6},{7}} => {{1},{2,3},{4},{5,7},{6}} => [1,3,2,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,3,7},{2},{4},{5},{6}} => {{1,5,7},{2},{3},{4},{6}} => [5,2,3,4,7,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2,7},{4},{5},{6}} => {{1,6},{2},{3},{4},{5,7}} => [6,2,3,4,7,1,5] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4,7},{5},{6}} => {{1,4},{2},{3},{5,7},{6}} => [4,2,3,1,7,6,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4},{5,7},{6}} => {{1,3},{2},{4},{5,7},{6}} => [3,2,1,4,7,6,5] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
{{1,3},{2},{4},{5},{6,7}} => {{1,2},{3},{4},{5,7},{6}} => [2,1,3,4,7,6,5] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,3},{2},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,7},{6}} => [1,2,3,4,7,6,5] => ([(4,5),(4,6),(5,6)],7)
{{1,4,5,6,7},{2,3}} => {{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5,6},{2,3,7}} => {{1,5,6},{2,3,4,7}} => [5,3,4,7,6,1,2] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,5,6},{2,3},{7}} => {{1},{2,3,4,7},{5,6}} => [1,3,4,7,6,5,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5,7},{2,3,6}} => {{1,3,4,7},{2,5,6}} => [3,5,4,7,6,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2,3,6,7}} => {{1,2,5,6},{3,4,7}} => [2,5,4,7,6,1,3] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,5},{2,3,6},{7}} => {{1},{2,5,6},{3,4,7}} => [1,5,4,7,6,2,3] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,5,7},{2,3},{6}} => {{1,3,4,7},{2},{5,6}} => [3,2,4,7,6,5,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2,3,7},{6}} => {{1,5,6},{2},{3,4,7}} => [5,2,4,7,6,1,3] => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,4,5},{2,3},{6,7}} => {{1,2},{3,4,7},{5,6}} => [2,1,4,7,6,5,3] => ([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2,3},{6},{7}} => {{1},{2},{3,4,7},{5,6}} => [1,2,4,7,6,5,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6,7},{2,3,5}} => {{1,2,4,7},{3,5,6}} => [2,4,5,7,6,3,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6},{2,3,5,7}} => {{1,3,5,6},{2,4,7}} => [3,4,5,7,6,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,6},{2,3,5},{7}} => {{1},{2,4,7},{3,5,6}} => [1,4,5,7,6,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2,3,5,6}} => {{1,4,7},{2,3,5,6}} => [4,3,5,7,6,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3,5,6,7}} => {{1,2,3,5,6},{4,7}} => [2,3,5,7,6,1,4] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4},{2,3,5,6},{7}} => {{1},{2,3,5,6},{4,7}} => [1,3,5,7,6,2,4] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,7},{2,3,5},{6}} => {{1,4,7},{2},{3,5,6}} => [4,2,5,7,6,3,1] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3,5,7},{6}} => {{1,3,5,6},{2},{4,7}} => [3,2,5,7,6,1,4] => ([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3,5},{6,7}} => {{1,2},{3,5,6},{4,7}} => [2,1,5,7,6,3,4] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4},{2,3,5},{6},{7}} => {{1},{2},{3,5,6},{4,7}} => [1,2,5,7,6,3,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,6,7},{2,3},{5}} => {{1,2,4,7},{3},{5,6}} => [2,4,3,7,6,5,1] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6},{2,3,7},{5}} => {{1,5,6},{2,4,7},{3}} => [5,4,3,7,6,1,2] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,6},{2,3},{5,7}} => {{1,3},{2,4,7},{5,6}} => [3,4,1,7,6,5,2] => ([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6},{2,3},{5},{7}} => {{1},{2,4,7},{3},{5,6}} => [1,4,3,7,6,5,2] => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2,3,6},{5}} => {{1,4,7},{2,5,6},{3}} => [4,5,3,7,6,2,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3,6,7},{5}} => {{1,2,5,6},{3},{4,7}} => [2,5,3,7,6,1,4] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1,4},{2,3,6},{5,7}} => {{1,3},{2,5,6},{4,7}} => [3,5,1,7,6,2,4] => ([(0,1),(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1,4},{2,3,6},{5},{7}} => {{1},{2,5,6},{3},{4,7}} => [1,5,3,7,6,2,4] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1,4,7},{2,3},{5,6}} => {{1,4,7},{2,3},{5,6}} => [4,3,2,7,6,5,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3,7},{5,6}} => {{1,5,6},{2,3},{4,7}} => [5,3,2,7,6,1,4] => ([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3},{5,6,7}} => {{1,2,3},{4,7},{5,6}} => [2,3,1,7,6,5,4] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3},{5,6},{7}} => {{1},{2,3},{4,7},{5,6}} => [1,3,2,7,6,5,4] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2,3},{5},{6}} => {{1,4,7},{2},{3},{5,6}} => [4,2,3,7,6,5,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,4},{2,3,7},{5},{6}} => {{1,5,6},{2},{3},{4,7}} => [5,2,3,7,6,1,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,4},{2,3},{5,7},{6}} => {{1,3},{2},{4,7},{5,6}} => [3,2,1,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3},{5},{6,7}} => {{1,2},{3},{4,7},{5,6}} => [2,1,3,7,6,5,4] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5,6}} => [1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6,7},{2,3,4}} => {{1,2,3,7},{4,5,6}} => [2,3,7,5,6,4,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6},{2,3,4,7}} => {{1,4,5,6},{2,3,7}} => [4,3,7,5,6,1,2] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,6},{2,3,4},{7}} => {{1},{2,3,7},{4,5,6}} => [1,3,7,5,6,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2,3,4,6}} => {{1,3,7},{2,4,5,6}} => [3,4,7,5,6,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,3,4,6,7}} => {{1,2,4,5,6},{3,7}} => [2,4,7,5,6,1,3] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2,3,4,6},{7}} => {{1},{2,4,5,6},{3,7}} => [1,4,7,5,6,2,3] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,7},{2,3,4},{6}} => {{1,3,7},{2},{4,5,6}} => [3,2,7,5,6,4,1] => ([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,3,4,7},{6}} => {{1,4,5,6},{2},{3,7}} => [4,2,7,5,6,1,3] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,5},{2,3,4},{6,7}} => {{1,2},{3,7},{4,5,6}} => [2,1,7,5,6,4,3] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,3,4},{6},{7}} => {{1},{2},{3,7},{4,5,6}} => [1,2,7,5,6,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2,3,4,5}} => {{1,2,7},{3,4,5,6}} => [2,7,4,5,6,3,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3,4,5,7}} => {{1,3,4,5,6},{2,7}} => [3,7,4,5,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2,3,4,5},{7}} => {{1},{2,7},{3,4,5,6}} => [1,7,4,5,6,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3,4,5,6}} => {{1,7},{2,3,4,5,6}} => [7,3,4,5,6,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4,5,6,7}} => {{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
{{1},{2,3,4,5,6},{7}} => {{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7)
{{1,7},{2,3,4,5},{6}} => {{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4,5,7},{6}} => {{1,3,4,5,6},{2},{7}} => [3,2,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4,5},{6,7}} => {{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => ([(1,2),(3,6),(4,6),(5,6)],7)
{{1},{2,3,4,5},{6},{7}} => {{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => ([(3,6),(4,6),(5,6)],7)
{{1,6,7},{2,3,4},{5}} => {{1,2,7},{3},{4,5,6}} => [2,7,3,5,6,4,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3,4,7},{5}} => {{1,4,5,6},{2,7},{3}} => [4,7,3,5,6,1,2] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,6},{2,3,4},{5,7}} => {{1,3},{2,7},{4,5,6}} => [3,7,1,5,6,4,2] => ([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3,4},{5},{7}} => {{1},{2,7},{3},{4,5,6}} => [1,7,3,5,6,4,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3,4,6},{5}} => {{1,7},{2,4,5,6},{3}} => [7,4,3,5,6,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4,6,7},{5}} => {{1,2,4,5,6},{3},{7}} => [2,4,3,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4,6},{5,7}} => {{1,3},{2,4,5,6},{7}} => [3,4,1,5,6,2,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1},{2,3,4,6},{5},{7}} => {{1},{2,4,5,6},{3},{7}} => [1,4,3,5,6,2,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3,4},{5,6}} => {{1,7},{2,3},{4,5,6}} => [7,3,2,5,6,4,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4,7},{5,6}} => {{1,4,5,6},{2,3},{7}} => [4,3,2,5,6,1,7] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4},{5,6,7}} => {{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7)
{{1},{2,3,4},{5,6},{7}} => {{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => ([(2,3),(4,6),(5,6)],7)
{{1,7},{2,3,4},{5},{6}} => {{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4,7},{5},{6}} => {{1,4,5,6},{2},{3},{7}} => [4,2,3,5,6,1,7] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,4},{5,7},{6}} => {{1,3},{2},{4,5,6},{7}} => [3,2,1,5,6,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1},{2,3,4},{5},{6,7}} => {{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => ([(2,3),(4,6),(5,6)],7)
{{1},{2,3,4},{5},{6},{7}} => {{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => ([(4,6),(5,6)],7)
{{1,5,6,7},{2,3},{4}} => {{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6},{2,3,7},{4}} => {{1,5,6},{2,3,7},{4}} => [5,3,7,4,6,1,2] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,6},{2,3},{4,7}} => {{1,4},{2,3,7},{5,6}} => [4,3,7,1,6,5,2] => ([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6},{2,3},{4},{7}} => {{1},{2,3,7},{4},{5,6}} => [1,3,7,4,6,5,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2,3,6},{4}} => {{1,3,7},{2,5,6},{4}} => [3,5,7,4,6,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,3,6,7},{4}} => {{1,2,5,6},{3,7},{4}} => [2,5,7,4,6,1,3] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2,3,6},{4,7}} => {{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => ([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,5},{2,3,6},{4},{7}} => {{1},{2,5,6},{3,7},{4}} => [1,5,7,4,6,2,3] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,7},{2,3},{4,6}} => {{1,3,7},{2,4},{5,6}} => [3,4,7,2,6,5,1] => ([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,3,7},{4,6}} => {{1,5,6},{2,4},{3,7}} => [5,4,7,2,6,1,3] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,5},{2,3},{4,6,7}} => {{1,2,4},{3,7},{5,6}} => [2,4,7,1,6,5,3] => ([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
{{1,5},{2,3},{4,6},{7}} => {{1},{2,4},{3,7},{5,6}} => [1,4,7,2,6,5,3] => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2,3},{4},{6}} => {{1,3,7},{2},{4},{5,6}} => [3,2,7,4,6,5,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,3,7},{4},{6}} => {{1,5,6},{2},{3,7},{4}} => [5,2,7,4,6,1,3] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,5},{2,3},{4,7},{6}} => {{1,4},{2},{3,7},{5,6}} => [4,2,7,1,6,5,3] => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,5},{2,3},{4},{6,7}} => {{1,2},{3,7},{4},{5,6}} => [2,1,7,4,6,5,3] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5,6}} => [1,2,7,4,6,5,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2,3,5},{4}} => {{1,2,7},{3,5,6},{4}} => [2,7,5,4,6,3,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3,5,7},{4}} => {{1,3,5,6},{2,7},{4}} => [3,7,5,4,6,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2,3,5},{4,7}} => {{1,4},{2,7},{3,5,6}} => [4,7,5,1,6,3,2] => ([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3,5},{4},{7}} => {{1},{2,7},{3,5,6},{4}} => [1,7,5,4,6,3,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3,5,6},{4}} => {{1,7},{2,3,5,6},{4}} => [7,3,5,4,6,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,5,6,7},{4}} => {{1,2,3,5,6},{4},{7}} => [2,3,5,4,6,1,7] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,5,6},{4,7}} => {{1,4},{2,3,5,6},{7}} => [4,3,5,1,6,2,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,3,5,6},{4},{7}} => {{1},{2,3,5,6},{4},{7}} => [1,3,5,4,6,2,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3,5},{4,6}} => {{1,7},{2,4},{3,5,6}} => [7,4,5,2,6,3,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,5,7},{4,6}} => {{1,3,5,6},{2,4},{7}} => [3,4,5,2,6,1,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,5},{4,6,7}} => {{1,2,4},{3,5,6},{7}} => [2,4,5,1,6,3,7] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,3,5},{4,6},{7}} => {{1},{2,4},{3,5,6},{7}} => [1,4,5,2,6,3,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,7},{2,3,5},{4},{6}} => {{1,7},{2},{3,5,6},{4}} => [7,2,5,4,6,3,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,5,7},{4},{6}} => {{1,3,5,6},{2},{4},{7}} => [3,2,5,4,6,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1},{2,3,5},{4,7},{6}} => {{1,4},{2},{3,5,6},{7}} => [4,2,5,1,6,3,7] => ([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,3,5},{4},{6,7}} => {{1,2},{3,5,6},{4},{7}} => [2,1,5,4,6,3,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,5},{4},{6},{7}} => {{1},{2},{3,5,6},{4},{7}} => [1,2,5,4,6,3,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2,3},{4,5}} => {{1,2,7},{3,4},{5,6}} => [2,7,4,3,6,5,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3,7},{4,5}} => {{1,5,6},{2,7},{3,4}} => [5,7,4,3,6,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2,3},{4,5,7}} => {{1,3,4},{2,7},{5,6}} => [3,7,4,1,6,5,2] => ([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,6},{2,3},{4,5},{7}} => {{1},{2,7},{3,4},{5,6}} => [1,7,4,3,6,5,2] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3,6},{4,5}} => {{1,7},{2,5,6},{3,4}} => [7,5,4,3,6,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,6,7},{4,5}} => {{1,2,5,6},{3,4},{7}} => [2,5,4,3,6,1,7] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,6},{4,5,7}} => {{1,3,4},{2,5,6},{7}} => [3,5,4,1,6,2,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,3,6},{4,5},{7}} => {{1},{2,5,6},{3,4},{7}} => [1,5,4,3,6,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3},{4,5,6}} => {{1,7},{2,3,4},{5,6}} => [7,3,4,2,6,5,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,7},{4,5,6}} => {{1,5,6},{2,3,4},{7}} => [5,3,4,2,6,1,7] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4,5,6,7}} => {{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7)
{{1},{2,3},{4,5,6},{7}} => {{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => ([(2,3),(4,6),(5,6)],7)
{{1,7},{2,3},{4,5},{6}} => {{1,7},{2},{3,4},{5,6}} => [7,2,4,3,6,5,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,7},{4,5},{6}} => {{1,5,6},{2},{3,4},{7}} => [5,2,4,3,6,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4,5,7},{6}} => {{1,3,4},{2},{5,6},{7}} => [3,2,4,1,6,5,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4,5},{6,7}} => {{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => ([(1,6),(2,5),(3,4)],7)
{{1},{2,3},{4,5},{6},{7}} => {{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7)
{{1,6,7},{2,3},{4},{5}} => {{1,2,7},{3},{4},{5,6}} => [2,7,3,4,6,5,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3,7},{4},{5}} => {{1,5,6},{2,7},{3},{4}} => [5,7,3,4,6,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,6},{2,3},{4,7},{5}} => {{1,4},{2,7},{3},{5,6}} => [4,7,3,1,6,5,2] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3},{4},{5,7}} => {{1,3},{2,7},{4},{5,6}} => [3,7,1,4,6,5,2] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5,6}} => [1,7,3,4,6,5,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3,6},{4},{5}} => {{1,7},{2,5,6},{3},{4}} => [7,5,3,4,6,2,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,6,7},{4},{5}} => {{1,2,5,6},{3},{4},{7}} => [2,5,3,4,6,1,7] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,6},{4,7},{5}} => {{1,4},{2,5,6},{3},{7}} => [4,5,3,1,6,2,7] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,6},{4},{5,7}} => {{1,3},{2,5,6},{4},{7}} => [3,5,1,4,6,2,7] => ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1},{2,3,6},{4},{5},{7}} => {{1},{2,5,6},{3},{4},{7}} => [1,5,3,4,6,2,7] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3},{4,6},{5}} => {{1,7},{2,4},{3},{5,6}} => [7,4,3,2,6,5,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,7},{4,6},{5}} => {{1,5,6},{2,4},{3},{7}} => [5,4,3,2,6,1,7] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4,6,7},{5}} => {{1,2,4},{3},{5,6},{7}} => [2,4,3,1,6,5,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4,6},{5,7}} => {{1,3},{2,4},{5,6},{7}} => [3,4,1,2,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,3},{4,6},{5},{7}} => {{1},{2,4},{3},{5,6},{7}} => [1,4,3,2,6,5,7] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,7},{2,3},{4},{5,6}} => {{1,7},{2,3},{4},{5,6}} => [7,3,2,4,6,5,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,7},{4},{5,6}} => {{1,5,6},{2,3},{4},{7}} => [5,3,2,4,6,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4,7},{5,6}} => {{1,4},{2,3},{5,6},{7}} => [4,3,2,1,6,5,7] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4},{5,6,7}} => {{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => ([(2,3),(4,6),(5,6)],7)
{{1},{2,3},{4},{5,6},{7}} => {{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7)
{{1,7},{2,3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3,7},{4},{5},{6}} => {{1,5,6},{2},{3},{4},{7}} => [5,2,3,4,6,1,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4,7},{5},{6}} => {{1,4},{2},{3},{5,6},{7}} => [4,2,3,1,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4},{5,7},{6}} => {{1,3},{2},{4},{5,6},{7}} => [3,2,1,4,6,5,7] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1},{2,3},{4},{5},{6,7}} => {{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => ([(3,6),(4,5)],7)
{{1},{2,3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => ([(5,6)],7)
{{1,4,5,6,7},{2},{3}} => {{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5,6},{2,7},{3}} => {{1,6},{2,3,4,7},{5}} => [6,3,4,7,5,1,2] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,4,5,6},{2},{3,7}} => {{1,5},{2,3,4,7},{6}} => [5,3,4,7,1,6,2] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,4,5,6},{2},{3},{7}} => {{1},{2,3,4,7},{5},{6}} => [1,3,4,7,5,6,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5,7},{2,6},{3}} => {{1,3,4,7},{2,6},{5}} => [3,6,4,7,5,2,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2,6,7},{3}} => {{1,2,6},{3,4,7},{5}} => [2,6,4,7,5,1,3] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,5},{2,6},{3,7}} => {{1,5},{2,6},{3,4,7}} => [5,6,4,7,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
{{1,4,5},{2,6},{3},{7}} => {{1},{2,6},{3,4,7},{5}} => [1,6,4,7,5,2,3] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,5,7},{2},{3,6}} => {{1,3,4,7},{2,5},{6}} => [3,5,4,7,2,6,1] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2,7},{3,6}} => {{1,6},{2,5},{3,4,7}} => [6,5,4,7,2,1,3] => ([(0,1),(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2},{3,6,7}} => {{1,2,5},{3,4,7},{6}} => [2,5,4,7,1,6,3] => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,5},{2},{3,6},{7}} => {{1},{2,5},{3,4,7},{6}} => [1,5,4,7,2,6,3] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1,4,5,7},{2},{3},{6}} => {{1,3,4,7},{2},{5},{6}} => [3,2,4,7,5,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2,7},{3},{6}} => {{1,6},{2},{3,4,7},{5}} => [6,2,4,7,5,1,3] => ([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2},{3,7},{6}} => {{1,5},{2},{3,4,7},{6}} => [5,2,4,7,1,6,3] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,5},{2},{3},{6,7}} => {{1,2},{3,4,7},{5},{6}} => [2,1,4,7,5,6,3] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,5},{2},{3},{6},{7}} => {{1},{2},{3,4,7},{5},{6}} => [1,2,4,7,5,6,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6,7},{2,5},{3}} => {{1,2,4,7},{3,6},{5}} => [2,4,6,7,5,3,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6},{2,5,7},{3}} => {{1,3,6},{2,4,7},{5}} => [3,4,6,7,5,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,6},{2,5},{3,7}} => {{1,5},{2,4,7},{3,6}} => [5,4,6,7,1,3,2] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
{{1,4,6},{2,5},{3},{7}} => {{1},{2,4,7},{3,6},{5}} => [1,4,6,7,5,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2,5,6},{3}} => {{1,4,7},{2,3,6},{5}} => [4,3,6,7,5,2,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,5,6,7},{3}} => {{1,2,3,6},{4,7},{5}} => [2,3,6,7,5,1,4] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,5,6},{3,7}} => {{1,5},{2,3,6},{4,7}} => [5,3,6,7,1,2,4] => ([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,4},{2,5,6},{3},{7}} => {{1},{2,3,6},{4,7},{5}} => [1,3,6,7,5,2,4] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2,5},{3,6}} => {{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,4},{2,5,7},{3,6}} => {{1,3,6},{2,5},{4,7}} => [3,5,6,7,2,1,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,5},{3,6,7}} => {{1,2,5},{3,6},{4,7}} => [2,5,6,7,1,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
{{1,4},{2,5},{3,6},{7}} => {{1},{2,5},{3,6},{4,7}} => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
{{1,4,7},{2,5},{3},{6}} => {{1,4,7},{2},{3,6},{5}} => [4,2,6,7,5,3,1] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,5,7},{3},{6}} => {{1,3,6},{2},{4,7},{5}} => [3,2,6,7,5,1,4] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,5},{3,7},{6}} => {{1,5},{2},{3,6},{4,7}} => [5,2,6,7,1,3,4] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)
{{1,4},{2,5},{3},{6,7}} => {{1,2},{3,6},{4,7},{5}} => [2,1,6,7,5,3,4] => ([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,4},{2,5},{3},{6},{7}} => {{1},{2},{3,6},{4,7},{5}} => [1,2,6,7,5,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,4,6,7},{2},{3,5}} => {{1,2,4,7},{3,5},{6}} => [2,4,5,7,3,6,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6},{2,7},{3,5}} => {{1,6},{2,4,7},{3,5}} => [6,4,5,7,3,1,2] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,4,6},{2},{3,5,7}} => {{1,3,5},{2,4,7},{6}} => [3,4,5,7,1,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)
{{1,4,6},{2},{3,5},{7}} => {{1},{2,4,7},{3,5},{6}} => [1,4,5,7,3,6,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2,6},{3,5}} => {{1,4,7},{2,6},{3,5}} => [4,6,5,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,6,7},{3,5}} => {{1,2,6},{3,5},{4,7}} => [2,6,5,7,3,1,4] => ([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,6},{3,5,7}} => {{1,3,5},{2,6},{4,7}} => [3,6,5,7,1,2,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4},{2,6},{3,5},{7}} => {{1},{2,6},{3,5},{4,7}} => [1,6,5,7,3,2,4] => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2},{3,5,6}} => {{1,4,7},{2,3,5},{6}} => [4,3,5,7,2,6,1] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,7},{3,5,6}} => {{1,6},{2,3,5},{4,7}} => [6,3,5,7,2,1,4] => ([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3,5,6,7}} => {{1,2,3,5},{4,7},{6}} => [2,3,5,7,1,6,4] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)
{{1,4},{2},{3,5,6},{7}} => {{1},{2,3,5},{4,7},{6}} => [1,3,5,7,2,6,4] => ([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,7},{2},{3,5},{6}} => {{1,4,7},{2},{3,5},{6}} => [4,2,5,7,3,6,1] => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,7},{3,5},{6}} => {{1,6},{2},{3,5},{4,7}} => [6,2,5,7,3,1,4] => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3,5,7},{6}} => {{1,3,5},{2},{4,7},{6}} => [3,2,5,7,1,6,4] => ([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
{{1,4},{2},{3,5},{6,7}} => {{1,2},{3,5},{4,7},{6}} => [2,1,5,7,3,6,4] => ([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3,5},{6},{7}} => {{1},{2},{3,5},{4,7},{6}} => [1,2,5,7,3,6,4] => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,4,6,7},{2},{3},{5}} => {{1,2,4,7},{3},{5},{6}} => [2,4,3,7,5,6,1] => ([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6},{2,7},{3},{5}} => {{1,6},{2,4,7},{3},{5}} => [6,4,3,7,5,1,2] => ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,6},{2},{3,7},{5}} => {{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4,6},{2},{3},{5,7}} => {{1,3},{2,4,7},{5},{6}} => [3,4,1,7,5,6,2] => ([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,6},{2},{3},{5},{7}} => {{1},{2,4,7},{3},{5},{6}} => [1,4,3,7,5,6,2] => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2,6},{3},{5}} => {{1,4,7},{2,6},{3},{5}} => [4,6,3,7,5,2,1] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,6,7},{3},{5}} => {{1,2,6},{3},{4,7},{5}} => [2,6,3,7,5,1,4] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,6},{3,7},{5}} => {{1,5},{2,6},{3},{4,7}} => [5,6,3,7,1,2,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,4},{2,6},{3},{5,7}} => {{1,3},{2,6},{4,7},{5}} => [3,6,1,7,5,2,4] => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,6},{3},{5},{7}} => {{1},{2,6},{3},{4,7},{5}} => [1,6,3,7,5,2,4] => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2},{3,6},{5}} => {{1,4,7},{2,5},{3},{6}} => [4,5,3,7,2,6,1] => ([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2,7},{3,6},{5}} => {{1,6},{2,5},{3},{4,7}} => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3,6,7},{5}} => {{1,2,5},{3},{4,7},{6}} => [2,5,3,7,1,6,4] => ([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,4},{2},{3,6},{5,7}} => {{1,3},{2,5},{4,7},{6}} => [3,5,1,7,2,6,4] => ([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
{{1,4},{2},{3,6},{5},{7}} => {{1},{2,5},{3},{4,7},{6}} => [1,5,3,7,2,6,4] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)
{{1,4,7},{2},{3},{5,6}} => {{1,4,7},{2,3},{5},{6}} => [4,3,2,7,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,4},{2,7},{3},{5,6}} => {{1,6},{2,3},{4,7},{5}} => [6,3,2,7,5,1,4] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3,7},{5,6}} => {{1,5},{2,3},{4,7},{6}} => [5,3,2,7,1,6,4] => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,4},{2},{3},{5,6,7}} => {{1,2,3},{4,7},{5},{6}} => [2,3,1,7,5,6,4] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)
{{1,4},{2},{3},{5,6},{7}} => {{1},{2,3},{4,7},{5},{6}} => [1,3,2,7,5,6,4] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4,7},{2},{3},{5},{6}} => {{1,4,7},{2},{3},{5},{6}} => [4,2,3,7,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,4},{2,7},{3},{5},{6}} => {{1,6},{2},{3},{4,7},{5}} => [6,2,3,7,5,1,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3,7},{5},{6}} => {{1,5},{2},{3},{4,7},{6}} => [5,2,3,7,1,6,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)
{{1,4},{2},{3},{5,7},{6}} => {{1,3},{2},{4,7},{5},{6}} => [3,2,1,7,5,6,4] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3},{5},{6,7}} => {{1,2},{3},{4,7},{5},{6}} => [2,1,3,7,5,6,4] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,4},{2},{3},{5},{6},{7}} => {{1},{2},{3},{4,7},{5},{6}} => [1,2,3,7,5,6,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6,7},{2,4},{3}} => {{1,2,3,7},{4,6},{5}} => [2,3,7,6,5,4,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6},{2,4,7},{3}} => {{1,4,6},{2,3,7},{5}} => [4,3,7,6,5,1,2] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,6},{2,4},{3,7}} => {{1,5},{2,3,7},{4,6}} => [5,3,7,6,1,4,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,5,6},{2,4},{3},{7}} => {{1},{2,3,7},{4,6},{5}} => [1,3,7,6,5,4,2] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2,4,6},{3}} => {{1,3,7},{2,4,6},{5}} => [3,4,7,6,5,2,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,4,6,7},{3}} => {{1,2,4,6},{3,7},{5}} => [2,4,7,6,5,1,3] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2,4,6},{3,7}} => {{1,5},{2,4,6},{3,7}} => [5,4,7,6,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
{{1,5},{2,4,6},{3},{7}} => {{1},{2,4,6},{3,7},{5}} => [1,4,7,6,5,2,3] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,7},{2,4},{3,6}} => {{1,3,7},{2,5},{4,6}} => [3,5,7,6,2,4,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,5},{2,4,7},{3,6}} => {{1,4,6},{2,5},{3,7}} => [4,5,7,6,2,1,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
{{1,5},{2,4},{3,6,7}} => {{1,2,5},{3,7},{4,6}} => [2,5,7,6,1,4,3] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
{{1,5},{2,4},{3,6},{7}} => {{1},{2,5},{3,7},{4,6}} => [1,5,7,6,2,4,3] => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2,4},{3},{6}} => {{1,3,7},{2},{4,6},{5}} => [3,2,7,6,5,4,1] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,4,7},{3},{6}} => {{1,4,6},{2},{3,7},{5}} => [4,2,7,6,5,1,3] => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2,4},{3,7},{6}} => {{1,5},{2},{3,7},{4,6}} => [5,2,7,6,1,4,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
{{1,5},{2,4},{3},{6,7}} => {{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,4},{3},{6},{7}} => {{1},{2},{3,7},{4,6},{5}} => [1,2,7,6,5,4,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2,4,5},{3}} => {{1,2,7},{3,4,6},{5}} => [2,7,4,6,5,3,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,4,5,7},{3}} => {{1,3,4,6},{2,7},{5}} => [3,7,4,6,5,1,2] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2,4,5},{3,7}} => {{1,5},{2,7},{3,4,6}} => [5,7,4,6,1,3,2] => ([(0,2),(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,4,5},{3},{7}} => {{1},{2,7},{3,4,6},{5}} => [1,7,4,6,5,3,2] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,4,5,6},{3}} => {{1,7},{2,3,4,6},{5}} => [7,3,4,6,5,2,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,5,6,7},{3}} => {{1,2,3,4,6},{5},{7}} => [2,3,4,6,5,1,7] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,5,6},{3,7}} => {{1,5},{2,3,4,6},{7}} => [5,3,4,6,1,2,7] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,4,5,6},{3},{7}} => {{1},{2,3,4,6},{5},{7}} => [1,3,4,6,5,2,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,4,5},{3,6}} => {{1,7},{2,5},{3,4,6}} => [7,5,4,6,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,5,7},{3,6}} => {{1,3,4,6},{2,5},{7}} => [3,5,4,6,2,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,5},{3,6,7}} => {{1,2,5},{3,4,6},{7}} => [2,5,4,6,1,3,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,4,5},{3,6},{7}} => {{1},{2,5},{3,4,6},{7}} => [1,5,4,6,2,3,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,7},{2,4,5},{3},{6}} => {{1,7},{2},{3,4,6},{5}} => [7,2,4,6,5,3,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,5,7},{3},{6}} => {{1,3,4,6},{2},{5},{7}} => [3,2,4,6,5,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1},{2,4,5},{3,7},{6}} => {{1,5},{2},{3,4,6},{7}} => [5,2,4,6,1,3,7] => ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,5},{3},{6,7}} => {{1,2},{3,4,6},{5},{7}} => [2,1,4,6,5,3,7] => ([(1,2),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,5},{3},{6},{7}} => {{1},{2},{3,4,6},{5},{7}} => [1,2,4,6,5,3,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2,4},{3,5}} => {{1,2,7},{3,5},{4,6}} => [2,7,5,6,3,4,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,4,7},{3,5}} => {{1,4,6},{2,7},{3,5}} => [4,7,5,6,3,1,2] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,6},{2,4},{3,5,7}} => {{1,3,5},{2,7},{4,6}} => [3,7,5,6,1,4,2] => ([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,6},{2,4},{3,5},{7}} => {{1},{2,7},{3,5},{4,6}} => [1,7,5,6,3,4,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,4,6},{3,5}} => {{1,7},{2,4,6},{3,5}} => [7,4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,6,7},{3,5}} => {{1,2,4,6},{3,5},{7}} => [2,4,5,6,3,1,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,6},{3,5,7}} => {{1,3,5},{2,4,6},{7}} => [3,4,5,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,4,6},{3,5},{7}} => {{1},{2,4,6},{3,5},{7}} => [1,4,5,6,3,2,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,4},{3,5,6}} => {{1,7},{2,3,5},{4,6}} => [7,3,5,6,2,4,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,7},{3,5,6}} => {{1,4,6},{2,3,5},{7}} => [4,3,5,6,2,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3,5,6,7}} => {{1,2,3,5},{4,6},{7}} => [2,3,5,6,1,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1},{2,4},{3,5,6},{7}} => {{1},{2,3,5},{4,6},{7}} => [1,3,5,6,2,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,7},{2,4},{3,5},{6}} => {{1,7},{2},{3,5},{4,6}} => [7,2,5,6,3,4,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,7},{3,5},{6}} => {{1,4,6},{2},{3,5},{7}} => [4,2,5,6,3,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3,5,7},{6}} => {{1,3,5},{2},{4,6},{7}} => [3,2,5,6,1,4,7] => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1},{2,4},{3,5},{6,7}} => {{1,2},{3,5},{4,6},{7}} => [2,1,5,6,3,4,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,4},{3,5},{6},{7}} => {{1},{2},{3,5},{4,6},{7}} => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7)
{{1,6,7},{2,4},{3},{5}} => {{1,2,7},{3},{4,6},{5}} => [2,7,3,6,5,4,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,4,7},{3},{5}} => {{1,4,6},{2,7},{3},{5}} => [4,7,3,6,5,1,2] => ([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2,4},{3,7},{5}} => {{1,5},{2,7},{3},{4,6}} => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,4},{3},{5,7}} => {{1,3},{2,7},{4,6},{5}} => [3,7,1,6,5,4,2] => ([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,4},{3},{5},{7}} => {{1},{2,7},{3},{4,6},{5}} => [1,7,3,6,5,4,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,4,6},{3},{5}} => {{1,7},{2,4,6},{3},{5}} => [7,4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,6,7},{3},{5}} => {{1,2,4,6},{3},{5},{7}} => [2,4,3,6,5,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1},{2,4,6},{3,7},{5}} => {{1,5},{2,4,6},{3},{7}} => [5,4,3,6,1,2,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,4,6},{3},{5,7}} => {{1,3},{2,4,6},{5},{7}} => [3,4,1,6,5,2,7] => ([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
{{1},{2,4,6},{3},{5},{7}} => {{1},{2,4,6},{3},{5},{7}} => [1,4,3,6,5,2,7] => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1,7},{2,4},{3,6},{5}} => {{1,7},{2,5},{3},{4,6}} => [7,5,3,6,2,4,1] => ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,7},{3,6},{5}} => {{1,4,6},{2,5},{3},{7}} => [4,5,3,6,2,1,7] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3,6,7},{5}} => {{1,2,5},{3},{4,6},{7}} => [2,5,3,6,1,4,7] => ([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3,6},{5,7}} => {{1,3},{2,5},{4,6},{7}} => [3,5,1,6,2,4,7] => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
{{1},{2,4},{3,6},{5},{7}} => {{1},{2,5},{3},{4,6},{7}} => [1,5,3,6,2,4,7] => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,7},{2,4},{3},{5,6}} => {{1,7},{2,3},{4,6},{5}} => [7,3,2,6,5,4,1] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,7},{3},{5,6}} => {{1,4,6},{2,3},{5},{7}} => [4,3,2,6,5,1,7] => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3,7},{5,6}} => {{1,5},{2,3},{4,6},{7}} => [5,3,2,6,1,4,7] => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3},{5,6,7}} => {{1,2,3},{4,6},{5},{7}} => [2,3,1,6,5,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,5)],7)
{{1},{2,4},{3},{5,6},{7}} => {{1},{2,3},{4,6},{5},{7}} => [1,3,2,6,5,4,7] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1,7},{2,4},{3},{5},{6}} => {{1,7},{2},{3},{4,6},{5}} => [7,2,3,6,5,4,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4,7},{3},{5},{6}} => {{1,4,6},{2},{3},{5},{7}} => [4,2,3,6,5,1,7] => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3,7},{5},{6}} => {{1,5},{2},{3},{4,6},{7}} => [5,2,3,6,1,4,7] => ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3},{5,7},{6}} => {{1,3},{2},{4,6},{5},{7}} => [3,2,1,6,5,4,7] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)
{{1},{2,4},{3},{5},{6,7}} => {{1,2},{3},{4,6},{5},{7}} => [2,1,3,6,5,4,7] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1},{2,4},{3},{5},{6},{7}} => {{1},{2},{3},{4,6},{5},{7}} => [1,2,3,6,5,4,7] => ([(4,5),(4,6),(5,6)],7)
{{1,5,6,7},{2},{3,4}} => {{1,2,3,7},{4,5},{6}} => [2,3,7,5,4,6,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6},{2,7},{3,4}} => {{1,6},{2,3,7},{4,5}} => [6,3,7,5,4,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,6},{2},{3,4,7}} => {{1,4,5},{2,3,7},{6}} => [4,3,7,5,1,6,2] => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,5,6},{2},{3,4},{7}} => {{1},{2,3,7},{4,5},{6}} => [1,3,7,5,4,6,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2,6},{3,4}} => {{1,3,7},{2,6},{4,5}} => [3,6,7,5,4,2,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,6,7},{3,4}} => {{1,2,6},{3,7},{4,5}} => [2,6,7,5,4,1,3] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,6},{3,4,7}} => {{1,4,5},{2,6},{3,7}} => [4,6,7,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
{{1,5},{2,6},{3,4},{7}} => {{1},{2,6},{3,7},{4,5}} => [1,6,7,5,4,2,3] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2},{3,4,6}} => {{1,3,7},{2,4,5},{6}} => [3,4,7,5,2,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,7},{3,4,6}} => {{1,6},{2,4,5},{3,7}} => [6,4,7,5,2,1,3] => ([(0,2),(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2},{3,4,6,7}} => {{1,2,4,5},{3,7},{6}} => [2,4,7,5,1,6,3] => ([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2},{3,4,6},{7}} => {{1},{2,4,5},{3,7},{6}} => [1,4,7,5,2,6,3] => ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2},{3,4},{6}} => {{1,3,7},{2},{4,5},{6}} => [3,2,7,5,4,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,7},{3,4},{6}} => {{1,6},{2},{3,7},{4,5}} => [6,2,7,5,4,1,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2},{3,4,7},{6}} => {{1,4,5},{2},{3,7},{6}} => [4,2,7,5,1,6,3] => ([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2},{3,4},{6,7}} => {{1,2},{3,7},{4,5},{6}} => [2,1,7,5,4,6,3] => ([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2},{3,4},{6},{7}} => {{1},{2},{3,7},{4,5},{6}} => [1,2,7,5,4,6,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2,5},{3,4}} => {{1,2,7},{3,6},{4,5}} => [2,7,6,5,4,3,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,5,7},{3,4}} => {{1,3,6},{2,7},{4,5}} => [3,7,6,5,4,1,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2,5},{3,4,7}} => {{1,4,5},{2,7},{3,6}} => [4,7,6,5,1,3,2] => ([(0,1),(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,5},{3,4},{7}} => {{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,5,6},{3,4}} => {{1,7},{2,3,6},{4,5}} => [7,3,6,5,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,6,7},{3,4}} => {{1,2,3,6},{4,5},{7}} => [2,3,6,5,4,1,7] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,6},{3,4,7}} => {{1,4,5},{2,3,6},{7}} => [4,3,6,5,1,2,7] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,5,6},{3,4},{7}} => {{1},{2,3,6},{4,5},{7}} => [1,3,6,5,4,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,5},{3,4,6}} => {{1,7},{2,4,5},{3,6}} => [7,4,6,5,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,7},{3,4,6}} => {{1,3,6},{2,4,5},{7}} => [3,4,6,5,2,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3,4,6,7}} => {{1,2,4,5},{3,6},{7}} => [2,4,6,5,1,3,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,5},{3,4,6},{7}} => {{1},{2,4,5},{3,6},{7}} => [1,4,6,5,2,3,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,7},{2,5},{3,4},{6}} => {{1,7},{2},{3,6},{4,5}} => [7,2,6,5,4,3,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,7},{3,4},{6}} => {{1,3,6},{2},{4,5},{7}} => [3,2,6,5,4,1,7] => ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3,4,7},{6}} => {{1,4,5},{2},{3,6},{7}} => [4,2,6,5,1,3,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1},{2,5},{3,4},{6,7}} => {{1,2},{3,6},{4,5},{7}} => [2,1,6,5,4,3,7] => ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3,4},{6},{7}} => {{1},{2},{3,6},{4,5},{7}} => [1,2,6,5,4,3,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2},{3,4,5}} => {{1,2,7},{3,4,5},{6}} => [2,7,4,5,3,6,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,7},{3,4,5}} => {{1,6},{2,7},{3,4,5}} => [6,7,4,5,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,6},{2},{3,4,5,7}} => {{1,3,4,5},{2,7},{6}} => [3,7,4,5,1,6,2] => ([(0,5),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,6},{2},{3,4,5},{7}} => {{1},{2,7},{3,4,5},{6}} => [1,7,4,5,3,6,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,6},{3,4,5}} => {{1,7},{2,6},{3,4,5}} => [7,6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6,7},{3,4,5}} => {{1,2,6},{3,4,5},{7}} => [2,6,4,5,3,1,7] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3,4,5,7}} => {{1,3,4,5},{2,6},{7}} => [3,6,4,5,1,2,7] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,6},{3,4,5},{7}} => {{1},{2,6},{3,4,5},{7}} => [1,6,4,5,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3,4,5,6}} => {{1,7},{2,3,4,5},{6}} => [7,3,4,5,2,6,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,4,5,6}} => {{1,6},{2,3,4,5},{7}} => [6,3,4,5,2,1,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4,5,6,7}} => {{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7)
{{1},{2},{3,4,5,6},{7}} => {{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => ([(3,6),(4,6),(5,6)],7)
{{1,7},{2},{3,4,5},{6}} => {{1,7},{2},{3,4,5},{6}} => [7,2,4,5,3,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,4,5},{6}} => {{1,6},{2},{3,4,5},{7}} => [6,2,4,5,3,1,7] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4,5,7},{6}} => {{1,3,4,5},{2},{6},{7}} => [3,2,4,5,1,6,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4,5},{6,7}} => {{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => ([(2,3),(4,6),(5,6)],7)
{{1},{2},{3,4,5},{6},{7}} => {{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => ([(4,6),(5,6)],7)
{{1,6,7},{2},{3,4},{5}} => {{1,2,7},{3},{4,5},{6}} => [2,7,3,5,4,6,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,7},{3,4},{5}} => {{1,6},{2,7},{3},{4,5}} => [6,7,3,5,4,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2},{3,4,7},{5}} => {{1,4,5},{2,7},{3},{6}} => [4,7,3,5,1,6,2] => ([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3,4},{5,7}} => {{1,3},{2,7},{4,5},{6}} => [3,7,1,5,4,6,2] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3,4},{5},{7}} => {{1},{2,7},{3},{4,5},{6}} => [1,7,3,5,4,6,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,6},{3,4},{5}} => {{1,7},{2,6},{3},{4,5}} => [7,6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6,7},{3,4},{5}} => {{1,2,6},{3},{4,5},{7}} => [2,6,3,5,4,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3,4,7},{5}} => {{1,4,5},{2,6},{3},{7}} => [4,6,3,5,1,2,7] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,6},{3,4},{5,7}} => {{1,3},{2,6},{4,5},{7}} => [3,6,1,5,4,2,7] => ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3,4},{5},{7}} => {{1},{2,6},{3},{4,5},{7}} => [1,6,3,5,4,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3,4,6},{5}} => {{1,7},{2,4,5},{3},{6}} => [7,4,3,5,2,6,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,4,6},{5}} => {{1,6},{2,4,5},{3},{7}} => [6,4,3,5,2,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4,6,7},{5}} => {{1,2,4,5},{3},{6},{7}} => [2,4,3,5,1,6,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4,6},{5,7}} => {{1,3},{2,4,5},{6},{7}} => [3,4,1,5,2,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1},{2},{3,4,6},{5},{7}} => {{1},{2,4,5},{3},{6},{7}} => [1,4,3,5,2,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3,4},{5,6}} => {{1,7},{2,3},{4,5},{6}} => [7,3,2,5,4,6,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,4},{5,6}} => {{1,6},{2,3},{4,5},{7}} => [6,3,2,5,4,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4,7},{5,6}} => {{1,4,5},{2,3},{6},{7}} => [4,3,2,5,1,6,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4},{5,6,7}} => {{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => ([(2,3),(4,6),(5,6)],7)
{{1},{2},{3,4},{5,6},{7}} => {{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7)
{{1,7},{2},{3,4},{5},{6}} => {{1,7},{2},{3},{4,5},{6}} => [7,2,3,5,4,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,4},{5},{6}} => {{1,6},{2},{3},{4,5},{7}} => [6,2,3,5,4,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4,7},{5},{6}} => {{1,4,5},{2},{3},{6},{7}} => [4,2,3,5,1,6,7] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4},{5,7},{6}} => {{1,3},{2},{4,5},{6},{7}} => [3,2,1,5,4,6,7] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,4},{5},{6,7}} => {{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => ([(3,6),(4,5)],7)
{{1},{2},{3,4},{5},{6},{7}} => {{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => ([(5,6)],7)
{{1,5,6,7},{2},{3},{4}} => {{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,6},{2,7},{3},{4}} => {{1,6},{2,3,7},{4},{5}} => [6,3,7,4,5,1,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,5,6},{2},{3,7},{4}} => {{1,5},{2,3,7},{4},{6}} => [5,3,7,4,1,6,2] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,5,6},{2},{3},{4,7}} => {{1,4},{2,3,7},{5},{6}} => [4,3,7,1,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,5,6},{2},{3},{4},{7}} => {{1},{2,3,7},{4},{5},{6}} => [1,3,7,4,5,6,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2,6},{3},{4}} => {{1,3,7},{2,6},{4},{5}} => [3,6,7,4,5,2,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,6,7},{3},{4}} => {{1,2,6},{3,7},{4},{5}} => [2,6,7,4,5,1,3] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,5},{2,6},{3,7},{4}} => {{1,5},{2,6},{3,7},{4}} => [5,6,7,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
{{1,5},{2,6},{3},{4,7}} => {{1,4},{2,6},{3,7},{5}} => [4,6,7,1,5,2,3] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2,6},{3},{4},{7}} => {{1},{2,6},{3,7},{4},{5}} => [1,6,7,4,5,2,3] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5,7},{2},{3,6},{4}} => {{1,3,7},{2,5},{4},{6}} => [3,5,7,4,2,6,1] => ([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,7},{3,6},{4}} => {{1,6},{2,5},{3,7},{4}} => [6,5,7,4,2,1,3] => ([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2},{3,6,7},{4}} => {{1,2,5},{3,7},{4},{6}} => [2,5,7,4,1,6,3] => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,5},{2},{3,6},{4,7}} => {{1,4},{2,5},{3,7},{6}} => [4,5,7,1,2,6,3] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)
{{1,5},{2},{3,6},{4},{7}} => {{1},{2,5},{3,7},{4},{6}} => [1,5,7,4,2,6,3] => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2},{3},{4,6}} => {{1,3,7},{2,4},{5},{6}} => [3,4,7,2,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,7},{3},{4,6}} => {{1,6},{2,4},{3,7},{5}} => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2},{3,7},{4,6}} => {{1,5},{2,4},{3,7},{6}} => [5,4,7,2,1,6,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
{{1,5},{2},{3},{4,6,7}} => {{1,2,4},{3,7},{5},{6}} => [2,4,7,1,5,6,3] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1,5},{2},{3},{4,6},{7}} => {{1},{2,4},{3,7},{5},{6}} => [1,4,7,2,5,6,3] => ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5,7},{2},{3},{4},{6}} => {{1,3,7},{2},{4},{5},{6}} => [3,2,7,4,5,6,1] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2,7},{3},{4},{6}} => {{1,6},{2},{3,7},{4},{5}} => [6,2,7,4,5,1,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2},{3,7},{4},{6}} => {{1,5},{2},{3,7},{4},{6}} => [5,2,7,4,1,6,3] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
{{1,5},{2},{3},{4,7},{6}} => {{1,4},{2},{3,7},{5},{6}} => [4,2,7,1,5,6,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)
{{1,5},{2},{3},{4},{6,7}} => {{1,2},{3,7},{4},{5},{6}} => [2,1,7,4,5,6,3] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,5},{2},{3},{4},{6},{7}} => {{1},{2},{3,7},{4},{5},{6}} => [1,2,7,4,5,6,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2,5},{3},{4}} => {{1,2,7},{3,6},{4},{5}} => [2,7,6,4,5,3,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,5,7},{3},{4}} => {{1,3,6},{2,7},{4},{5}} => [3,7,6,4,5,1,2] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2,5},{3,7},{4}} => {{1,5},{2,7},{3,6},{4}} => [5,7,6,4,1,3,2] => ([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,5},{3},{4,7}} => {{1,4},{2,7},{3,6},{5}} => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,5},{3},{4},{7}} => {{1},{2,7},{3,6},{4},{5}} => [1,7,6,4,5,3,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,5,6},{3},{4}} => {{1,7},{2,3,6},{4},{5}} => [7,3,6,4,5,2,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,6,7},{3},{4}} => {{1,2,3,6},{4},{5},{7}} => [2,3,6,4,5,1,7] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,6},{3,7},{4}} => {{1,5},{2,3,6},{4},{7}} => [5,3,6,4,1,2,7] => ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,5,6},{3},{4,7}} => {{1,4},{2,3,6},{5},{7}} => [4,3,6,1,5,2,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
{{1},{2,5,6},{3},{4},{7}} => {{1},{2,3,6},{4},{5},{7}} => [1,3,6,4,5,2,7] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,5},{3,6},{4}} => {{1,7},{2,5},{3,6},{4}} => [7,5,6,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,7},{3,6},{4}} => {{1,3,6},{2,5},{4},{7}} => [3,5,6,4,2,1,7] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3,6,7},{4}} => {{1,2,5},{3,6},{4},{7}} => [2,5,6,4,1,3,7] => ([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3,6},{4,7}} => {{1,4},{2,5},{3,6},{7}} => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
{{1},{2,5},{3,6},{4},{7}} => {{1},{2,5},{3,6},{4},{7}} => [1,5,6,4,2,3,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1,7},{2,5},{3},{4,6}} => {{1,7},{2,4},{3,6},{5}} => [7,4,6,2,5,3,1] => ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,7},{3},{4,6}} => {{1,3,6},{2,4},{5},{7}} => [3,4,6,2,5,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3,7},{4,6}} => {{1,5},{2,4},{3,6},{7}} => [5,4,6,2,1,3,7] => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3},{4,6,7}} => {{1,2,4},{3,6},{5},{7}} => [2,4,6,1,5,3,7] => ([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,5},{3},{4,6},{7}} => {{1},{2,4},{3,6},{5},{7}} => [1,4,6,2,5,3,7] => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1,7},{2,5},{3},{4},{6}} => {{1,7},{2},{3,6},{4},{5}} => [7,2,6,4,5,3,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5,7},{3},{4},{6}} => {{1,3,6},{2},{4},{5},{7}} => [3,2,6,4,5,1,7] => ([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3,7},{4},{6}} => {{1,5},{2},{3,6},{4},{7}} => [5,2,6,4,1,3,7] => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3},{4,7},{6}} => {{1,4},{2},{3,6},{5},{7}} => [4,2,6,1,5,3,7] => ([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)
{{1},{2,5},{3},{4},{6,7}} => {{1,2},{3,6},{4},{5},{7}} => [2,1,6,4,5,3,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,5},{3},{4},{6},{7}} => {{1},{2},{3,6},{4},{5},{7}} => [1,2,6,4,5,3,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6,7},{2},{3,5},{4}} => {{1,2,7},{3,5},{4},{6}} => [2,7,5,4,3,6,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,7},{3,5},{4}} => {{1,6},{2,7},{3,5},{4}} => [6,7,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3,5,7},{4}} => {{1,3,5},{2,7},{4},{6}} => [3,7,5,4,1,6,2] => ([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)
{{1,6},{2},{3,5},{4,7}} => {{1,4},{2,7},{3,5},{6}} => [4,7,5,1,3,6,2] => ([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3,5},{4},{7}} => {{1},{2,7},{3,5},{4},{6}} => [1,7,5,4,3,6,2] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,6},{3,5},{4}} => {{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6,7},{3,5},{4}} => {{1,2,6},{3,5},{4},{7}} => [2,6,5,4,3,1,7] => ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3,5,7},{4}} => {{1,3,5},{2,6},{4},{7}} => [3,6,5,4,1,2,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,6},{3,5},{4,7}} => {{1,4},{2,6},{3,5},{7}} => [4,6,5,1,3,2,7] => ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3,5},{4},{7}} => {{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3,5,6},{4}} => {{1,7},{2,3,5},{4},{6}} => [7,3,5,4,2,6,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,5,6},{4}} => {{1,6},{2,3,5},{4},{7}} => [6,3,5,4,2,1,7] => ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,5,6,7},{4}} => {{1,2,3,5},{4},{6},{7}} => [2,3,5,4,1,6,7] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,5,6},{4,7}} => {{1,4},{2,3,5},{6},{7}} => [4,3,5,1,2,6,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2},{3,5,6},{4},{7}} => {{1},{2,3,5},{4},{6},{7}} => [1,3,5,4,2,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3,5},{4,6}} => {{1,7},{2,4},{3,5},{6}} => [7,4,5,2,3,6,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,5},{4,6}} => {{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,5,7},{4,6}} => {{1,3,5},{2,4},{6},{7}} => [3,4,5,2,1,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,5},{4,6,7}} => {{1,2,4},{3,5},{6},{7}} => [2,4,5,1,3,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
{{1},{2},{3,5},{4,6},{7}} => {{1},{2,4},{3,5},{6},{7}} => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7)
{{1,7},{2},{3,5},{4},{6}} => {{1,7},{2},{3,5},{4},{6}} => [7,2,5,4,3,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,5},{4},{6}} => {{1,6},{2},{3,5},{4},{7}} => [6,2,5,4,3,1,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,5,7},{4},{6}} => {{1,3,5},{2},{4},{6},{7}} => [3,2,5,4,1,6,7] => ([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
{{1},{2},{3,5},{4,7},{6}} => {{1,4},{2},{3,5},{6},{7}} => [4,2,5,1,3,6,7] => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,5},{4},{6,7}} => {{1,2},{3,5},{4},{6},{7}} => [2,1,5,4,3,6,7] => ([(2,3),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,5},{4},{6},{7}} => {{1},{2},{3,5},{4},{6},{7}} => [1,2,5,4,3,6,7] => ([(4,5),(4,6),(5,6)],7)
{{1,6,7},{2},{3},{4,5}} => {{1,2,7},{3,4},{5},{6}} => [2,7,4,3,5,6,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,7},{3},{4,5}} => {{1,6},{2,7},{3,4},{5}} => [6,7,4,3,5,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2},{3,7},{4,5}} => {{1,5},{2,7},{3,4},{6}} => [5,7,4,3,1,6,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3},{4,5,7}} => {{1,3,4},{2,7},{5},{6}} => [3,7,4,1,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3},{4,5},{7}} => {{1},{2,7},{3,4},{5},{6}} => [1,7,4,3,5,6,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,6},{3},{4,5}} => {{1,7},{2,6},{3,4},{5}} => [7,6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6,7},{3},{4,5}} => {{1,2,6},{3,4},{5},{7}} => [2,6,4,3,5,1,7] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3,7},{4,5}} => {{1,5},{2,6},{3,4},{7}} => [5,6,4,3,1,2,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3},{4,5,7}} => {{1,3,4},{2,6},{5},{7}} => [3,6,4,1,5,2,7] => ([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3},{4,5},{7}} => {{1},{2,6},{3,4},{5},{7}} => [1,6,4,3,5,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3,6},{4,5}} => {{1,7},{2,5},{3,4},{6}} => [7,5,4,3,2,6,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,6},{4,5}} => {{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,6,7},{4,5}} => {{1,2,5},{3,4},{6},{7}} => [2,5,4,3,1,6,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,6},{4,5,7}} => {{1,3,4},{2,5},{6},{7}} => [3,5,4,1,2,6,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2},{3,6},{4,5},{7}} => {{1},{2,5},{3,4},{6},{7}} => [1,5,4,3,2,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3},{4,5,6}} => {{1,7},{2,3,4},{5},{6}} => [7,3,4,2,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3},{4,5,6}} => {{1,6},{2,3,4},{5},{7}} => [6,3,4,2,5,1,7] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,7},{4,5,6}} => {{1,5},{2,3,4},{6},{7}} => [5,3,4,2,1,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4,5,6,7}} => {{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7)
{{1},{2},{3},{4,5,6},{7}} => {{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => ([(4,6),(5,6)],7)
{{1,7},{2},{3},{4,5},{6}} => {{1,7},{2},{3,4},{5},{6}} => [7,2,4,3,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3},{4,5},{6}} => {{1,6},{2},{3,4},{5},{7}} => [6,2,4,3,5,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,7},{4,5},{6}} => {{1,5},{2},{3,4},{6},{7}} => [5,2,4,3,1,6,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4,5,7},{6}} => {{1,3,4},{2},{5},{6},{7}} => [3,2,4,1,5,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4,5},{6,7}} => {{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => ([(3,6),(4,5)],7)
{{1},{2},{3},{4,5},{6},{7}} => {{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => ([(5,6)],7)
{{1,6,7},{2},{3},{4},{5}} => {{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2,7},{3},{4},{5}} => {{1,6},{2,7},{3},{4},{5}} => [6,7,3,4,5,1,2] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1,6},{2},{3,7},{4},{5}} => {{1,5},{2,7},{3},{4},{6}} => [5,7,3,4,1,6,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3},{4,7},{5}} => {{1,4},{2,7},{3},{5},{6}} => [4,7,3,1,5,6,2] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3},{4},{5,7}} => {{1,3},{2,7},{4},{5},{6}} => [3,7,1,4,5,6,2] => ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,6},{2},{3},{4},{5},{7}} => {{1},{2,7},{3},{4},{5},{6}} => [1,7,3,4,5,6,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2,6},{3},{4},{5}} => {{1,7},{2,6},{3},{4},{5}} => [7,6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6,7},{3},{4},{5}} => {{1,2,6},{3},{4},{5},{7}} => [2,6,3,4,5,1,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3,7},{4},{5}} => {{1,5},{2,6},{3},{4},{7}} => [5,6,3,4,1,2,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2,6},{3},{4,7},{5}} => {{1,4},{2,6},{3},{5},{7}} => [4,6,3,1,5,2,7] => ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3},{4},{5,7}} => {{1,3},{2,6},{4},{5},{7}} => [3,6,1,4,5,2,7] => ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,6},{3},{4},{5},{7}} => {{1},{2,6},{3},{4},{5},{7}} => [1,6,3,4,5,2,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3,6},{4},{5}} => {{1,7},{2,5},{3},{4},{6}} => [7,5,3,4,2,6,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3,6},{4},{5}} => {{1,6},{2,5},{3},{4},{7}} => [6,5,3,4,2,1,7] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,6,7},{4},{5}} => {{1,2,5},{3},{4},{6},{7}} => [2,5,3,4,1,6,7] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,6},{4,7},{5}} => {{1,4},{2,5},{3},{6},{7}} => [4,5,3,1,2,6,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
{{1},{2},{3,6},{4},{5,7}} => {{1,3},{2,5},{4},{6},{7}} => [3,5,1,4,2,6,7] => ([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,6},{4},{5},{7}} => {{1},{2,5},{3},{4},{6},{7}} => [1,5,3,4,2,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3},{4,6},{5}} => {{1,7},{2,4},{3},{5},{6}} => [7,4,3,2,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3},{4,6},{5}} => {{1,6},{2,4},{3},{5},{7}} => [6,4,3,2,5,1,7] => ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,7},{4,6},{5}} => {{1,5},{2,4},{3},{6},{7}} => [5,4,3,2,1,6,7] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4,6,7},{5}} => {{1,2,4},{3},{5},{6},{7}} => [2,4,3,1,5,6,7] => ([(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4,6},{5,7}} => {{1,3},{2,4},{5},{6},{7}} => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7)
{{1},{2},{3},{4,6},{5},{7}} => {{1},{2,4},{3},{5},{6},{7}} => [1,4,3,2,5,6,7] => ([(4,5),(4,6),(5,6)],7)
{{1,7},{2},{3},{4},{5,6}} => {{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3},{4},{5,6}} => {{1,6},{2,3},{4},{5},{7}} => [6,3,2,4,5,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,7},{4},{5,6}} => {{1,5},{2,3},{4},{6},{7}} => [5,3,2,4,1,6,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4,7},{5,6}} => {{1,4},{2,3},{5},{6},{7}} => [4,3,2,1,5,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4},{5,6,7}} => {{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => ([(4,6),(5,6)],7)
{{1},{2},{3},{4},{5,6},{7}} => {{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => ([(5,6)],7)
{{1,7},{2},{3},{4},{5},{6}} => {{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2,7},{3},{4},{5},{6}} => {{1,6},{2},{3},{4},{5},{7}} => [6,2,3,4,5,1,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3,7},{4},{5},{6}} => {{1,5},{2},{3},{4},{6},{7}} => [5,2,3,4,1,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4,7},{5},{6}} => {{1,4},{2},{3},{5},{6},{7}} => [4,2,3,1,5,6,7] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4},{5,7},{6}} => {{1,3},{2},{4},{5},{6},{7}} => [3,2,1,4,5,6,7] => ([(4,5),(4,6),(5,6)],7)
{{1},{2},{3},{4},{5},{6,7}} => {{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => ([(5,6)],7)
{{1},{2},{3},{4},{5},{6},{7}} => {{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => ([],7)
{{1,2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7,8}} => [2,1,4,3,6,5,8,7] => ([(0,7),(1,6),(2,5),(3,4)],8)
{{1,3},{2,4},{5,6},{7,8}} => {{1,2},{3,4},{5,7},{6,8}} => [2,1,4,3,7,8,5,6] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,3},{5,6},{7,8}} => {{1,2},{3,4},{5,8},{6,7}} => [2,1,4,3,8,7,6,5] => ([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3},{4,6},{7,8}} => {{1,2},{3,5},{4,8},{6,7}} => [2,1,5,8,3,7,6,4] => ([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3},{4,5},{7,8}} => {{1,2},{3,8},{4,5},{6,7}} => [2,1,8,5,4,7,6,3] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3},{4,5},{6,8}} => {{1,3},{2,8},{4,5},{6,7}} => [3,8,1,5,4,7,6,2] => ([(0,1),(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3},{4,5},{6,7}} => {{1,8},{2,3},{4,5},{6,7}} => [8,3,2,5,4,7,6,1] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4},{3,5},{6,7}} => {{1,8},{2,3},{4,6},{5,7}} => [8,3,2,6,7,4,5,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4},{3,5},{6,8}} => {{1,3},{2,8},{4,6},{5,7}} => [3,8,1,6,7,4,5,2] => ([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,4},{3,5},{7,8}} => {{1,2},{3,8},{4,6},{5,7}} => [2,1,8,6,7,4,5,3] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4},{3,6},{7,8}} => {{1,2},{3,6},{4,8},{5,7}} => [2,1,6,8,7,3,5,4] => ([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5},{3,6},{7,8}} => {{1,2},{3,6},{4,7},{5,8}} => [2,1,6,7,8,3,4,5] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,3},{2,5},{4,6},{7,8}} => {{1,2},{3,5},{4,7},{6,8}} => [2,1,5,7,3,8,4,6] => ([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
{{1,2},{3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6},{7,8}} => [2,1,5,6,3,4,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,6},{4,5},{7,8}} => {{1,2},{3,6},{4,5},{7,8}} => [2,1,6,5,4,3,8,7] => ([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6},{4,5},{7,8}} => {{1,2},{3,7},{4,5},{6,8}} => [2,1,7,5,4,8,3,6] => ([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,6},{3,5},{7,8}} => {{1,2},{3,7},{4,6},{5,8}} => [2,1,7,6,8,4,3,5] => ([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6},{3,4},{7,8}} => {{1,2},{3,7},{4,8},{5,6}} => [2,1,7,8,6,5,3,4] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5},{3,4},{7,8}} => {{1,2},{3,8},{4,7},{5,6}} => [2,1,8,7,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,5},{3,4},{6,8}} => {{1,3},{2,8},{4,7},{5,6}} => [3,8,1,7,6,5,4,2] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5},{3,4},{6,7}} => {{1,8},{2,3},{4,7},{5,6}} => [8,3,2,7,6,5,4,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6},{3,4},{5,7}} => {{1,8},{2,4},{3,7},{5,6}} => [8,4,7,2,6,5,3,1] => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3,4},{5,8}} => {{1,4},{2,8},{3,7},{5,6}} => [4,8,7,1,6,5,3,2] => ([(0,1),(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,7},{3,4},{5,8}} => {{1,4},{2,7},{3,8},{5,6}} => [4,7,8,1,6,5,2,3] => ([(0,1),(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2,7},{3,4},{6,8}} => {{1,3},{2,7},{4,8},{5,6}} => [3,7,1,8,6,5,2,4] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,7},{3,5},{6,8}} => {{1,3},{2,7},{4,6},{5,8}} => [3,7,1,6,8,4,2,5] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,7},{4,5},{6,8}} => {{1,3},{2,7},{4,5},{6,8}} => [3,7,1,5,4,8,2,6] => ([(0,3),(0,7),(1,2),(1,7),(2,6),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,7},{4,5},{6,8}} => {{1,3},{2,6},{4,5},{7,8}} => [3,6,1,5,4,2,8,7] => ([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,8},{4,5},{6,7}} => {{1,6},{2,3},{4,5},{7,8}} => [6,3,2,5,4,1,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,8},{4,5},{6,7}} => {{1,7},{2,3},{4,5},{6,8}} => [7,3,2,5,4,8,1,6] => ([(0,1),(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,8},{3,5},{6,7}} => {{1,7},{2,3},{4,6},{5,8}} => [7,3,2,6,8,4,1,5] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3,4},{6,7}} => {{1,7},{2,3},{4,8},{5,6}} => [7,3,2,8,6,5,1,4] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,8},{3,4},{5,7}} => {{1,7},{2,4},{3,8},{5,6}} => [7,4,8,2,6,5,1,3] => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3,4},{5,6}} => {{1,7},{2,8},{3,4},{5,6}} => [7,8,4,3,6,5,1,2] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,8},{2,7},{3,4},{5,6}} => {{1,8},{2,7},{3,4},{5,6}} => [8,7,4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,7},{3,5},{4,6}} => {{1,8},{2,7},{3,5},{4,6}} => [8,7,5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3,5},{4,6}} => {{1,7},{2,8},{3,5},{4,6}} => [7,8,5,6,3,4,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,8},{3,5},{4,7}} => {{1,7},{2,5},{3,8},{4,6}} => [7,5,8,6,2,4,1,3] => ([(0,2),(0,3),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3,6},{4,7}} => {{1,7},{2,5},{3,6},{4,8}} => [7,5,6,8,2,3,1,4] => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,8},{3,6},{5,7}} => {{1,7},{2,4},{3,6},{5,8}} => [7,4,6,2,8,3,1,5] => ([(0,1),(0,5),(0,7),(1,4),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,8},{4,6},{5,7}} => {{1,7},{2,4},{3,5},{6,8}} => [7,4,5,2,3,8,1,6] => ([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,8},{4,6},{5,7}} => {{1,6},{2,4},{3,5},{7,8}} => [6,4,5,2,3,1,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,7},{4,6},{5,8}} => {{1,4},{2,6},{3,5},{7,8}} => [4,6,5,1,3,2,8,7] => ([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,7},{4,6},{5,8}} => {{1,4},{2,7},{3,5},{6,8}} => [4,7,5,1,3,8,2,6] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,7},{3,6},{5,8}} => {{1,4},{2,7},{3,6},{5,8}} => [4,7,6,1,8,3,2,5] => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,7},{3,6},{4,8}} => {{1,5},{2,7},{3,6},{4,8}} => [5,7,6,8,1,3,2,4] => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,7},{3,5},{4,8}} => {{1,5},{2,7},{3,8},{4,6}} => [5,7,8,6,1,4,2,3] => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3,5},{4,8}} => {{1,5},{2,8},{3,7},{4,6}} => [5,8,7,6,1,4,3,2] => ([(0,1),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6},{3,5},{4,7}} => {{1,8},{2,5},{3,7},{4,6}} => [8,5,7,6,2,4,3,1] => ([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5},{3,6},{4,7}} => {{1,8},{2,5},{3,6},{4,7}} => [8,5,6,7,2,3,4,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,5},{3,6},{4,8}} => {{1,5},{2,8},{3,6},{4,7}} => [5,8,6,7,1,3,4,2] => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5},{3,7},{4,8}} => {{1,5},{2,6},{3,8},{4,7}} => [5,6,8,7,1,2,4,3] => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6},{3,7},{4,8}} => {{1,5},{2,6},{3,7},{4,8}} => [5,6,7,8,1,2,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
{{1,4},{2,6},{3,7},{5,8}} => {{1,4},{2,6},{3,7},{5,8}} => [4,6,7,1,8,2,3,5] => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,6},{4,7},{5,8}} => {{1,4},{2,5},{3,7},{6,8}} => [4,5,7,1,2,8,3,6] => ([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1,2},{3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6},{7,8}} => [4,5,6,1,2,3,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,2},{3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6},{7,8}} => [3,5,1,6,2,4,8,7] => ([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
{{1,3},{2,5},{4,7},{6,8}} => {{1,3},{2,5},{4,7},{6,8}} => [3,5,1,7,2,8,4,6] => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1,4},{2,5},{3,7},{6,8}} => {{1,3},{2,6},{4,7},{5,8}} => [3,6,1,7,8,2,4,5] => ([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1,5},{2,4},{3,7},{6,8}} => {{1,3},{2,6},{4,8},{5,7}} => [3,6,1,8,7,2,5,4] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,6},{2,4},{3,7},{5,8}} => {{1,4},{2,6},{3,8},{5,7}} => [4,6,8,1,7,2,5,3] => ([(0,1),(0,5),(0,7),(1,4),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,7},{2,4},{3,6},{5,8}} => {{1,4},{2,8},{3,6},{5,7}} => [4,8,6,1,7,3,5,2] => ([(0,1),(0,5),(0,7),(1,4),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4},{3,6},{5,7}} => {{1,8},{2,4},{3,6},{5,7}} => [8,4,6,2,7,3,5,1] => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3},{4,6},{5,7}} => {{1,8},{2,4},{3,5},{6,7}} => [8,4,5,2,3,7,6,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3},{4,6},{5,8}} => {{1,4},{2,8},{3,5},{6,7}} => [4,8,5,1,3,7,6,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3},{4,7},{5,8}} => {{1,4},{2,5},{3,8},{6,7}} => [4,5,8,1,2,7,6,3] => ([(0,2),(0,3),(0,7),(1,2),(1,3),(1,7),(2,6),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3},{4,7},{6,8}} => {{1,3},{2,5},{4,8},{6,7}} => [3,5,1,8,2,7,6,4] => ([(0,1),(0,5),(1,4),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5,7},{6,8}} => {{1,3},{2,4},{5,8},{6,7}} => [3,4,1,2,8,7,6,5] => ([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4},{5,7},{6,8}} => {{1,3},{2,4},{5,7},{6,8}} => [3,4,1,2,7,8,5,6] => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)
{{1,2},{3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6},{7,8}} => [3,4,1,2,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7,8}} => [4,3,2,1,6,5,8,7] => ([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4},{5,8},{6,7}} => {{1,4},{2,3},{5,7},{6,8}} => [4,3,2,1,7,8,5,6] => ([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6,7}} => [4,3,2,1,8,7,6,5] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3},{4,8},{6,7}} => {{1,5},{2,3},{4,8},{6,7}} => [5,3,2,8,1,7,6,4] => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,6},{2,3},{4,8},{5,7}} => {{1,5},{2,4},{3,8},{6,7}} => [5,4,8,2,1,7,6,3] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,7},{2,3},{4,8},{5,6}} => {{1,5},{2,8},{3,4},{6,7}} => [5,8,4,3,1,7,6,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3},{4,7},{5,6}} => {{1,8},{2,5},{3,4},{6,7}} => [8,5,4,3,2,7,6,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4},{3,7},{5,6}} => {{1,8},{2,6},{3,4},{5,7}} => [8,6,4,3,7,2,5,1] => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4},{3,8},{5,6}} => {{1,6},{2,8},{3,4},{5,7}} => [6,8,4,3,7,1,5,2] => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,6},{2,4},{3,8},{5,7}} => {{1,6},{2,4},{3,8},{5,7}} => [6,4,8,2,7,1,5,3] => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2,4},{3,8},{6,7}} => {{1,6},{2,3},{4,8},{5,7}} => [6,3,2,8,7,1,5,4] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,4},{2,5},{3,8},{6,7}} => {{1,6},{2,3},{4,7},{5,8}} => [6,3,2,7,8,1,4,5] => ([(0,2),(0,3),(0,7),(1,2),(1,3),(1,7),(2,6),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,5},{4,8},{6,7}} => {{1,5},{2,3},{4,7},{6,8}} => [5,3,2,7,1,8,4,6] => ([(0,1),(0,5),(1,4),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,2},{3,5},{4,8},{6,7}} => {{1,5},{2,3},{4,6},{7,8}} => [5,3,2,6,1,4,8,7] => ([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,6},{4,8},{5,7}} => {{1,5},{2,4},{3,6},{7,8}} => [5,4,6,2,1,3,8,7] => ([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6},{4,8},{5,7}} => {{1,5},{2,4},{3,7},{6,8}} => [5,4,7,2,1,8,3,6] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4},{2,6},{3,8},{5,7}} => {{1,6},{2,4},{3,7},{5,8}} => [6,4,7,2,8,1,3,5] => ([(0,1),(0,5),(0,7),(1,4),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2,6},{3,8},{4,7}} => {{1,6},{2,5},{3,7},{4,8}} => [6,5,7,8,2,1,3,4] => ([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5},{3,8},{4,7}} => {{1,6},{2,5},{3,8},{4,7}} => [6,5,8,7,2,1,4,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)
{{1,7},{2,5},{3,8},{4,6}} => {{1,6},{2,8},{3,5},{4,7}} => [6,8,5,7,3,1,4,2] => ([(0,2),(0,3),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5},{3,7},{4,6}} => {{1,8},{2,6},{3,5},{4,7}} => [8,6,5,7,3,2,4,1] => ([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6},{3,7},{4,5}} => {{1,8},{2,6},{3,7},{4,5}} => [8,6,7,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3,8},{4,5}} => {{1,6},{2,8},{3,7},{4,5}} => [6,8,7,5,4,1,3,2] => ([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,7},{3,8},{4,5}} => {{1,6},{2,7},{3,8},{4,5}} => [6,7,8,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,7},{3,8},{4,6}} => {{1,6},{2,7},{3,5},{4,8}} => [6,7,5,8,3,1,2,4] => ([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,7},{3,8},{5,6}} => {{1,6},{2,7},{3,4},{5,8}} => [6,7,4,3,8,1,2,5] => ([(0,1),(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,7},{4,8},{5,6}} => {{1,5},{2,7},{3,4},{6,8}} => [5,7,4,3,1,8,2,6] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,7},{4,8},{5,6}} => {{1,5},{2,6},{3,4},{7,8}} => [5,6,4,3,1,2,8,7] => ([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,8},{4,7},{5,6}} => {{1,6},{2,5},{3,4},{7,8}} => [6,5,4,3,2,1,8,7] => ([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,8},{4,7},{5,6}} => {{1,7},{2,5},{3,4},{6,8}} => [7,5,4,3,2,8,1,6] => ([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,8},{3,7},{5,6}} => {{1,7},{2,6},{3,4},{5,8}} => [7,6,4,3,8,2,1,5] => ([(0,1),(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3,7},{4,6}} => {{1,7},{2,6},{3,5},{4,8}} => [7,6,5,8,3,2,1,4] => ([(0,1),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,8},{3,7},{4,5}} => {{1,7},{2,6},{3,8},{4,5}} => [7,6,8,5,4,2,1,3] => ([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3,6},{4,5}} => {{1,7},{2,8},{3,6},{4,5}} => [7,8,6,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,7},{3,6},{4,5}} => {{1,8},{2,7},{3,6},{4,5}} => [8,7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7,8},{9,10}} => [2,1,4,3,6,5,8,7,10,9] => ([(0,9),(1,8),(2,7),(3,6),(4,5)],10)
{{1,6},{2,7},{3,8},{4,9},{5,10}} => {{1,6},{2,7},{3,8},{4,9},{5,10}} => [6,7,8,9,10,1,2,3,4,5] => ([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9)],10)
{{1},{2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7},{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},{8}} => [2,1,3,4,5,6,7,8] => ([(6,7)],8)
{{1},{2},{3},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6},{7},{8}} => [3,2,1,4,5,6,7,8] => ([(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6},{7},{8}} => [2,3,1,4,5,6,7,8] => ([(5,7),(6,7)],8)
{{1},{2},{3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6},{7},{8}} => [2,1,4,3,5,6,7,8] => ([(4,7),(5,6)],8)
{{1},{2},{3},{4},{5,8},{6},{7}} => {{1,4},{2},{3},{5},{6},{7},{8}} => [4,2,3,1,5,6,7,8] => ([(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6},{7},{8}} => [4,3,2,1,5,6,7,8] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4},{5,6,8},{7}} => {{1,3,4},{2},{5},{6},{7},{8}} => [3,2,4,1,5,6,7,8] => ([(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6},{7},{8}} => [2,3,4,1,5,6,7,8] => ([(4,7),(5,7),(6,7)],8)
{{1},{2},{3},{4,5},{6},{7,8}} => {{1,2},{3},{4,5},{6},{7},{8}} => [2,1,3,5,4,6,7,8] => ([(4,7),(5,6)],8)
{{1},{2},{3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6},{7},{8}} => [2,3,1,5,4,6,7,8] => ([(3,4),(5,7),(6,7)],8)
{{1},{2},{3},{4,6},{5},{7,8}} => {{1,2},{3,5},{4},{6},{7},{8}} => [2,1,5,4,3,6,7,8] => ([(3,4),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4,8},{5},{6},{7}} => {{1,5},{2},{3},{4},{6},{7},{8}} => [5,2,3,4,1,6,7,8] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4,6,8},{5},{7}} => {{1,3,5},{2},{4},{6},{7},{8}} => [3,2,5,4,1,6,7,8] => ([(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1},{2},{3},{4,5,6},{7,8}} => {{1,2},{3,4,5},{6},{7},{8}} => [2,1,4,5,3,6,7,8] => ([(3,4),(5,7),(6,7)],8)
{{1},{2},{3},{4,8},{5,6},{7}} => {{1,5},{2},{3,4},{6},{7},{8}} => [5,2,4,3,1,6,7,8] => ([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6},{7},{8}} => [5,4,3,2,1,6,7,8] => ([(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4,8},{5,6,7}} => {{1,5},{2,3,4},{6},{7},{8}} => [5,3,4,2,1,6,7,8] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4,5,6,7,8}} => {{1,2,3,4,5},{6},{7},{8}} => [2,3,4,5,1,6,7,8] => ([(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2},{3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6},{7},{8}} => [2,1,3,4,6,5,7,8] => ([(4,7),(5,6)],8)
{{1},{2},{3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => ([(4,7),(5,6)],8)
{{1},{2},{3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6},{7},{8}} => [2,1,4,3,6,5,7,8] => ([(2,7),(3,6),(4,5)],8)
{{1},{2},{3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6},{7},{8}} => [4,3,2,1,6,5,7,8] => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7},{8}} => [2,3,4,1,6,5,7,8] => ([(2,3),(4,7),(5,7),(6,7)],8)
{{1},{2},{3,8},{4},{5},{6},{7}} => {{1,6},{2},{3},{4},{5},{7},{8}} => [6,2,3,4,5,1,7,8] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,5,6,7,8},{4}} => {{1,2,3,4,6},{5},{7},{8}} => [2,3,4,6,5,1,7,8] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,4,5},{6,7,8}} => {{1,2,3},{4,5,6},{7},{8}} => [2,3,1,5,6,4,7,8] => ([(2,7),(3,7),(4,6),(5,6)],8)
{{1},{2},{3,8},{4,5},{6},{7}} => {{1,6},{2},{3},{4,5},{7},{8}} => [6,2,3,5,4,1,7,8] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,8},{4,6},{5},{7}} => {{1,6},{2},{3,5},{4},{7},{8}} => [6,2,5,4,3,1,7,8] => ([(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,4,6,7,8},{5}} => {{1,2,3,5,6},{4},{7},{8}} => [2,3,5,4,6,1,7,8] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,4,5,6,8},{7}} => {{1,3,4,5,6},{2},{7},{8}} => [3,2,4,5,6,1,7,8] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7},{8}} => [2,3,4,5,6,1,7,8] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2,3},{4},{5},{6,7},{8}} => {{1},{2,3},{4},{5},{6,7},{8}} => [1,3,2,4,5,7,6,8] => ([(4,7),(5,6)],8)
{{1},{2,3},{4},{5,6,7,8}} => {{1,2,3,4},{5},{6,7},{8}} => [2,3,4,1,5,7,6,8] => ([(2,3),(4,7),(5,7),(6,7)],8)
{{1},{2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7},{8}} => [1,3,2,5,4,7,6,8] => ([(2,7),(3,6),(4,5)],8)
{{1},{2,3},{4,5},{6,8},{7}} => {{1,3},{2},{4,5},{6,7},{8}} => [3,2,1,5,4,7,6,8] => ([(1,4),(2,3),(5,6),(5,7),(6,7)],8)
{{1},{2,3},{4,5},{6,7,8}} => {{1,2,3},{4,5},{6,7},{8}} => [2,3,1,5,4,7,6,8] => ([(1,4),(2,3),(5,7),(6,7)],8)
{{1},{2,3},{4,8},{5},{6,7}} => {{1,5},{2,3},{4},{6,7},{8}} => [5,3,2,4,1,7,6,8] => ([(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3},{4,6,8},{5},{7}} => {{1,3,5},{2},{4},{6,7},{8}} => [3,2,5,4,1,7,6,8] => ([(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1},{2,3},{4,7},{5,6},{8}} => {{1},{2,5},{3,4},{6,7},{8}} => [1,5,4,3,2,7,6,8] => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3},{4,7,8},{5,6}} => {{1,2,5},{3,4},{6,7},{8}} => [2,5,4,3,1,7,6,8] => ([(1,2),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3},{4,5,7},{6},{8}} => {{1},{2,4,5},{3},{6,7},{8}} => [1,4,3,5,2,7,6,8] => ([(2,3),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6,7},{8}} => [5,4,3,2,1,7,6,8] => ([(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7},{8}} => [2,3,4,5,1,7,6,8] => ([(1,2),(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2,4},{3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,7},{6},{8}} => [1,4,3,2,7,6,5,8] => ([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
{{1},{2,4},{3},{5,8},{6,7}} => {{1,4},{2,3},{5,7},{6},{8}} => [4,3,2,1,7,6,5,8] => ([(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3},{4},{5},{6},{7}} => {{1,7},{2},{3},{4},{5},{6},{8}} => [7,2,3,4,5,6,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,8},{3},{4},{5},{7}} => {{1,3,7},{2},{4},{5},{6},{8}} => [3,2,7,4,5,6,1,8] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,6,7,8},{3},{4}} => {{1,2,3,4,7},{5},{6},{8}} => [2,3,4,7,5,6,1,8] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3},{4,5},{6,7}} => {{1,7},{2,3},{4,5},{6},{8}} => [7,3,2,5,4,6,1,8] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,8},{3},{4,5},{7}} => {{1,3,7},{2},{4,5},{6},{8}} => [3,2,7,5,4,6,1,8] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,7,8},{3},{4,5}} => {{1,2,3,7},{4,5},{6},{8}} => [2,3,7,5,4,6,1,8] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,6,7},{3},{5},{8}} => {{1},{2,3,5,7},{4},{6},{8}} => [1,3,5,4,7,6,2,8] => ([(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1},{2,4,8},{3},{5},{6,7}} => {{1,5,7},{2,3},{4},{6},{8}} => [5,3,2,4,7,6,1,8] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,6,8},{3},{5},{7}} => {{1,3,5,7},{2},{4},{6},{8}} => [3,2,5,4,7,6,1,8] => ([(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2,8},{3},{4,7},{5,6}} => {{1,7},{2,5},{3,4},{6},{8}} => [7,5,4,3,2,6,1,8] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,8},{3},{5,6},{7}} => {{1,5,7},{2},{3,4},{6},{8}} => [5,2,4,3,7,6,1,8] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3},{4,5,7},{6}} => {{1,7},{2,4,5},{3},{6},{8}} => [7,4,3,5,2,6,1,8] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,8},{3},{5,7},{6}} => {{1,5,7},{2,4},{3},{6},{8}} => [5,4,3,2,7,6,1,8] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7},{6},{8}} => [1,3,4,5,7,6,2,8] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,8},{3},{5,6,7}} => {{1,5,7},{2,3,4},{6},{8}} => [5,3,4,2,7,6,1,8] => ([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5,8},{3},{6,7}} => {{1,4,5,7},{2,3},{6},{8}} => [4,3,2,5,7,6,1,8] => ([(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7},{6},{8}} => [2,3,4,5,7,6,1,8] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6,7},{8}} => [1,3,4,2,6,7,5,8] => ([(2,7),(3,7),(4,6),(5,6)],8)
{{1},{2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7},{8}} => [2,3,4,1,6,7,5,8] => ([(1,7),(2,7),(3,7),(4,6),(5,6)],8)
{{1},{2,5},{3,4},{6,7},{8}} => {{1},{2,3},{4,7},{5,6},{8}} => [1,3,2,7,6,5,4,8] => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5},{3,4},{6,8},{7}} => {{1,3},{2},{4,7},{5,6},{8}} => [3,2,1,7,6,5,4,8] => ([(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,4},{5},{6},{7}} => {{1,7},{2},{3},{4},{5,6},{8}} => [7,2,3,4,6,5,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,8},{3,4},{5},{7}} => {{1,3,7},{2},{4},{5,6},{8}} => [3,2,7,4,6,5,1,8] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,4},{5,7},{6}} => {{1,7},{2,4},{3},{5,6},{8}} => [7,4,3,2,6,5,1,8] => ([(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,6,7,8},{3,4}} => {{1,2,3,4,7},{5,6},{8}} => [2,3,4,7,6,5,1,8] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5},{4},{6,7},{8}} => {{1},{2,3},{4,6,7},{5},{8}} => [1,3,2,6,5,7,4,8] => ([(2,3),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5},{4},{6,8},{7}} => {{1,3},{2},{4,6,7},{5},{8}} => [3,2,1,6,5,7,4,8] => ([(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5},{4},{6,7,8}} => {{1,2,3},{4,6,7},{5},{8}} => [2,3,1,6,5,7,4,8] => ([(1,7),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,5},{4},{6},{7}} => {{1,7},{2},{3},{4,6},{5},{8}} => [7,2,3,6,5,4,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,8},{3,5},{4},{7}} => {{1,3,7},{2},{4,6},{5},{8}} => [3,2,7,6,5,4,1,8] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,7,8},{3,5},{4}} => {{1,2,3,7},{4,6},{5},{8}} => [2,3,7,6,5,4,1,8] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,6,7},{4},{5},{8}} => {{1},{2,3,6,7},{4},{5},{8}} => [1,3,6,4,5,7,2,8] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,7,8},{3,5,6},{4}} => {{1,2,7},{3,4,6},{5},{8}} => [2,7,4,6,5,3,1,8] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,7},{4},{5,6}} => {{1,7},{2,6},{3,4},{5},{8}} => [7,6,4,3,5,2,1,8] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5,7},{4},{6},{8}} => {{1},{2,4,6,7},{3},{5},{8}} => [1,4,3,6,5,7,2,8] => ([(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1},{2,8},{3,5,7},{4},{6}} => {{1,7},{2,4,6},{3},{5},{8}} => [7,4,3,6,5,2,1,8] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5,8},{4},{6,7}} => {{1,4,6,7},{2,3},{5},{8}} => [4,3,2,6,5,7,1,8] => ([(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7},{5},{8}} => [2,3,4,6,5,7,1,8] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7},{8}} => [2,3,1,5,6,7,4,8] => ([(1,7),(2,7),(3,7),(4,6),(5,6)],8)
{{1},{2,8},{3,4,5},{6},{7}} => {{1,7},{2},{3},{4,5,6},{8}} => [7,2,3,5,6,4,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,8},{3,4,5},{7}} => {{1,3,7},{2},{4,5,6},{8}} => [3,2,7,5,6,4,1,8] => ([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,7},{3,6},{4,5},{8}} => {{1},{2,7},{3,6},{4,5},{8}} => [1,7,6,5,4,3,2,8] => ([(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,6},{4,5},{7}} => {{1,7},{2},{3,6},{4,5},{8}} => [7,2,6,5,4,3,1,8] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,7,8},{3,6},{4,5}} => {{1,2,7},{3,6},{4,5},{8}} => [2,7,6,5,4,3,1,8] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,7},{4,5},{6}} => {{1,7},{2,6},{3},{4,5},{8}} => [7,6,3,5,4,2,1,8] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,8},{4,5},{6},{7}} => {{1,6,7},{2},{3},{4,5},{8}} => [6,2,3,5,4,7,1,8] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,6,7},{4,5},{8}} => {{1},{2,3,6,7},{4,5},{8}} => [1,3,6,5,4,7,2,8] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,8},{4,5},{6,7}} => {{1,6,7},{2,3},{4,5},{8}} => [6,3,2,5,4,7,1,8] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,7},{4,6},{5}} => {{1,7},{2,6},{3,5},{4},{8}} => [7,6,5,4,3,2,1,8] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,7,8},{5},{6}} => {{1,2,5,6,7},{3},{4},{8}} => [2,5,3,4,6,7,1,8] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,4,6,7},{5}} => {{1,7},{2,3,5,6},{4},{8}} => [7,3,5,4,6,2,1,8] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,8},{4,6,7},{5}} => {{1,6,7},{2,3,5},{4},{8}} => [6,3,5,4,2,7,1,8] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,6,7,8},{5}} => {{1,2,3,5,6,7},{4},{8}} => [2,3,5,4,6,7,1,8] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7},{8}} => [1,2,4,5,6,7,3,8] => ([(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2,8},{3,7},{4,5,6}} => {{1,7},{2,6},{3,4,5},{8}} => [7,6,4,5,3,2,1,8] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,8},{4,7},{5,6}} => {{1,6,7},{2,5},{3,4},{8}} => [6,5,4,3,2,7,1,8] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,8},{5,7},{6}} => {{1,5,6,7},{2,4},{3},{8}} => [5,4,3,2,6,7,1,8] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,5,8},{6},{7}} => {{1,4,5,6,7},{2},{3},{8}} => [4,2,3,5,6,7,1,8] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,4,5,6,7}} => {{1,7},{2,3,4,5,6},{8}} => [7,3,4,5,6,2,1,8] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,5,8},{6,7}} => {{1,4,5,6,7},{2,3},{8}} => [4,3,2,5,6,7,1,8] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,5,6,8},{7}} => {{1,3,4,5,6,7},{2},{8}} => [3,2,4,5,6,7,1,8] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7},{8}} => [2,3,4,5,6,7,1,8] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1,2},{3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6},{7,8}} => [1,2,3,4,5,6,8,7] => ([(6,7)],8)
{{1,2},{3},{4},{5},{6},{7,8}} => {{1,2},{3},{4},{5},{6},{7,8}} => [2,1,3,4,5,6,8,7] => ([(4,7),(5,6)],8)
{{1,2},{3},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6},{7,8}} => [3,2,1,4,5,6,8,7] => ([(3,4),(5,6),(5,7),(6,7)],8)
{{1,2},{3},{4},{5,7},{6},{8}} => {{1},{2,4},{3},{5},{6},{7,8}} => [1,4,3,2,5,6,8,7] => ([(3,4),(5,6),(5,7),(6,7)],8)
{{1,2},{3},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6},{7,8}} => [4,3,2,1,5,6,8,7] => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3},{4,6,8},{5},{7}} => {{1,3,5},{2},{4},{6},{7,8}} => [3,2,5,4,1,6,8,7] => ([(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2},{3},{4,6,7,8},{5}} => {{1,2,3,5},{4},{6},{7,8}} => [2,3,5,4,1,6,8,7] => ([(1,2),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3},{4,8},{5,6},{7}} => {{1,5},{2},{3,4},{6},{7,8}} => [5,2,4,3,1,6,8,7] => ([(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3},{4,7,8},{5,6}} => {{1,2,5},{3,4},{6},{7,8}} => [2,5,4,3,1,6,8,7] => ([(1,2),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6},{7,8}} => [5,4,3,2,1,6,8,7] => ([(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4},{5},{6,7,8}} => {{1,2,3},{4},{5,6},{7,8}} => [2,3,1,4,6,5,8,7] => ([(1,4),(2,3),(5,7),(6,7)],8)
{{1,2},{3,4},{5,8},{6},{7}} => {{1,4},{2},{3},{5,6},{7,8}} => [4,2,3,1,6,5,8,7] => ([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4},{5,7,8},{6}} => {{1,2,4},{3},{5,6},{7,8}} => [2,4,3,1,6,5,8,7] => ([(0,3),(1,2),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4},{5,6,7},{8}} => {{1},{2,3,4},{5,6},{7,8}} => [1,3,4,2,6,5,8,7] => ([(1,4),(2,3),(5,7),(6,7)],8)
{{1,2},{3,4},{5,6,8},{7}} => {{1,3,4},{2},{5,6},{7,8}} => [3,2,4,1,6,5,8,7] => ([(0,3),(1,2),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4},{5,6,7,8}} => {{1,2,3,4},{5,6},{7,8}} => [2,3,4,1,6,5,8,7] => ([(0,3),(1,2),(4,7),(5,7),(6,7)],8)
{{1,2},{3,5},{4},{6,8},{7}} => {{1,3},{2},{4,6},{5},{7,8}} => [3,2,1,6,5,4,8,7] => ([(0,1),(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
{{1,2},{3,5},{4},{6,7,8}} => {{1,2,3},{4,6},{5},{7,8}} => [2,3,1,6,5,4,8,7] => ([(0,1),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,2},{3,8},{4},{5},{6},{7}} => {{1,6},{2},{3},{4},{5},{7,8}} => [6,2,3,4,5,1,8,7] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,6,7,8},{4},{5}} => {{1,2,3,6},{4},{5},{7,8}} => [2,3,6,4,5,1,8,7] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5,6},{4},{7,8}} => {{1,2},{3,4,6},{5},{7,8}} => [2,1,4,6,5,3,8,7] => ([(0,3),(1,2),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,7,8},{4},{5,6}} => {{1,2,6},{3,4},{5},{7,8}} => [2,6,4,3,5,1,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5,7,8},{4},{6}} => {{1,2,4,6},{3},{5},{7,8}} => [2,4,3,6,5,1,8,7] => ([(0,7),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2},{3,8},{4},{5,6,7}} => {{1,6},{2,3,4},{5},{7,8}} => [6,3,4,2,5,1,8,7] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5,8},{4},{6,7}} => {{1,4,6},{2,3},{5},{7,8}} => [4,3,2,6,5,1,8,7] => ([(0,1),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,5},{6},{7,8}} => {{1,2},{3},{4,5,6},{7,8}} => [2,1,3,5,6,4,8,7] => ([(1,4),(2,3),(5,7),(6,7)],8)
{{1,2},{3,7,8},{4,5},{6}} => {{1,2,6},{3},{4,5},{7,8}} => [2,6,3,5,4,1,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,6,7},{4,5},{8}} => {{1},{2,3,6},{4,5},{7,8}} => [1,3,6,5,4,2,8,7] => ([(1,2),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,6,8},{4,5},{7}} => {{1,3,6},{2},{4,5},{7,8}} => [3,2,6,5,4,1,8,7] => ([(0,1),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,6,7,8},{4,5}} => {{1,2,3,6},{4,5},{7,8}} => [2,3,6,5,4,1,8,7] => ([(0,1),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,6},{5},{7,8}} => {{1,2},{3,5,6},{4},{7,8}} => [2,1,5,4,6,3,8,7] => ([(0,3),(1,2),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,7},{4,6},{5},{8}} => {{1},{2,6},{3,5},{4},{7,8}} => [1,6,5,4,3,2,8,7] => ([(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,7,8},{4,6},{5}} => {{1,2,6},{3,5},{4},{7,8}} => [2,6,5,4,3,1,8,7] => ([(0,7),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,8},{4,6,7},{5}} => {{1,6},{2,3,5},{4},{7,8}} => [6,3,5,4,2,1,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,8},{5},{6,7}} => {{1,5,6},{2,3},{4},{7,8}} => [5,3,2,4,6,1,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,6,8},{5},{7}} => {{1,3,5,6},{2},{4},{7,8}} => [3,2,5,4,6,1,8,7] => ([(0,7),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2},{3,4,5,6},{7,8}} => {{1,2},{3,4,5,6},{7,8}} => [2,1,4,5,6,3,8,7] => ([(0,3),(1,2),(4,7),(5,7),(6,7)],8)
{{1,2},{3,4,8},{5,6},{7}} => {{1,5,6},{2},{3,4},{7,8}} => [5,2,4,3,6,1,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,8},{4,5,7},{6}} => {{1,6},{2,4,5},{3},{7,8}} => [6,4,3,5,2,1,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,8},{5,7},{6}} => {{1,5,6},{2,4},{3},{7,8}} => [5,4,3,2,6,1,8,7] => ([(0,7),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,5,8},{6},{7}} => {{1,4,5,6},{2},{3},{7,8}} => [4,2,3,5,6,1,8,7] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,5,7,8},{6}} => {{1,2,4,5,6},{3},{7,8}} => [2,4,3,5,6,1,8,7] => ([(0,1),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,5,8},{6,7}} => {{1,4,5,6},{2,3},{7,8}} => [4,3,2,5,6,1,8,7] => ([(0,1),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,5,6,7,8}} => {{1,2,3,4,5,6},{7,8}} => [2,3,4,5,6,1,8,7] => ([(0,1),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3},{2},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,8},{7}} => [1,2,3,4,5,8,7,6] => ([(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6,8},{7}} => [3,2,1,4,5,8,7,6] => ([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
{{1,3},{2},{4},{5,7},{6},{8}} => {{1},{2,4},{3},{5},{6,8},{7}} => [1,4,3,2,5,8,7,6] => ([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)
{{1,3},{2},{4},{5,8},{6},{7}} => {{1,4},{2},{3},{5},{6,8},{7}} => [4,2,3,1,5,8,7,6] => ([(1,2),(1,3),(2,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4},{5,6,8},{7}} => {{1,3,4},{2},{5},{6,8},{7}} => [3,2,4,1,5,8,7,6] => ([(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,8},{7}} => [1,3,2,5,4,8,7,6] => ([(1,4),(2,3),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,8},{5},{6,7}} => {{1,5},{2,3},{4},{6,8},{7}} => [5,3,2,4,1,8,7,6] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,6,8},{5},{7}} => {{1,3,5},{2},{4},{6,8},{7}} => [3,2,5,4,1,8,7,6] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3},{2},{4,6,7,8},{5}} => {{1,2,3,5},{4},{6,8},{7}} => [2,3,5,4,1,8,7,6] => ([(0,7),(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,7},{5,6},{8}} => {{1},{2,5},{3,4},{6,8},{7}} => [1,5,4,3,2,8,7,6] => ([(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,8},{5,6},{7}} => {{1,5},{2},{3,4},{6,8},{7}} => [5,2,4,3,1,8,7,6] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,7,8},{5,6}} => {{1,2,5},{3,4},{6,8},{7}} => [2,5,4,3,1,8,7,6] => ([(0,7),(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6,8},{7}} => [5,4,3,2,1,8,7,6] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,5,8},{6},{7}} => {{1,4,5},{2},{3},{6,8},{7}} => [4,2,3,5,1,8,7,6] => ([(0,7),(1,2),(1,3),(2,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,8},{5,6,7}} => {{1,5},{2,3,4},{6,8},{7}} => [5,3,4,2,1,8,7,6] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,5,8},{6,7}} => {{1,4,5},{2,3},{6,8},{7}} => [4,3,2,5,1,8,7,6] => ([(0,7),(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,5,6,8},{7}} => {{1,3,4,5},{2},{6,8},{7}} => [3,2,4,5,1,8,7,6] => ([(0,7),(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,5,6,7,8}} => {{1,2,3,4,5},{6,8},{7}} => [2,3,4,5,1,8,7,6] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,6)],8)
{{1,4},{2},{3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,8},{6},{7}} => [1,2,3,4,8,6,7,5] => ([(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3},{5,8},{6},{7}} => {{1,4},{2},{3},{5,8},{6},{7}} => [4,2,3,1,8,6,7,5] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)
{{1,4},{2},{3},{5,8},{6,7}} => {{1,4},{2,3},{5,8},{6},{7}} => [4,3,2,1,8,6,7,5] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(6,7)],8)
{{1,5},{2},{3},{4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5},{6},{7}} => [1,2,3,8,5,6,7,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2},{3},{4},{5},{7},{8}} => {{1},{2},{3,8},{4},{5},{6},{7}} => [1,2,8,4,5,6,7,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3},{4},{5},{6},{8}} => {{1},{2,8},{3},{4},{5},{6},{7}} => [1,8,3,4,5,6,7,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6},{7}} => [8,2,3,4,5,6,7,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2},{3},{4},{5},{6}} => {{1,2,8},{3},{4},{5},{6},{7}} => [2,8,3,4,5,6,7,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2},{3},{4},{5},{8}} => {{1},{2,3,8},{4},{5},{6},{7}} => [1,3,8,4,5,6,7,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3},{4},{5},{6,7}} => {{1,8},{2,3},{4},{5},{6},{7}} => [8,3,2,4,5,6,7,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2},{3},{4},{5},{7}} => {{1,3,8},{2},{4},{5},{6},{7}} => [3,2,8,4,5,6,7,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7,8},{2},{3},{4},{5}} => {{1,2,3,8},{4},{5},{6},{7}} => [2,3,8,4,5,6,7,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2},{3},{4},{7},{8}} => {{1},{2},{3,4,8},{5},{6},{7}} => [1,2,4,8,5,6,7,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2},{3},{4},{6},{8}} => {{1},{2,4,8},{3},{5},{6},{7}} => [1,4,3,8,5,6,7,2] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3},{4},{5,7},{6}} => {{1,8},{2,4},{3},{5},{6},{7}} => [8,4,3,2,5,6,7,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7},{2},{3},{4},{8}} => {{1},{2,3,4,8},{5},{6},{7}} => [1,3,4,8,5,6,7,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3},{4},{5,6,7}} => {{1,8},{2,3,4},{5},{6},{7}} => [8,3,4,2,5,6,7,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7,8},{2},{3},{4}} => {{1,2,3,4,8},{5},{6},{7}} => [2,3,4,8,5,6,7,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2},{3},{6},{7},{8}} => {{1},{2},{3},{4,5,8},{6},{7}} => [1,2,3,5,8,6,7,4] => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3},{4,5},{6},{7}} => {{1,8},{2},{3},{4,5},{6},{7}} => [8,2,3,5,4,6,7,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2},{3},{4,5},{8}} => {{1},{2,3,8},{4,5},{6},{7}} => [1,3,8,5,4,6,7,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7,8},{2},{3},{4,5}} => {{1,2,3,8},{4,5},{6},{7}} => [2,3,8,5,4,6,7,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2},{3},{5},{7},{8}} => {{1},{2},{3,5,8},{4},{6},{7}} => [1,2,5,4,8,6,7,3] => ([(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2},{3},{5},{6},{8}} => {{1},{2,5,8},{3},{4},{6},{7}} => [1,5,3,4,8,6,7,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,8},{2},{3},{4,7},{5},{6}} => {{1,8},{2,5},{3},{4},{6},{7}} => [8,5,3,4,2,6,7,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,7,8},{2},{3},{5}} => {{1,2,3,5,8},{4},{6},{7}} => [2,3,5,4,8,6,7,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6},{2},{3},{7},{8}} => {{1},{2},{3,4,5,8},{6},{7}} => [1,2,4,5,8,6,7,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6},{2},{3},{7,8}} => {{1,2},{3,4,5,8},{6},{7}} => [2,1,4,5,8,6,7,3] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7,8},{2},{3},{5,6}} => {{1,2,5,8},{3,4},{6},{7}} => [2,5,4,3,8,6,7,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4,5,6,7},{2},{3},{8}} => {{1},{2,3,4,5,8},{6},{7}} => [1,3,4,5,8,6,7,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2},{3},{5,6,7}} => {{1,5,8},{2,3,4},{6},{7}} => [5,3,4,2,8,6,7,1] => ([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6,7,8},{2},{3}} => {{1,2,3,4,5,8},{6},{7}} => [2,3,4,5,8,6,7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,8},{7}} => [1,2,3,4,6,8,7,5] => ([(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2},{5,6},{7,8}} => {{1,2},{3,4},{5,6,8},{7}} => [2,1,4,3,6,8,7,5] => ([(0,3),(1,2),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2},{5,7,8},{6}} => {{1,2,4},{3},{5,6,8},{7}} => [2,4,3,1,6,8,7,5] => ([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,3,4},{2},{5,6,7},{8}} => {{1},{2,3,4},{5,6,8},{7}} => [1,3,4,2,6,8,7,5] => ([(1,7),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2},{5,8},{6,7}} => {{1,4},{2,3},{5,6,8},{7}} => [4,3,2,1,6,8,7,5] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)
{{1,3,4},{2},{5,6,8},{7}} => {{1,3,4},{2},{5,6,8},{7}} => [3,2,4,1,6,8,7,5] => ([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,3,4},{2},{5,6,7,8}} => {{1,2,3,4},{5,6,8},{7}} => [2,3,4,1,6,8,7,5] => ([(0,7),(1,6),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,5},{2},{3,4},{6,7},{8}} => {{1},{2,3},{4,8},{5,6},{7}} => [1,3,2,8,6,5,7,4] => ([(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2},{3,4},{6,8},{7}} => {{1,3},{2},{4,8},{5,6},{7}} => [3,2,1,8,6,5,7,4] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2},{3,4},{7,8}} => {{1,2},{3,4,8},{5,6},{7}} => [2,1,4,8,6,5,7,3] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3,4},{5,6},{8}} => {{1},{2,8},{3,4},{5,6},{7}} => [1,8,4,3,6,5,7,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2},{3,4},{5,6}} => {{1,2,8},{3,4},{5,6},{7}} => [2,8,4,3,6,5,7,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2},{3,4},{6},{8}} => {{1},{2,4,8},{3},{5,6},{7}} => [1,4,3,8,6,5,7,2] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7,8},{2},{3,4},{6}} => {{1,2,4,8},{3},{5,6},{7}} => [2,4,3,8,6,5,7,1] => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7,8},{2},{3,4}} => {{1,2,3,4,8},{5,6},{7}} => [2,3,4,8,6,5,7,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2},{4},{6},{7},{8}} => {{1},{2},{3},{4,6,8},{5},{7}} => [1,2,3,6,5,8,7,4] => ([(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,5},{2},{4},{6,7},{8}} => {{1},{2,3},{4,6,8},{5},{7}} => [1,3,2,6,5,8,7,4] => ([(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,5},{2},{4},{6,8},{7}} => {{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,6,5,8,7,4] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,5},{2},{4},{6,7,8}} => {{1,2,3},{4,6,8},{5},{7}} => [2,3,1,6,5,8,7,4] => ([(0,6),(1,6),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7)],8)
{{1,6,7,8},{2},{3,5},{4}} => {{1,2,3,8},{4,6},{5},{7}} => [2,3,8,6,5,4,7,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,7},{2},{4},{5},{8}} => {{1},{2,3,6,8},{4},{5},{7}} => [1,3,6,4,5,8,7,2] => ([(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,7,8},{2},{4},{5}} => {{1,2,3,6,8},{4},{5},{7}} => [2,3,6,4,5,8,7,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,6},{2},{4},{7,8}} => {{1,2},{3,4,6,8},{5},{7}} => [2,1,4,6,5,8,7,3] => ([(0,7),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,7},{2},{3,5,6},{4},{8}} => {{1},{2,8},{3,4,6},{5},{7}} => [1,8,4,6,5,3,7,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2},{3,5,6},{4}} => {{1,2,8},{3,4,6},{5},{7}} => [2,8,4,6,5,3,7,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2},{4},{5,6},{8}} => {{1},{2,6,8},{3,4},{5},{7}} => [1,6,4,3,5,8,7,2] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3,7},{4},{5,6}} => {{1,8},{2,6},{3,4},{5},{7}} => [8,6,4,3,5,2,7,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7,8},{2},{4},{5,6}} => {{1,2,6,8},{3,4},{5},{7}} => [2,6,4,3,5,8,7,1] => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,7},{2},{4},{6},{8}} => {{1},{2,4,6,8},{3},{5},{7}} => [1,4,3,6,5,8,7,2] => ([(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3,5,7,8},{2},{4},{6}} => {{1,2,4,6,8},{3},{5},{7}} => [2,4,3,6,5,8,7,1] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3,5,8},{2},{4},{6,7}} => {{1,4,6,8},{2,3},{5},{7}} => [4,3,2,6,5,8,7,1] => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,6,8},{2},{4},{7}} => {{1,3,4,6,8},{2},{5},{7}} => [3,2,4,6,5,8,7,1] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3,5,6,7,8},{2},{4}} => {{1,2,3,4,6,8},{5},{7}} => [2,3,4,6,5,8,7,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,4,5},{2},{6},{7},{8}} => {{1},{2},{3},{4,5,6,8},{7}} => [1,2,3,5,6,8,7,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5},{2},{6,7},{8}} => {{1},{2,3},{4,5,6,8},{7}} => [1,3,2,5,6,8,7,4] => ([(1,2),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5},{2},{6,8},{7}} => {{1,3},{2},{4,5,6,8},{7}} => [3,2,1,5,6,8,7,4] => ([(0,7),(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,6},{2},{3,4,5},{7,8}} => {{1,2},{3,8},{4,5,6},{7}} => [2,1,8,5,6,4,7,3] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2},{3,4,5},{7}} => {{1,3,8},{2},{4,5,6},{7}} => [3,2,8,5,6,4,7,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7,8},{2},{3,4,5}} => {{1,2,3,8},{4,5,6},{7}} => [2,3,8,5,6,4,7,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2},{4,5},{7,8}} => {{1,2},{3,6,8},{4,5},{7}} => [2,1,6,5,4,8,7,3] => ([(0,1),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3,6},{4,5},{8}} => {{1},{2,8},{3,6},{4,5},{7}} => [1,8,6,5,4,3,7,2] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2},{4,5},{6},{8}} => {{1},{2,6,8},{3},{4,5},{7}} => [1,6,3,5,4,8,7,2] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7,8},{2},{4,5},{6}} => {{1,2,6,8},{3},{4,5},{7}} => [2,6,3,5,4,8,7,1] => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,7},{2},{4,5},{8}} => {{1},{2,3,6,8},{4,5},{7}} => [1,3,6,5,4,8,7,2] => ([(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3,6,7},{4,5}} => {{1,8},{2,3,6},{4,5},{7}} => [8,3,6,5,4,2,7,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2},{4,5},{6,7}} => {{1,6,8},{2,3},{4,5},{7}} => [6,3,2,5,4,8,7,1] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,8},{2},{4,5},{7}} => {{1,3,6,8},{2},{4,5},{7}} => [3,2,6,5,4,8,7,1] => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2},{5},{7,8}} => {{1,2},{3,5,6,8},{4},{7}} => [2,1,5,4,6,8,7,3] => ([(0,7),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,7},{2},{3,4,6},{5},{8}} => {{1},{2,8},{3,5,6},{4},{7}} => [1,8,5,4,6,3,7,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2},{4,6},{5},{8}} => {{1},{2,6,8},{3,5},{4},{7}} => [1,6,5,4,3,8,7,2] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7,8},{2},{4,6},{5}} => {{1,2,6,8},{3,5},{4},{7}} => [2,6,5,4,3,8,7,1] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,7,8},{2},{5},{6}} => {{1,2,5,6,8},{3},{4},{7}} => [2,5,3,4,6,8,7,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2},{4,6,7},{5}} => {{1,6,8},{2,3,5},{4},{7}} => [6,3,5,4,2,8,7,1] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6,8},{2},{5},{7}} => {{1,3,5,6,8},{2},{4},{7}} => [3,2,5,4,6,8,7,1] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3,4,5,6},{2},{7},{8}} => {{1},{2},{3,4,5,6,8},{7}} => [1,2,4,5,6,8,7,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,6},{2},{7,8}} => {{1,2},{3,4,5,6,8},{7}} => [2,1,4,5,6,8,7,3] => ([(0,1),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2},{4,5,6},{8}} => {{1},{2,6,8},{3,4,5},{7}} => [1,6,4,5,3,8,7,2] => ([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3,7},{4,5,6}} => {{1,8},{2,6},{3,4,5},{7}} => [8,6,4,5,3,2,7,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3,4,7},{5,6}} => {{1,8},{2,5,6},{3,4},{7}} => [8,5,4,3,6,2,7,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2},{4,7},{5,6}} => {{1,6,8},{2,5},{3,4},{7}} => [6,5,4,3,2,8,7,1] => ([(0,1),(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3,4,5,7},{6}} => {{1,8},{2,4,5,6},{3},{7}} => [8,4,3,5,6,2,7,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,8},{2},{5,7},{6}} => {{1,5,6,8},{2,4},{3},{7}} => [5,4,3,2,6,8,7,1] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,8},{2},{6},{7}} => {{1,4,5,6,8},{2},{3},{7}} => [4,2,3,5,6,8,7,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,7,8},{2},{6}} => {{1,2,4,5,6,8},{3},{7}} => [2,4,3,5,6,8,7,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,4,5,6,7},{2},{8}} => {{1},{2,3,4,5,6,8},{7}} => [1,3,4,5,6,8,7,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,8},{2},{6,7}} => {{1,4,5,6,8},{2,3},{7}} => [4,3,2,5,6,8,7,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,6,8},{2},{7}} => {{1,3,4,5,6,8},{2},{7}} => [3,2,4,5,6,8,7,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,4,5,6,7,8},{2}} => {{1,2,3,4,5,6,8},{7}} => [2,3,4,5,6,8,7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5},{6,7,8}} => [1,2,3,4,5,7,8,6] => ([(5,7),(6,7)],8)
{{1,2,3},{4},{5},{6,8},{7}} => {{1,3},{2},{4},{5},{6,7,8}} => [3,2,1,4,5,7,8,6] => ([(2,7),(3,7),(4,5),(4,6),(5,6)],8)
{{1,2,3},{4},{5},{6,7,8}} => {{1,2,3},{4},{5},{6,7,8}} => [2,3,1,4,5,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8)
{{1,2,3},{4},{5,6},{7,8}} => {{1,2},{3,4},{5},{6,7,8}} => [2,1,4,3,5,7,8,6] => ([(1,4),(2,3),(5,7),(6,7)],8)
{{1,2,3},{4},{5,7},{6},{8}} => {{1},{2,4},{3},{5},{6,7,8}} => [1,4,3,2,5,7,8,6] => ([(2,7),(3,7),(4,5),(4,6),(5,6)],8)
{{1,2,3},{4},{5,8},{6,7}} => {{1,4},{2,3},{5},{6,7,8}} => [4,3,2,1,5,7,8,6] => ([(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4},{5,6,8},{7}} => {{1,3,4},{2},{5},{6,7,8}} => [3,2,4,1,5,7,8,6] => ([(1,7),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4,5},{6},{7,8}} => {{1,2},{3},{4,5},{6,7,8}} => [2,1,3,5,4,7,8,6] => ([(1,4),(2,3),(5,7),(6,7)],8)
{{1,2,3},{4,5},{6,7},{8}} => {{1},{2,3},{4,5},{6,7,8}} => [1,3,2,5,4,7,8,6] => ([(1,4),(2,3),(5,7),(6,7)],8)
{{1,2,3},{4,6},{5},{7},{8}} => {{1},{2},{3,5},{4},{6,7,8}} => [1,2,5,4,3,7,8,6] => ([(2,7),(3,7),(4,5),(4,6),(5,6)],8)
{{1,2,3},{4,6,7},{5},{8}} => {{1},{2,3,5},{4},{6,7,8}} => [1,3,5,4,2,7,8,6] => ([(1,7),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4,6,8},{5},{7}} => {{1,3,5},{2},{4},{6,7,8}} => [3,2,5,4,1,7,8,6] => ([(0,6),(1,6),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7)],8)
{{1,2,3},{4,5,6},{7},{8}} => {{1},{2},{3,4,5},{6,7,8}} => [1,2,4,5,3,7,8,6] => ([(2,7),(3,7),(4,6),(5,6)],8)
{{1,2,3},{4,7},{5,6},{8}} => {{1},{2,5},{3,4},{6,7,8}} => [1,5,4,3,2,7,8,6] => ([(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4,8},{5,7},{6}} => {{1,5},{2,4},{3},{6,7,8}} => [5,4,3,2,1,7,8,6] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4,5,8},{6},{7}} => {{1,4,5},{2},{3},{6,7,8}} => [4,2,3,5,1,7,8,6] => ([(0,7),(1,3),(2,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4,8},{5,6,7}} => {{1,5},{2,3,4},{6,7,8}} => [5,3,4,2,1,7,8,6] => ([(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3},{4,5,6,7,8}} => {{1,2,3,4,5},{6,7,8}} => [2,3,4,5,1,7,8,6] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6)],8)
{{1,4},{2,3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,8},{6,7}} => [1,2,3,4,8,7,6,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5},{6},{7,8}} => {{1,2},{3},{4},{5,8},{6,7}} => [2,1,3,4,8,7,6,5] => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5},{6,7},{8}} => {{1},{2,3},{4},{5,8},{6,7}} => [1,3,2,4,8,7,6,5] => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5},{6,8},{7}} => {{1,3},{2},{4},{5,8},{6,7}} => [3,2,1,4,8,7,6,5] => ([(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5},{6,7,8}} => {{1,2,3},{4},{5,8},{6,7}} => [2,3,1,4,8,7,6,5] => ([(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5,6},{7},{8}} => {{1},{2},{3,4},{5,8},{6,7}} => [1,2,4,3,8,7,6,5] => ([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,8},{6,7}} => [1,4,3,2,8,7,6,5] => ([(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5,8},{6},{7}} => {{1,4},{2},{3},{5,8},{6,7}} => [4,2,3,1,8,7,6,5] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(6,7)],8)
{{1,4},{2,3},{5,7,8},{6}} => {{1,2,4},{3},{5,8},{6,7}} => [2,4,3,1,8,7,6,5] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)
{{1,4},{2,3},{5,6,7},{8}} => {{1},{2,3,4},{5,8},{6,7}} => [1,3,4,2,8,7,6,5] => ([(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3},{5,6,8},{7}} => {{1,3,4},{2},{5,8},{6,7}} => [3,2,4,1,8,7,6,5] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)
{{1,4},{2,3},{5,6,7,8}} => {{1,2,3,4},{5,8},{6,7}} => [2,3,4,1,8,7,6,5] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)
{{1,5},{2,3},{4},{6,8},{7}} => {{1,3},{2},{4,8},{5},{6,7}} => [3,2,1,8,5,7,6,4] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3},{4},{5},{6},{7}} => {{1,8},{2},{3},{4},{5},{6,7}} => [8,2,3,4,5,7,6,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2,3},{4},{7,8}} => {{1,2},{3,4,8},{5},{6,7}} => [2,1,4,8,5,7,6,3] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,3},{4},{5,6}} => {{1,2,8},{3,4},{5},{6,7}} => [2,8,4,3,5,7,6,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,3},{4},{6},{8}} => {{1},{2,4,8},{3},{5},{6,7}} => [1,4,3,8,5,7,6,2] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7,8},{2,3},{4},{6}} => {{1,2,4,8},{3},{5},{6,7}} => [2,4,3,8,5,7,6,1] => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,3},{4},{6,7}} => {{1,4,8},{2,3},{5},{6,7}} => [4,3,2,8,5,7,6,1] => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7,8},{2,3},{4}} => {{1,2,3,4,8},{5},{6,7}} => [2,3,4,8,5,7,6,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,3},{6,7},{8}} => {{1},{2,3},{4,5,8},{6,7}} => [1,3,2,5,8,7,6,4] => ([(1,2),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,3},{6,8},{7}} => {{1,3},{2},{4,5,8},{6,7}} => [3,2,1,5,8,7,6,4] => ([(0,7),(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,3},{4,5},{6}} => {{1,2,8},{3},{4,5},{6,7}} => [2,8,3,5,4,7,6,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,3},{4,5},{8}} => {{1},{2,3,8},{4,5},{6,7}} => [1,3,8,5,4,7,6,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,3},{4,5},{7}} => {{1,3,8},{2},{4,5},{6,7}} => [3,2,8,5,4,7,6,1] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2,3},{5},{7},{8}} => {{1},{2},{3,5,8},{4},{6,7}} => [1,2,5,4,8,7,6,3] => ([(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2,3},{5},{7,8}} => {{1,2},{3,5,8},{4},{6,7}} => [2,1,5,4,8,7,6,3] => ([(0,1),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3},{4,6},{5},{8}} => {{1},{2,8},{3,5},{4},{6,7}} => [1,8,5,4,3,7,6,2] => ([(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,3},{4,6},{5}} => {{1,2,8},{3,5},{4},{6,7}} => [2,8,5,4,3,7,6,1] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7,8},{2,3},{5},{6}} => {{1,2,5,8},{3},{4},{6,7}} => [2,5,3,4,8,7,6,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,8},{2,3},{4,6,7},{5}} => {{1,8},{2,3,5},{4},{6,7}} => [8,3,5,4,2,7,6,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6},{2,3},{7},{8}} => {{1},{2},{3,4,5,8},{6,7}} => [1,2,4,5,8,7,6,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6},{2,3},{7,8}} => {{1,2},{3,4,5,8},{6,7}} => [2,1,4,5,8,7,6,3] => ([(0,1),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3},{4,5,6},{7}} => {{1,8},{2},{3,4,5},{6,7}} => [8,2,4,5,3,7,6,1] => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,3},{5,6},{8}} => {{1},{2,5,8},{3,4},{6,7}} => [1,5,4,3,8,7,6,2] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2,3},{5,6},{7}} => {{1,5,8},{2},{3,4},{6,7}} => [5,2,4,3,8,7,6,1] => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,7},{2,3},{6},{8}} => {{1},{2,4,5,8},{3},{6,7}} => [1,4,3,5,8,7,6,2] => ([(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3},{4,5,7},{6}} => {{1,8},{2,4,5},{3},{6,7}} => [8,4,3,5,2,7,6,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2,3},{5,7},{6}} => {{1,5,8},{2,4},{3},{6,7}} => [5,4,3,2,8,7,6,1] => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,8},{2,3},{6},{7}} => {{1,4,5,8},{2},{3},{6,7}} => [4,2,3,5,8,7,6,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4,5,6,7},{2,3},{8}} => {{1},{2,3,4,5,8},{6,7}} => [1,3,4,5,8,7,6,2] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,8},{2,3},{6,7}} => {{1,4,5,8},{2,3},{6,7}} => [4,3,2,5,8,7,6,1] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6,7,8},{2,3}} => {{1,2,3,4,5,8},{6,7}} => [2,3,4,5,8,7,6,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,7,8},{6}} => [1,2,3,4,7,6,8,5] => ([(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3},{5},{6,8},{7}} => {{1,3},{2},{4},{5,7,8},{6}} => [3,2,1,4,7,6,8,5] => ([(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3},{5,6},{7,8}} => {{1,2},{3,4},{5,7,8},{6}} => [2,1,4,3,7,6,8,5] => ([(0,3),(1,2),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3},{5,7},{6},{8}} => {{1},{2,4},{3},{5,7,8},{6}} => [1,4,3,2,7,6,8,5] => ([(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3},{5,7,8},{6}} => {{1,2,4},{3},{5,7,8},{6}} => [2,4,3,1,7,6,8,5] => ([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,2,4},{3},{5,8},{6,7}} => {{1,4},{2,3},{5,7,8},{6}} => [4,3,2,1,7,6,8,5] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)
{{1,2,4},{3},{5,6,8},{7}} => {{1,3,4},{2},{5,7,8},{6}} => [3,2,4,1,7,6,8,5] => ([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,2,4},{3},{5,6,7,8}} => {{1,2,3,4},{5,7,8},{6}} => [2,3,4,1,7,6,8,5] => ([(0,7),(1,6),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,5},{2,4},{3},{6,7},{8}} => {{1},{2,3},{4,8},{5,7},{6}} => [1,3,2,8,7,6,5,4] => ([(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4},{3},{6,8},{7}} => {{1,3},{2},{4,8},{5,7},{6}} => [3,2,1,8,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4},{3},{6,7,8}} => {{1,2,3},{4,8},{5,7},{6}} => [2,3,1,8,7,6,5,4] => ([(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4},{3},{5},{6},{7}} => {{1,8},{2},{3},{4},{5,7},{6}} => [8,2,3,4,7,6,5,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2,4},{3},{7,8}} => {{1,2},{3,4,8},{5,7},{6}} => [2,1,4,8,7,6,5,3] => ([(0,7),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,4},{3},{5,6}} => {{1,2,8},{3,4},{5,7},{6}} => [2,8,4,3,7,6,5,1] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,4},{3},{6},{8}} => {{1},{2,4,8},{3},{5,7},{6}} => [1,4,3,8,7,6,5,2] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4},{3},{5,7},{6}} => {{1,8},{2,4},{3},{5,7},{6}} => [8,4,3,2,7,6,5,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7,8},{2,4},{3},{6}} => {{1,2,4,8},{3},{5,7},{6}} => [2,4,3,8,7,6,5,1] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7},{2,4},{3},{8}} => {{1},{2,3,4,8},{5,7},{6}} => [1,3,4,8,7,6,5,2] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,4},{3},{6,7}} => {{1,4,8},{2,3},{5,7},{6}} => [4,3,2,8,7,6,5,1] => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,8},{2,4},{3},{7}} => {{1,3,4,8},{2},{5,7},{6}} => [3,2,4,8,7,6,5,1] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7,8},{2,4},{3}} => {{1,2,3,4,8},{5,7},{6}} => [2,3,4,8,7,6,5,1] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3},{4},{5},{6},{7}} => {{1,7,8},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,8,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6,7},{3},{4},{5},{8}} => {{1},{2,3,7,8},{4},{5},{6}} => [1,3,7,4,5,6,8,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6,7,8},{3},{4},{5}} => {{1,2,3,7,8},{4},{5},{6}} => [2,3,7,4,5,6,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7,8},{3},{4},{5,6}} => {{1,2,7,8},{3,4},{5},{6}} => [2,7,4,3,5,6,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5,7},{3},{4},{6}} => {{1,8},{2,4,7},{3},{5},{6}} => [8,4,3,7,5,6,2,1] => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,7,8},{3},{4},{6}} => {{1,2,4,7,8},{3},{5},{6}} => [2,4,3,7,5,6,8,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,8},{3},{4},{6,7}} => {{1,4,7,8},{2,3},{5},{6}} => [4,3,2,7,5,6,8,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,5,6,8},{3},{4},{7}} => {{1,3,4,7,8},{2},{5},{6}} => [3,2,4,7,5,6,8,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,6,7,8},{3},{4}} => {{1,2,3,4,7,8},{5},{6}} => [2,3,4,7,5,6,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5},{3},{6,8},{7}} => {{1,3},{2},{4,5,7,8},{6}} => [3,2,1,5,7,6,8,4] => ([(0,7),(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,6},{2,4,5},{3},{7,8}} => {{1,2},{3,8},{4,5,7},{6}} => [2,1,8,5,7,6,4,3] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,4,5},{3},{6}} => {{1,2,8},{3},{4,5,7},{6}} => [2,8,3,5,7,6,4,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,4,5},{3},{8}} => {{1},{2,3,8},{4,5,7},{6}} => [1,3,8,5,7,6,4,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,5},{3},{6,7}} => {{1,8},{2,3},{4,5,7},{6}} => [8,3,2,5,7,6,4,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,4,5},{3},{7}} => {{1,3,8},{2},{4,5,7},{6}} => [3,2,8,5,7,6,4,1] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3},{4,5},{8}} => {{1},{2,8},{3,7},{4,5},{6}} => [1,8,7,5,4,6,3,2] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,6},{3},{4,5}} => {{1,2,8},{3,7},{4,5},{6}} => [2,8,7,5,4,6,3,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7,8},{3},{4,5},{6}} => {{1,2,7,8},{3},{4,5},{6}} => [2,7,3,5,4,6,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6,7},{3},{4,5}} => {{1,8},{2,3,7},{4,5},{6}} => [8,3,7,5,4,6,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6},{3},{5},{7},{8}} => {{1},{2},{3,5,7,8},{4},{6}} => [1,2,5,4,7,6,8,3] => ([(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,4,6},{3},{5},{7,8}} => {{1,2},{3,5,7,8},{4},{6}} => [2,1,5,4,7,6,8,3] => ([(0,7),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,7},{2,4,6},{3},{5},{8}} => {{1},{2,8},{3,5,7},{4},{6}} => [1,8,5,4,7,6,3,2] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,4,6},{3},{5}} => {{1,2,8},{3,5,7},{4},{6}} => [2,8,5,4,7,6,3,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7,8},{3},{4,6},{5}} => {{1,2,7,8},{3,5},{4},{6}} => [2,7,5,4,3,6,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,7},{3},{5},{6}} => {{1,8},{2,5,7},{3},{4},{6}} => [8,5,3,4,7,6,2,1] => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,7,8},{3},{5},{6}} => {{1,2,5,7,8},{3},{4},{6}} => [2,5,3,4,7,6,8,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6,7},{3},{5},{8}} => {{1},{2,3,5,7,8},{4},{6}} => [1,3,5,4,7,6,8,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,8},{2,4,6,7},{3},{5}} => {{1,8},{2,3,5,7},{4},{6}} => [8,3,5,4,7,6,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6,8},{3},{5},{7}} => {{1,3,5,7,8},{2},{4},{6}} => [3,2,5,4,7,6,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,2,4,6,7,8},{3},{5}} => {{1,2,3,5,7,8},{4},{6}} => [2,3,5,4,7,6,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,8},{2,4,5,6},{3},{7}} => {{1,8},{2},{3,4,5,7},{6}} => [8,2,4,5,7,6,3,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,7},{3},{4,5,6}} => {{1,8},{2,7},{3,4,5},{6}} => [8,7,4,5,3,6,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3},{4,5,6},{7}} => {{1,7,8},{2},{3,4,5},{6}} => [7,2,4,5,3,6,8,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,7},{3},{5,6}} => {{1,8},{2,5,7},{3,4},{6}} => [8,5,4,3,7,6,2,1] => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3},{4,7},{5,6}} => {{1,7,8},{2,5},{3,4},{6}} => [7,5,4,3,2,6,8,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,8},{3},{5,6},{7}} => {{1,5,7,8},{2},{3,4},{6}} => [5,2,4,3,7,6,8,1] => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,5,7},{3},{6}} => {{1,8},{2,4,5,7},{3},{6}} => [8,4,3,5,7,6,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3},{4,5,7},{6}} => {{1,7,8},{2,4,5},{3},{6}} => [7,4,3,5,2,6,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,8},{3},{5,7},{6}} => {{1,5,7,8},{2,4},{3},{6}} => [5,4,3,2,7,6,8,1] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,7,8},{3},{6}} => {{1,2,4,5,7,8},{3},{6}} => [2,4,3,5,7,6,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,4,5,6,7},{3},{8}} => {{1},{2,3,4,5,7,8},{6}} => [1,3,4,5,7,6,8,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,5,6,7},{3}} => {{1,8},{2,3,4,5,7},{6}} => [8,3,4,5,7,6,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,8},{3},{6,7}} => {{1,4,5,7,8},{2,3},{6}} => [4,3,2,5,7,6,8,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,6,8},{3},{7}} => {{1,3,4,5,7,8},{2},{6}} => [3,2,4,5,7,6,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,4,5,6,7,8},{3}} => {{1,2,3,4,5,7,8},{6}} => [2,3,4,5,7,6,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,6,7,8}} => [1,2,3,4,6,7,8,5] => ([(4,7),(5,7),(6,7)],8)
{{1,2,3,4},{5},{6},{7,8}} => {{1,2},{3},{4},{5,6,7,8}} => [2,1,3,4,6,7,8,5] => ([(2,3),(4,7),(5,7),(6,7)],8)
{{1,2,3,4},{5},{6,7},{8}} => {{1},{2,3},{4},{5,6,7,8}} => [1,3,2,4,6,7,8,5] => ([(2,3),(4,7),(5,7),(6,7)],8)
{{1,2,3,4},{5},{6,8},{7}} => {{1,3},{2},{4},{5,6,7,8}} => [3,2,1,4,6,7,8,5] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(5,6)],8)
{{1,2,3,4},{5,6},{7},{8}} => {{1},{2},{3,4},{5,6,7,8}} => [1,2,4,3,6,7,8,5] => ([(2,3),(4,7),(5,7),(6,7)],8)
{{1,2,3,4},{5,6},{7,8}} => {{1,2},{3,4},{5,6,7,8}} => [2,1,4,3,6,7,8,5] => ([(0,3),(1,2),(4,7),(5,7),(6,7)],8)
{{1,2,3,4},{5,7},{6},{8}} => {{1},{2,4},{3},{5,6,7,8}} => [1,4,3,2,6,7,8,5] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(5,6)],8)
{{1,2,3,4},{5,8},{6},{7}} => {{1,4},{2},{3},{5,6,7,8}} => [4,2,3,1,6,7,8,5] => ([(0,5),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(6,7)],8)
{{1,2,3,4},{5,7,8},{6}} => {{1,2,4},{3},{5,6,7,8}} => [2,4,3,1,6,7,8,5] => ([(0,7),(1,6),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,2,3,4},{5,8},{6,7}} => {{1,4},{2,3},{5,6,7,8}} => [4,3,2,1,6,7,8,5] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)
{{1,2,3,4},{5,6,8},{7}} => {{1,3,4},{2},{5,6,7,8}} => [3,2,4,1,6,7,8,5] => ([(0,7),(1,6),(2,6),(3,6),(4,5),(4,7),(5,7)],8)
{{1,2,3,4},{5,6,7,8}} => {{1,2,3,4},{5,6,7,8}} => [2,3,4,1,6,7,8,5] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)
{{1,5},{2,3,4},{6},{7},{8}} => {{1},{2},{3},{4,8},{5,6,7}} => [1,2,3,8,6,7,5,4] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3,4},{6,8},{7}} => {{1,3},{2},{4,8},{5,6,7}} => [3,2,1,8,6,7,5,4] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3,4},{6,7,8}} => {{1,2,3},{4,8},{5,6,7}} => [2,3,1,8,6,7,5,4] => ([(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,4},{5},{7},{8}} => {{1},{2},{3,8},{4},{5,6,7}} => [1,2,8,4,6,7,5,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,4},{5},{7,8}} => {{1,2},{3,8},{4},{5,6,7}} => [2,1,8,4,6,7,5,3] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,4},{5},{6},{8}} => {{1},{2,8},{3},{4},{5,6,7}} => [1,8,3,4,6,7,5,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,3,4},{5},{8}} => {{1},{2,3,8},{4},{5,6,7}} => [1,3,8,4,6,7,5,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,4},{5},{6,7}} => {{1,8},{2,3},{4},{5,6,7}} => [8,3,2,4,6,7,5,1] => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7,8},{2,3,4},{5}} => {{1,2,3,8},{4},{5,6,7}} => [2,3,8,4,6,7,5,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,4},{5,6},{8}} => {{1},{2,8},{3,4},{5,6,7}} => [1,8,4,3,6,7,5,2] => ([(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,4},{5,6},{7}} => {{1,8},{2},{3,4},{5,6,7}} => [8,2,4,3,6,7,5,1] => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,3,4},{6},{8}} => {{1},{2,4,8},{3},{5,6,7}} => [1,4,3,8,6,7,5,2] => ([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,4},{5,7},{6}} => {{1,8},{2,4},{3},{5,6,7}} => [8,4,3,2,6,7,5,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,3,4},{6,7}} => {{1,4,8},{2,3},{5,6,7}} => [4,3,2,8,6,7,5,1] => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7,8},{2,3,4}} => {{1,2,3,4,8},{5,6,7}} => [2,3,4,8,6,7,5,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5},{3,4},{6},{7},{8}} => {{1},{2},{3},{4,7,8},{5,6}} => [1,2,3,7,6,5,8,4] => ([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5},{3,4},{6,7},{8}} => {{1},{2,3},{4,7,8},{5,6}} => [1,3,2,7,6,5,8,4] => ([(1,2),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5},{3,4},{6,8},{7}} => {{1,3},{2},{4,7,8},{5,6}} => [3,2,1,7,6,5,8,4] => ([(0,7),(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5},{3,4},{7},{8}} => {{1},{2},{3,8},{4,7},{5,6}} => [1,2,8,7,6,5,4,3] => ([(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,5},{3,4},{6},{8}} => {{1},{2,8},{3},{4,7},{5,6}} => [1,8,3,7,6,5,4,2] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,5},{3,4},{6}} => {{1,2,8},{3},{4,7},{5,6}} => [2,8,3,7,6,5,4,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,5},{3,4},{8}} => {{1},{2,3,8},{4,7},{5,6}} => [1,3,8,7,6,5,4,2] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,5},{3,4},{7}} => {{1,3,8},{2},{4,7},{5,6}} => [3,2,8,7,6,5,4,1] => ([(0,1),(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7,8},{2,5},{3,4}} => {{1,2,3,8},{4,7},{5,6}} => [2,3,8,7,6,5,4,1] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6},{3,4},{5},{7,8}} => {{1,2},{3,7,8},{4},{5,6}} => [2,1,7,4,6,5,8,3] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3,4},{5},{8}} => {{1},{2,8},{3,7},{4},{5,6}} => [1,8,7,4,6,5,3,2] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,6},{3,4},{5}} => {{1,2,8},{3,7},{4},{5,6}} => [2,8,7,4,6,5,3,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6,7},{3,4},{5}} => {{1,8},{2,3,7},{4},{5,6}} => [8,3,7,4,6,5,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6,8},{3,4},{5},{7}} => {{1,3,7,8},{2},{4},{5,6}} => [3,2,7,4,6,5,8,1] => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,6},{3,4},{7},{8}} => {{1},{2},{3,4,7,8},{5,6}} => [1,2,4,7,6,5,8,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,5,6},{3,4},{8}} => {{1},{2,8},{3,4,7},{5,6}} => [1,8,4,7,6,5,3,2] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5,6},{3,4},{7}} => {{1,8},{2},{3,4,7},{5,6}} => [8,2,4,7,6,5,3,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,5,6},{3,4}} => {{1,2,8},{3,4,7},{5,6}} => [2,8,4,7,6,5,3,1] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3,4},{5,6},{8}} => {{1},{2,7,8},{3,4},{5,6}} => [1,7,4,3,6,5,8,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,4},{5,6},{7}} => {{1,7,8},{2},{3,4},{5,6}} => [7,2,4,3,6,5,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7,8},{3,4},{5,6}} => {{1,2,7,8},{3,4},{5,6}} => [2,7,4,3,6,5,8,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5,7},{3,4},{6}} => {{1,8},{2,4,7},{3},{5,6}} => [8,4,3,7,6,5,2,1] => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,4},{5,7},{6}} => {{1,7,8},{2,4},{3},{5,6}} => [7,4,3,2,6,5,8,1] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,8},{3,4},{6},{7}} => {{1,4,7,8},{2},{3},{5,6}} => [4,2,3,7,6,5,8,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,8},{2,5,6,7},{3,4}} => {{1,8},{2,3,4,7},{5,6}} => [8,3,4,7,6,5,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,6,7,8},{3,4}} => {{1,2,3,4,7,8},{5,6}} => [2,3,4,7,6,5,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5},{4},{6},{7},{8}} => {{1},{2},{3},{4,6,7,8},{5}} => [1,2,3,6,5,7,8,4] => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5},{4},{6,7},{8}} => {{1},{2,3},{4,6,7,8},{5}} => [1,3,2,6,5,7,8,4] => ([(1,2),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5},{4},{6,8},{7}} => {{1,3},{2},{4,6,7,8},{5}} => [3,2,1,6,5,7,8,4] => ([(0,7),(1,7),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,5},{4},{7},{8}} => {{1},{2},{3,8},{4,6,7},{5}} => [1,2,8,6,5,7,4,3] => ([(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,5},{4},{7,8}} => {{1,2},{3,8},{4,6,7},{5}} => [2,1,8,6,5,7,4,3] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,3,5},{4},{8}} => {{1},{2,3,8},{4,6,7},{5}} => [1,3,8,6,5,7,4,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,5},{4},{6,7}} => {{1,8},{2,3},{4,6,7},{5}} => [8,3,2,6,5,7,4,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,3,5},{4},{7}} => {{1,3,8},{2},{4,6,7},{5}} => [3,2,8,6,5,7,4,1] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6},{3,5},{4},{7},{8}} => {{1},{2},{3,7,8},{4,6},{5}} => [1,2,7,6,5,4,8,3] => ([(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6},{3,5},{4},{7,8}} => {{1,2},{3,7,8},{4,6},{5}} => [2,1,7,6,5,4,8,3] => ([(0,7),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3,5},{4},{8}} => {{1},{2,8},{3,7},{4,6},{5}} => [1,8,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,6},{3,5},{4}} => {{1,2,8},{3,7},{4,6},{5}} => [2,8,7,6,5,4,3,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6,7},{3,5},{4}} => {{1,8},{2,3,7},{4,6},{5}} => [8,3,7,6,5,4,2,1] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6,8},{3,5},{4},{7}} => {{1,3,7,8},{2},{4,6},{5}} => [3,2,7,6,5,4,8,1] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6,7,8},{3,5},{4}} => {{1,2,3,7,8},{4,6},{5}} => [2,3,7,6,5,4,8,1] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,6},{4},{5},{7,8}} => {{1,2},{3,6,7,8},{4},{5}} => [2,1,6,4,5,7,8,3] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7,8},{3,6},{4},{5}} => {{1,2,7,8},{3,6},{4},{5}} => [2,7,6,4,5,3,8,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4},{5},{6},{7}} => {{1,6,7,8},{2},{3},{4},{5}} => [6,2,3,4,5,7,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,7,8},{4},{5},{6}} => {{1,2,6,7,8},{3},{4},{5}} => [2,6,3,4,5,7,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,6,7},{4},{5},{8}} => {{1},{2,3,6,7,8},{4},{5}} => [1,3,6,4,5,7,8,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,6,7},{4},{5}} => {{1,7,8},{2,3,6},{4},{5}} => [7,3,6,4,5,2,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,6,7,8},{4},{5}} => {{1,2,3,6,7,8},{4},{5}} => [2,3,6,4,5,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,5,6},{4},{8}} => {{1},{2,8},{3,4,6,7},{5}} => [1,8,4,6,5,7,3,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,7},{3,5,6},{4}} => {{1,8},{2,7},{3,4,6},{5}} => [8,7,4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,5,6},{4},{7}} => {{1,7,8},{2},{3,4,6},{5}} => [7,2,4,6,5,3,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,7},{4},{5,6}} => {{1,8},{2,6,7},{3,4},{5}} => [8,6,4,3,5,7,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,7},{4},{5,6}} => {{1,7,8},{2,6},{3,4},{5}} => [7,6,4,3,5,2,8,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,7},{4},{6},{8}} => {{1},{2,4,6,7,8},{3},{5}} => [1,4,3,6,5,7,8,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,8},{3,5,7},{4},{6}} => {{1,7,8},{2,4,6},{3},{5}} => [7,4,3,6,5,2,8,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,7,8},{4},{6}} => {{1,2,4,6,7,8},{3},{5}} => [2,4,3,6,5,7,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,3,5,6,7},{4},{8}} => {{1},{2,3,4,6,7,8},{5}} => [1,3,4,6,5,7,8,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,8},{4},{6,7}} => {{1,4,6,7,8},{2,3},{5}} => [4,3,2,6,5,7,8,1] => ([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,6,7,8},{4}} => {{1,2,3,4,6,7,8},{5}} => [2,3,4,6,5,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5},{6},{7},{8}} => {{1},{2},{3},{4,5,6,7,8}} => [1,2,3,5,6,7,8,4] => ([(3,7),(4,7),(5,7),(6,7)],8)
{{1,2,3,4,5},{6,7},{8}} => {{1},{2,3},{4,5,6,7,8}} => [1,3,2,5,6,7,8,4] => ([(1,2),(3,7),(4,7),(5,7),(6,7)],8)
{{1,2,3,4,5},{6,8},{7}} => {{1,3},{2},{4,5,6,7,8}} => [3,2,1,5,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,6)],8)
{{1,2,3,4,5},{6,7,8}} => {{1,2,3},{4,5,6,7,8}} => [2,3,1,5,6,7,8,4] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6)],8)
{{1,6},{2,3,4,5},{7},{8}} => {{1},{2},{3,8},{4,5,6,7}} => [1,2,8,5,6,7,4,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7,8},{2,3,4,5}} => {{1,2,3,8},{4,5,6,7}} => [2,3,8,5,6,7,4,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3,4,5},{8}} => {{1},{2,8},{3,7},{4,5,6}} => [1,8,7,5,6,4,3,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,6},{3,4,5}} => {{1,2,8},{3,7},{4,5,6}} => [2,8,7,5,6,4,3,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,7},{3,4,5},{6}} => {{1,8},{2,7},{3},{4,5,6}} => [8,7,3,5,6,4,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6,7,8},{3,4,5}} => {{1,2,3,7,8},{4,5,6}} => [2,3,7,5,6,4,8,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,6},{4,5},{7},{8}} => {{1},{2},{3,6,7,8},{4,5}} => [1,2,6,5,4,7,8,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,6},{4,5},{8}} => {{1},{2,8},{3,6,7},{4,5}} => [1,8,6,5,4,7,3,2] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,6},{4,5},{7}} => {{1,8},{2},{3,6,7},{4,5}} => [8,2,6,5,4,7,3,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3,6},{4,5},{8}} => {{1},{2,7,8},{3,6},{4,5}} => [1,7,6,5,4,3,8,2] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,6},{4,5},{7}} => {{1,7,8},{2},{3,6},{4,5}} => [7,2,6,5,4,3,8,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,7},{4,5},{6}} => {{1,8},{2,6,7},{3},{4,5}} => [8,6,3,5,4,7,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,7},{4,5},{6}} => {{1,7,8},{2,6},{3},{4,5}} => [7,6,3,5,4,2,8,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4,5},{6},{7}} => {{1,6,7,8},{2},{3},{4,5}} => [6,2,3,5,4,7,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,6,7},{4,5}} => {{1,8},{2,3,6,7},{4,5}} => [8,3,6,5,4,7,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,6,7},{4,5}} => {{1,7,8},{2,3,6},{4,5}} => [7,3,6,5,4,2,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4,5},{6,7}} => {{1,6,7,8},{2,3},{4,5}} => [6,3,2,5,4,7,8,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,6,7,8},{4,5}} => {{1,2,3,6,7,8},{4,5}} => [2,3,6,5,4,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,6},{5},{7},{8}} => {{1},{2},{3,5,6,7,8},{4}} => [1,2,5,4,6,7,8,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,6},{5},{7,8}} => {{1,2},{3,5,6,7,8},{4}} => [2,1,5,4,6,7,8,3] => ([(0,1),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,4,6},{5},{8}} => {{1},{2,8},{3,5,6,7},{4}} => [1,8,5,4,6,7,3,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,7},{3,4,6},{5}} => {{1,8},{2,7},{3,5,6},{4}} => [8,7,5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,4,6},{5},{7}} => {{1,7,8},{2},{3,5,6},{4}} => [7,2,5,4,6,3,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,7},{4,6},{5}} => {{1,8},{2,6,7},{3,5},{4}} => [8,6,5,4,3,7,2,1] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,7},{4,6},{5}} => {{1,7,8},{2,6},{3,5},{4}} => [7,6,5,4,3,2,8,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4,6},{5},{7}} => {{1,6,7,8},{2},{3,5},{4}} => [6,2,5,4,3,7,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,7,8},{4,6},{5}} => {{1,2,6,7,8},{3,5},{4}} => [2,6,5,4,3,7,8,1] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,7},{5},{6},{8}} => {{1},{2,5,6,7,8},{3},{4}} => [1,5,3,4,6,7,8,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,4,7},{5},{6}} => {{1,8},{2,5,6,7},{3},{4}} => [8,5,3,4,6,7,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,4,7},{5},{6}} => {{1,7,8},{2,5,6},{3},{4}} => [7,5,3,4,6,2,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4,7},{5},{6}} => {{1,6,7,8},{2,5},{3},{4}} => [6,5,3,4,2,7,8,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,8},{5},{6},{7}} => {{1,5,6,7,8},{2},{3},{4}} => [5,2,3,4,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,7,8},{5},{6}} => {{1,2,5,6,7,8},{3},{4}} => [2,5,3,4,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,4,6,7},{5}} => {{1,8},{2,3,5,6,7},{4}} => [8,3,5,4,6,7,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4,6,7},{5}} => {{1,6,7,8},{2,3,5},{4}} => [6,3,5,4,2,7,8,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,8},{5},{6,7}} => {{1,5,6,7,8},{2,3},{4}} => [5,3,2,4,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,6,8},{5},{7}} => {{1,3,5,6,7,8},{2},{4}} => [3,2,5,4,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,3,4,6,7,8},{5}} => {{1,2,3,5,6,7,8},{4}} => [2,3,5,4,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,6},{7},{8}} => {{1},{2},{3,4,5,6,7,8}} => [1,2,4,5,6,7,8,3] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1,2,3,4,5,6},{7,8}} => {{1,2},{3,4,5,6,7,8}} => [2,1,4,5,6,7,8,3] => ([(0,1),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1,7},{2,3,4,5,6},{8}} => {{1},{2,8},{3,4,5,6,7}} => [1,8,4,5,6,7,3,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,4,5,6},{7}} => {{1,8},{2},{3,4,5,6,7}} => [8,2,4,5,6,7,3,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7,8},{3,4,5,6}} => {{1,2,7,8},{3,4,5,6}} => [2,7,4,5,6,3,8,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,7},{4,5,6}} => {{1,7,8},{2,6},{3,4,5}} => [7,6,4,5,3,2,8,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,7,8},{4,5,6}} => {{1,2,6,7,8},{3,4,5}} => [2,6,4,5,3,7,8,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,7},{5,6},{8}} => {{1},{2,5,6,7,8},{3,4}} => [1,5,4,3,6,7,8,2] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,4,7},{5,6}} => {{1,7,8},{2,5,6},{3,4}} => [7,5,4,3,6,2,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4,7},{5,6}} => {{1,6,7,8},{2,5},{3,4}} => [6,5,4,3,2,7,8,1] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,7},{6},{8}} => {{1},{2,4,5,6,7,8},{3}} => [1,4,3,5,6,7,8,2] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,4,5,7},{6}} => {{1,8},{2,4,5,6,7},{3}} => [8,4,3,5,6,7,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,8},{5,7},{6}} => {{1,5,6,7,8},{2,4},{3}} => [5,4,3,2,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,8},{6},{7}} => {{1,4,5,6,7,8},{2},{3}} => [4,2,3,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,7,8},{6}} => {{1,2,4,5,6,7,8},{3}} => [2,4,3,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,6,7},{8}} => {{1},{2,3,4,5,6,7,8}} => [1,3,4,5,6,7,8,2] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1,8},{2,3,4,5,6,7}} => {{1,8},{2,3,4,5,6,7}} => [8,3,4,5,6,7,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,4,5,6,7}} => {{1,7,8},{2,3,4,5,6}} => [7,3,4,5,6,2,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,8},{4,5,6,7}} => {{1,6,7,8},{2,3,4,5}} => [6,3,4,5,2,7,8,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,8},{5,6,7}} => {{1,5,6,7,8},{2,3,4}} => [5,3,4,2,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,8},{6,7}} => {{1,4,5,6,7,8},{2,3}} => [4,3,2,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,6,8},{7}} => {{1,3,4,5,6,7,8},{2}} => [3,2,4,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,6,7,8}} => {{1,2,3,4,5,6,7,8}} => [2,3,4,5,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3,5,6,7,8},{2,4}} => {{1,2,3,4,6,8},{5,7}} => [2,3,4,6,7,8,5,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6,7,8},{2,5}} => {{1,2,3,5,6,8},{4,7}} => [2,3,5,7,6,8,4,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6,7,8},{3,5}} => {{1,2,3,5,7,8},{4,6}} => [2,3,5,6,7,4,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,7,8},{2,6}} => {{1,2,4,5,6,8},{3,7}} => [2,4,7,5,6,8,3,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,7,8},{3,6}} => {{1,2,4,5,7,8},{3,6}} => [2,4,6,5,7,3,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,7,8},{4,6}} => {{1,2,4,6,7,8},{3,5}} => [2,4,5,6,3,7,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,6,8},{3,7}} => {{1,3,4,5,7,8},{2,6}} => [3,6,4,5,7,2,8,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,6,8},{4,7}} => {{1,3,4,6,7,8},{2,5}} => [3,5,4,6,2,7,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,6,8},{5,7}} => {{1,3,5,6,7,8},{2,4}} => [3,4,5,2,6,7,8,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,6,7},{2,8}} => {{1,7},{2,3,4,5,6,8}} => [7,3,4,5,6,8,1,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5,6,7},{3,8}} => {{1,6},{2,3,4,5,7,8}} => [6,3,4,5,7,1,8,2] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,4,6,7},{5,8}} => {{1,4},{2,3,5,6,7,8}} => [4,3,5,1,6,7,8,2] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7,8}} => [3,4,1,5,6,7,8,2] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,7,8},{2,4,6}} => {{1,2,4,6,8},{3,5,7}} => [2,4,5,6,7,8,3,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,7,8},{2,5,6}} => {{1,2,5,6,8},{3,4,7}} => [2,5,4,7,6,8,3,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,7,8},{3,5,6}} => {{1,2,5,7,8},{3,4,6}} => [2,5,4,6,7,3,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,6,8},{2,4,7}} => {{1,3,4,6,8},{2,5,7}} => [3,5,4,6,7,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,6,8},{3,4,7}} => {{1,3,4,7,8},{2,5,6}} => [3,5,4,7,6,2,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6,8},{2,5,7}} => {{1,3,5,6,8},{2,4,7}} => [3,4,5,7,6,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6,8},{3,5,7}} => {{1,3,5,7,8},{2,4,6}} => [3,4,5,6,7,2,8,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,6,8},{4,5,7}} => {{1,3,6,7,8},{2,4,5}} => [3,4,6,5,2,7,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5,8},{2,6,7}} => {{1,4,5,6,8},{2,3,7}} => [4,3,7,5,6,8,2,1] => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,8},{3,6,7}} => {{1,4,5,7,8},{2,3,6}} => [4,3,6,5,7,2,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,8},{4,6,7}} => {{1,4,6,7,8},{2,3,5}} => [4,3,5,6,2,7,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,6,7},{2,4,8}} => {{1,5,7},{2,3,4,6,8}} => [5,3,4,6,7,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5,6,7},{3,4,8}} => {{1,5,6},{2,3,4,7,8}} => [5,3,4,7,6,1,8,2] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,4,6,7},{2,5,8}} => {{1,4,7},{2,3,5,6,8}} => [4,3,5,7,6,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,6,7},{3,5,8}} => {{1,4,6},{2,3,5,7,8}} => [4,3,5,6,7,1,8,2] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,6,7},{4,5,8}} => {{1,4,5},{2,3,6,7,8}} => [4,3,6,5,1,7,8,2] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5,7},{3,6,8}} => {{1,3,6},{2,4,5,7,8}} => [3,4,6,5,7,1,8,2] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5,7},{4,6,8}} => {{1,3,5},{2,4,6,7,8}} => [3,4,5,6,1,7,8,2] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,4,7},{5,6,8}} => {{1,3,4},{2,5,6,7,8}} => [3,5,4,1,6,7,8,2] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5,6},{3,7,8}} => {{1,2,6},{3,4,5,7,8}} => [2,6,4,5,7,1,8,3] => ([(0,7),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5,6},{4,7,8}} => {{1,2,5},{3,4,6,7,8}} => [2,5,4,6,1,7,8,3] => ([(0,7),(1,7),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,4,6},{5,7,8}} => {{1,2,4},{3,5,6,7,8}} => [2,4,5,1,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,7,8},{2,6},{4}} => {{1,2,4,6,8},{3,7},{5}} => [2,4,7,6,5,8,3,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,7,8},{3,6},{4}} => {{1,2,4,7,8},{3,6},{5}} => [2,4,6,7,5,3,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,7,8},{2,6},{5}} => {{1,2,5,6,8},{3,7},{4}} => [2,5,7,4,6,8,3,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,7,8},{2,4},{6}} => {{1,2,4,6,8},{3},{5,7}} => [2,4,3,6,7,8,5,1] => ([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,6,8},{3,7},{4}} => {{1,3,4,7,8},{2,6},{5}} => [3,6,4,7,5,2,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6,8},{2,7},{5}} => {{1,3,5,6,8},{2,7},{4}} => [3,7,5,4,6,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,6,8},{4,7},{5}} => {{1,3,6,7,8},{2,5},{4}} => [3,5,6,4,2,7,8,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6,8},{2,5},{7}} => {{1,3,5,6,8},{2},{4,7}} => [3,2,5,7,6,8,4,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,8},{3,6},{7}} => {{1,4,5,7,8},{2},{3,6}} => [4,2,6,5,7,3,8,1] => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6,7},{3,8},{5}} => {{1,6},{2,3,5,7,8},{4}} => [6,3,5,4,7,1,8,2] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5,7},{3,8},{6}} => {{1,6},{2,4,5,7,8},{3}} => [6,4,3,5,7,1,8,2] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5,7},{4,8},{6}} => {{1,5},{2,4,6,7,8},{3}} => [5,4,3,6,1,7,8,2] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5,6},{3,8},{7}} => {{1,6},{2},{3,4,5,7,8}} => [6,2,4,5,7,1,8,3] => ([(0,7),(1,5),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,4,6},{5,8},{7}} => {{1,4},{2},{3,5,6,7,8}} => [4,2,5,1,6,7,8,3] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7)],8)
{{1,3,5,6,7},{2,4},{8}} => {{1},{2,3,4,6,8},{5,7}} => [1,3,4,6,7,8,5,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6,7},{3,5},{8}} => {{1},{2,3,5,7,8},{4,6}} => [1,3,5,6,7,4,8,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7,8},{3,6}} => [1,4,6,5,7,3,8,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,5,6},{4,7},{8}} => {{1},{2,5},{3,4,6,7,8}} => [1,5,4,6,2,7,8,3] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6,7,8}} => [1,4,5,2,6,7,8,3] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,7},{2,4,6,8}} => {{1,3,5,7},{2,4,6,8}} => [3,4,5,6,7,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5,7},{3,4,6,8}} => {{1,3,5,6},{2,4,7,8}} => [3,4,5,7,6,1,8,2] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,4,7},{2,5,6,8}} => {{1,3,4,7},{2,5,6,8}} => [3,5,4,7,6,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,7},{3,5,6,8}} => {{1,3,4,6},{2,5,7,8}} => [3,5,4,6,7,1,8,2] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5,6},{3,4,7,8}} => {{1,2,5,6},{3,4,7,8}} => [2,5,4,7,6,1,8,3] => ([(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,6},{3,5,7,8}} => {{1,2,4,6},{3,5,7,8}} => [2,4,5,6,7,1,8,3] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,6},{4,5,7,8}} => {{1,2,4,5},{3,6,7,8}} => [2,4,6,5,1,7,8,3] => ([(0,7),(1,7),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5},{4,6,7,8}} => {{1,2,3,5},{4,6,7,8}} => [2,3,5,6,1,7,8,4] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6,8},{2,4,7},{5}} => {{1,3,6,8},{2,5,7},{4}} => [3,5,6,4,7,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,8},{3,6,7},{4}} => {{1,4,7,8},{2,3,6},{5}} => [4,3,6,7,5,2,8,1] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,8},{2,6,7},{5}} => {{1,5,6,8},{2,3,7},{4}} => [5,3,7,4,6,8,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,8},{3,6,7},{5}} => {{1,5,7,8},{2,3,6},{4}} => [5,3,6,4,7,2,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6,7},{3,5,8},{4}} => {{1,4,6},{2,3,7,8},{5}} => [4,3,7,6,5,1,8,2] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6,7},{2,4,8},{5}} => {{1,5,7},{2,3,6,8},{4}} => [5,3,6,4,7,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,7},{2,6,8},{3}} => {{1,3,7},{2,4,5,8},{6}} => [3,4,7,5,8,6,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,7},{2,4,8},{6}} => {{1,5,7},{2,4,6,8},{3}} => [5,4,3,6,7,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,6},{2,7,8},{4}} => {{1,2,7},{3,4,6,8},{5}} => [2,7,4,6,5,8,1,3] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5},{3,6,8},{7}} => {{1,3,6},{2},{4,5,7,8}} => [3,2,6,5,7,1,8,4] => ([(0,6),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,7},{2,4,6},{8}} => {{1},{2,4,6,8},{3,5,7}} => [1,4,5,6,7,8,3,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2,5,7},{8}} => {{1},{2,4,7},{3,5,6,8}} => [1,4,5,7,6,8,2,3] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7,8}} => [1,3,5,6,2,7,8,4] => ([(1,7),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,7,8},{2,5},{3,6}} => {{1,2,5,8},{3,6},{4,7}} => [2,5,6,7,8,3,4,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,7,8},{2,5},{4,6}} => {{1,2,6,8},{3,5},{4,7}} => [2,6,5,7,3,8,4,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4,6,8},{2,5},{3,7}} => {{1,3,5,8},{2,6},{4,7}} => [3,6,5,7,8,2,4,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,6,8},{2,4},{5,7}} => {{1,3,6,8},{2,4},{5,7}} => [3,4,6,2,7,8,5,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,5,8},{3,6},{4,7}} => {{1,4,7,8},{2,5},{3,6}} => [4,5,6,7,2,3,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,4,8},{3,6},{5,7}} => {{1,5,7,8},{2,4},{3,6}} => [5,4,6,2,7,3,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,4,8},{3,5},{6,7}} => {{1,5,7,8},{2,3},{4,6}} => [5,3,2,6,7,4,8,1] => ([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,7},{2,5},{3,8}} => {{1,6},{2,3,5,8},{4,7}} => [6,3,5,7,8,1,4,2] => ([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3,6,7},{2,5},{4,8}} => {{1,5},{2,3,6,8},{4,7}} => [5,3,6,7,1,8,4,2] => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,3,6,7},{2,4},{5,8}} => {{1,4},{2,3,6,8},{5,7}} => [4,3,6,1,7,8,5,2] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,7},{2,6},{4,8}} => {{1,5},{2,4,6,8},{3,7}} => [5,4,7,6,1,8,3,2] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,7},{2,6},{5,8}} => {{1,4},{2,5,6,8},{3,7}} => [4,5,7,1,6,8,3,2] => ([(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,7},{3,5},{6,8}} => {{1,3},{2,5,7,8},{4,6}} => [3,5,1,6,7,4,8,2] => ([(0,7),(1,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,3,5,6},{2,7},{4,8}} => {{1,5},{2,7},{3,4,6,8}} => [5,7,4,6,1,8,2,3] => ([(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5,6},{3,7},{4,8}} => {{1,5},{2,6},{3,4,7,8}} => [5,6,4,7,1,2,8,3] => ([(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(5,6),(6,7)],8)
{{1,3,4,6},{2,7},{5,8}} => {{1,4},{2,7},{3,5,6,8}} => [4,7,5,1,6,8,2,3] => ([(0,6),(0,7),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6,7,8}} => [4,5,6,1,2,7,8,3] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1,2,3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6,7,8}} => [3,5,1,6,2,7,8,4] => ([(0,7),(1,7),(2,3),(2,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,3,4},{5,7},{6,8}} => {{1,3},{2,4},{5,6,7,8}} => [3,4,1,2,6,7,8,5] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6)],8)
{{1,3,5,6},{2,4},{7,8}} => {{1,2},{3,4,6,8},{5,7}} => [2,1,4,6,7,8,5,3] => ([(0,1),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2,5},{7,8}} => {{1,2},{3,5,6,8},{4,7}} => [2,1,5,7,6,8,4,3] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6},{3,5},{7,8}} => {{1,2},{3,5,7,8},{4,6}} => [2,1,5,6,7,4,8,3] => ([(0,1),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5},{2,6},{7,8}} => {{1,2},{3,7},{4,5,6,8}} => [2,1,7,5,6,8,3,4] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5},{3,6},{7,8}} => {{1,2},{3,6},{4,5,7,8}} => [2,1,6,5,7,3,8,4] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5},{4,6},{7,8}} => {{1,2},{3,5},{4,6,7,8}} => [2,1,5,6,3,7,8,4] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,7,8},{2,6},{3},{4}} => {{1,2,4,8},{3,7},{5},{6}} => [2,4,7,8,5,6,3,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7,8},{2,6},{3},{5}} => {{1,2,5,8},{3,7},{4},{6}} => [2,5,7,4,8,6,3,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7,8},{2,5},{4},{6}} => {{1,2,6,8},{3},{4,7},{5}} => [2,6,3,7,5,8,4,1] => ([(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,8},{2,7},{3},{4}} => {{1,3,4,8},{2,7},{5},{6}} => [3,7,4,8,5,6,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,8},{2,7},{3},{5}} => {{1,3,5,8},{2,7},{4},{6}} => [3,7,5,4,8,6,2,1] => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,8},{2,7},{4},{5}} => {{1,3,6,8},{2,7},{4},{5}} => [3,7,6,4,5,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,8},{2,7},{3},{6}} => {{1,4,5,8},{2,7},{3},{6}} => [4,7,3,5,8,6,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,8},{3,7},{4},{6}} => {{1,4,7,8},{2,6},{3},{5}} => [4,6,3,7,5,2,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,8},{2,7},{5},{6}} => {{1,5,6,8},{2,7},{3},{4}} => [5,7,3,4,6,8,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,8},{3,7},{5},{6}} => {{1,5,7,8},{2,6},{3},{4}} => [5,6,3,4,7,2,8,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,8},{2,5},{3},{7}} => {{1,3,5,8},{2},{4,7},{6}} => [3,2,5,7,8,6,4,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,8},{2,4},{5},{7}} => {{1,3,6,8},{2},{4},{5,7}} => [3,2,6,4,7,8,5,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,8},{2,6},{3},{7}} => {{1,4,5,8},{2},{3,7},{6}} => [4,2,7,5,8,6,3,1] => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,8},{2,6},{4},{7}} => {{1,4,6,8},{2},{3,7},{5}} => [4,2,7,6,5,8,3,1] => ([(0,6),(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,8},{3,6},{4},{7}} => {{1,4,7,8},{2},{3,6},{5}} => [4,2,6,7,5,3,8,1] => ([(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,8},{2,6},{5},{7}} => {{1,5,6,8},{2},{3,7},{4}} => [5,2,7,4,6,8,3,1] => ([(0,5),(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,8},{3,6},{5},{7}} => {{1,5,7,8},{2},{3,6},{4}} => [5,2,6,4,7,3,8,1] => ([(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,8},{3,5},{6},{7}} => {{1,5,7,8},{2},{3},{4,6}} => [5,2,3,6,7,4,8,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7},{2,8},{3},{4}} => {{1,7},{2,3,4,8},{5},{6}} => [7,3,4,8,5,6,1,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4,6,7},{2,8},{3},{5}} => {{1,7},{2,3,5,8},{4},{6}} => [7,3,5,4,8,6,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,6,7},{3,8},{4},{5}} => {{1,6},{2,3,7,8},{4},{5}} => [6,3,7,4,5,1,8,2] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,5,7},{2,8},{4},{6}} => {{1,7},{2,4,6,8},{3},{5}} => [7,4,3,6,5,8,1,2] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5,7},{3,8},{4},{6}} => {{1,6},{2,4,7,8},{3},{5}} => [6,4,3,7,5,1,8,2] => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,4,7},{2,8},{5},{6}} => {{1,7},{2,5,6,8},{3},{4}} => [7,5,3,4,6,8,1,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,7},{4,8},{5},{6}} => {{1,5},{2,6,7,8},{3},{4}} => [5,6,3,4,1,7,8,2] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,4,6},{3,8},{5},{7}} => {{1,6},{2},{3,5,7,8},{4}} => [6,2,5,4,7,1,8,3] => ([(0,7),(1,5),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,6},{4,8},{5},{7}} => {{1,5},{2},{3,6,7,8},{4}} => [5,2,6,4,1,7,8,3] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5},{4,8},{6},{7}} => {{1,5},{2},{3},{4,6,7,8}} => [5,2,3,6,1,7,8,4] => ([(0,7),(1,7),(2,5),(2,7),(3,5),(3,6),(4,5),(4,6),(5,6),(6,7)],8)
{{1,4,6,7},{2,5},{3},{8}} => {{1},{2,3,5,8},{4,7},{6}} => [1,3,5,7,8,6,4,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,7},{2,5},{4},{8}} => {{1},{2,3,6,8},{4,7},{5}} => [1,3,6,7,5,8,4,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,7},{2,6},{3},{8}} => {{1},{2,4,5,8},{3,7},{6}} => [1,4,7,5,8,6,3,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,7},{2,6},{4},{8}} => {{1},{2,4,6,8},{3,7},{5}} => [1,4,7,6,5,8,3,2] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,7},{3,6},{4},{8}} => {{1},{2,4,7,8},{3,6},{5}} => [1,4,6,7,5,3,8,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,7},{2,6},{5},{8}} => {{1},{2,5,6,8},{3,7},{4}} => [1,5,7,4,6,8,3,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,7},{3,6},{5},{8}} => {{1},{2,5,7,8},{3,6},{4}} => [1,5,6,4,7,3,8,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,7},{2,4},{6},{8}} => {{1},{2,4,6,8},{3},{5,7}} => [1,4,3,6,7,8,5,2] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,7},{2,5},{6},{8}} => {{1},{2,5,6,8},{3},{4,7}} => [1,5,3,7,6,8,4,2] => ([(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,6},{2,7},{4},{8}} => {{1},{2,7},{3,4,6,8},{5}} => [1,7,4,6,5,8,2,3] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,4,5},{2,7},{6},{8}} => {{1},{2,7},{3},{4,5,6,8}} => [1,7,3,5,6,8,2,4] => ([(1,6),(1,7),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,4,5},{3,7},{6},{8}} => {{1},{2,6},{3},{4,5,7,8}} => [1,6,3,5,7,2,8,4] => ([(1,7),(2,5),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5},{4,7},{6},{8}} => {{1},{2,5},{3},{4,6,7,8}} => [1,5,3,6,2,7,8,4] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7)],8)
{{1,3,5,6},{2,4},{7},{8}} => {{1},{2},{3,4,6,8},{5,7}} => [1,2,4,6,7,8,5,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2,5},{7},{8}} => {{1},{2},{3,5,6,8},{4,7}} => [1,2,5,7,6,8,4,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,6},{3,5},{7},{8}} => {{1},{2},{3,5,7,8},{4,6}} => [1,2,5,6,7,4,8,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,5},{2,6},{7},{8}} => {{1},{2},{3,7},{4,5,6,8}} => [1,2,7,5,6,8,3,4] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,5},{3,6},{7},{8}} => {{1},{2},{3,6},{4,5,7,8}} => [1,2,6,5,7,3,8,4] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6,7,8}} => [1,2,5,6,3,7,8,4] => ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,4,7},{2,5,8},{3,6}} => {{1,4,7},{2,5,8},{3,6}} => [4,5,6,7,8,3,1,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,7},{3,4,8},{5,6}} => {{1,5,6},{2,7,8},{3,4}} => [5,7,4,3,6,1,8,2] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6},{2,5,8},{4,7}} => {{1,4,7},{2,5},{3,6,8}} => [4,5,6,7,2,8,1,3] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)
{{1,2,5},{3,4,8},{6,7}} => {{1,5,6},{2,3},{4,7,8}} => [5,3,2,7,6,1,8,4] => ([(0,6),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,2,4},{3,5,8},{6,7}} => {{1,4,6},{2,3},{5,7,8}} => [4,3,2,6,7,1,8,5] => ([(0,6),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7)],8)
{{1,3,6},{2,5,7},{4,8}} => {{1,5},{2,4,7},{3,6,8}} => [5,4,6,7,1,8,2,3] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,2,4},{3,6,7},{5,8}} => {{1,4},{2,3,6},{5,7,8}} => [4,3,6,1,7,2,8,5] => ([(0,6),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,7),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2,4,6},{7,8}} => {{1,2},{3,5,7},{4,6,8}} => [2,1,5,6,7,8,3,4] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5},{3,4,6},{7,8}} => {{1,2},{3,5,6},{4,7,8}} => [2,1,5,7,6,3,8,4] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,7,8}} => [2,1,4,6,7,3,8,5] => ([(0,1),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,7},{2,6,8},{3},{4}} => {{1,3,7},{2,4,8},{5},{6}} => [3,4,7,8,5,6,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,7},{2,6,8},{3},{5}} => {{1,3,7},{2,5,8},{4},{6}} => [3,5,7,4,8,6,1,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,7},{2,6,8},{4},{5}} => {{1,3,7},{2,6,8},{4},{5}} => [3,6,7,4,5,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,7},{3,6,8},{4},{5}} => {{1,3,6},{2,7,8},{4},{5}} => [3,7,6,4,5,1,8,2] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,7},{2,5,8},{3},{6}} => {{1,4,7},{2,5,8},{3},{6}} => [4,5,3,7,8,6,1,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,7},{2,5,8},{4},{6}} => {{1,4,7},{2,6,8},{3},{5}} => [4,6,3,7,5,8,1,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,7},{3,5,8},{4},{6}} => {{1,4,6},{2,7,8},{3},{5}} => [4,7,3,6,5,1,8,2] => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,7},{2,4,8},{5},{6}} => {{1,5,7},{2,6,8},{3},{4}} => [5,6,3,4,7,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,7},{3,4,8},{5},{6}} => {{1,5,6},{2,7,8},{3},{4}} => [5,7,3,4,6,1,8,2] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5,6},{2,7,8},{3},{4}} => {{1,2,7},{3,4,8},{5},{6}} => [2,7,4,8,5,6,1,3] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,6},{2,7,8},{3},{5}} => {{1,2,7},{3,5,8},{4},{6}} => [2,7,5,4,8,6,1,3] => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6},{2,7,8},{4},{5}} => {{1,2,7},{3,6,8},{4},{5}} => [2,7,6,4,5,8,1,3] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,6},{3,7,8},{4},{5}} => {{1,2,6},{3,7,8},{4},{5}} => [2,6,7,4,5,1,8,3] => ([(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2,7,8},{3},{6}} => {{1,2,7},{3},{4,5,8},{6}} => [2,7,3,5,8,6,1,4] => ([(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2,7,8},{4},{6}} => {{1,2,7},{3},{4,6,8},{5}} => [2,7,3,6,5,8,1,4] => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2,5},{3,7,8},{4},{6}} => {{1,2,6},{3},{4,7,8},{5}} => [2,6,3,7,5,1,8,4] => ([(0,6),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,6},{2,5,8},{3},{7}} => {{1,4,7},{2},{3,5,8},{6}} => [4,2,5,7,8,6,1,3] => ([(0,4),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6},{2,5,8},{4},{7}} => {{1,4,7},{2},{3,6,8},{5}} => [4,2,6,7,5,8,1,3] => ([(0,4),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,6},{3,4,8},{5},{7}} => {{1,5,6},{2},{3,7,8},{4}} => [5,2,7,4,6,1,8,3] => ([(0,7),(1,5),(1,6),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2,6,8},{3},{7}} => {{1,3,7},{2},{4,5,8},{6}} => [3,2,7,5,8,6,1,4] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2,6,8},{4},{7}} => {{1,3,7},{2},{4,6,8},{5}} => [3,2,7,6,5,8,1,4] => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2,6,8},{5},{7}} => {{1,3,7},{2},{4},{5,6,8}} => [3,2,7,4,6,8,1,5] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3,6,8},{5},{7}} => {{1,3,6},{2},{4},{5,7,8}} => [3,2,6,4,7,1,8,5] => ([(0,6),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,2,5},{3,4,8},{6},{7}} => {{1,5,6},{2},{3},{4,7,8}} => [5,2,3,7,6,1,8,4] => ([(0,6),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2,6,7},{3},{8}} => {{1},{2,3,7},{4,5,8},{6}} => [1,3,7,5,8,6,2,4] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2,6,7},{4},{8}} => {{1},{2,3,7},{4,6,8},{5}} => [1,3,7,6,5,8,2,4] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5},{3,6,7},{4},{8}} => {{1},{2,3,6},{4,7,8},{5}} => [1,3,6,7,5,2,8,4] => ([(1,7),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,4},{2,6,7},{5},{8}} => {{1},{2,3,7},{4},{5,6,8}} => [1,3,7,4,6,8,2,5] => ([(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3,6,7},{5},{8}} => {{1},{2,3,6},{4},{5,7,8}} => [1,3,6,4,7,2,8,5] => ([(1,7),(2,5),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,5},{2,4,7},{6},{8}} => {{1},{2,5,7},{3},{4,6,8}} => [1,5,3,6,7,8,2,4] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,3,4},{2,5,7},{6},{8}} => {{1},{2,4,7},{3},{5,6,8}} => [1,4,3,7,6,8,2,5] => ([(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3,5,7},{6},{8}} => {{1},{2,4,6},{3},{5,7,8}} => [1,4,3,6,7,2,8,5] => ([(1,6),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2,4,6},{7},{8}} => {{1},{2},{3,5,7},{4,6,8}} => [1,2,5,6,7,8,3,4] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,4},{2,5,6},{7},{8}} => {{1},{2},{3,4,7},{5,6,8}} => [1,2,4,7,6,8,3,5] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,8},{2,6},{3,7},{4}} => {{1,4,8},{2,6},{3,7},{5}} => [4,6,7,8,5,2,3,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,8},{2,6},{4,7},{5}} => {{1,6,8},{2,5},{3,7},{4}} => [6,5,7,4,2,8,3,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,6},{4,7},{5}} => {{1,7,8},{2,5},{3,6},{4}} => [7,5,6,4,2,3,8,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2,5},{3,7},{6}} => {{1,5,8},{2,6},{3},{4,7}} => [5,6,3,7,8,2,4,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,8},{2,5},{4,7},{6}} => {{1,6,8},{2,5},{3},{4,7}} => [6,5,3,7,2,8,4,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,8},{3,5},{4,7},{6}} => {{1,7,8},{2,5},{3},{4,6}} => [7,5,3,6,2,4,8,1] => ([(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2,4},{5,7},{6}} => {{1,6,8},{2,4},{3},{5,7}} => [6,4,3,2,7,8,5,1] => ([(0,5),(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3,5},{4,6},{7}} => {{1,7,8},{2},{3,5},{4,6}} => [7,2,5,6,3,4,8,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,6},{3,8},{4}} => {{1,6},{2,4,8},{3,7},{5}} => [6,4,7,8,5,1,3,2] => ([(0,3),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,6},{3,8},{5}} => {{1,6},{2,5,8},{3,7},{4}} => [6,5,7,4,8,1,3,2] => ([(0,4),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3,6},{4,8},{5}} => {{1,5},{2,7,8},{3,6},{4}} => [5,7,6,4,1,3,8,2] => ([(0,7),(1,2),(1,3),(1,4),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,5},{4,8},{6}} => {{1,5},{2,6,8},{3},{4,7}} => [5,6,3,7,1,8,4,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,2,7},{3,5},{4,8},{6}} => {{1,5},{2,7,8},{3},{4,6}} => [5,7,3,6,1,4,8,2] => ([(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,4},{5,8},{6}} => {{1,4},{2,6,8},{3},{5,7}} => [4,6,3,1,7,8,5,2] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5,6},{2,7},{3,8},{4}} => {{1,6},{2,7},{3,4,8},{5}} => [6,7,4,8,5,1,2,3] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
{{1,4,6},{2,7},{3,8},{5}} => {{1,6},{2,7},{3,5,8},{4}} => [6,7,5,4,8,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2,7},{4,8},{5}} => {{1,5},{2,7},{3,6,8},{4}} => [5,7,6,4,1,8,2,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,6},{3,7},{4,8},{5}} => {{1,5},{2,6},{3,7,8},{4}} => [5,6,7,4,1,2,8,3] => ([(0,6),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,7},{3,8},{6}} => {{1,6},{2,7},{3},{4,5,8}} => [6,7,3,5,8,1,2,4] => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2,7},{4,8},{6}} => {{1,5},{2,7},{3},{4,6,8}} => [5,7,3,6,1,8,2,4] => ([(0,5),(0,7),(1,2),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,4},{2,7},{5,8},{6}} => {{1,4},{2,7},{3},{5,6,8}} => [4,7,3,1,6,8,2,5] => ([(0,4),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(4,6),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3,7},{5,8},{6}} => {{1,4},{2,6},{3},{5,7,8}} => [4,6,3,1,7,2,8,5] => ([(0,4),(1,4),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2,4},{5,8},{7}} => {{1,4},{2},{3,6,8},{5,7}} => [4,2,6,1,7,8,5,3] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(3,5),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,3,4},{2,6},{5,8},{7}} => {{1,4},{2},{3,7},{5,6,8}} => [4,2,7,1,6,8,3,5] => ([(0,3),(0,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
{{1,2,4},{3,6},{5,8},{7}} => {{1,4},{2},{3,6},{5,7,8}} => [4,2,6,1,7,3,8,5] => ([(0,7),(1,4),(1,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6)],8)
{{1,2,3},{4,6},{5,8},{7}} => {{1,4},{2},{3,5},{6,7,8}} => [4,2,5,1,3,7,8,6] => ([(0,5),(1,5),(2,3),(2,7),(3,6),(4,6),(4,7),(6,7)],8)
{{1,3,5},{2,4},{6,8},{7}} => {{1,3},{2},{4,6,8},{5,7}} => [3,2,1,6,7,8,5,4] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2,5},{6,8},{7}} => {{1,3},{2},{4,7},{5,6,8}} => [3,2,1,7,6,8,4,5] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3,5},{6,8},{7}} => {{1,3},{2},{4,6},{5,7,8}} => [3,2,1,6,7,4,8,5] => ([(0,7),(1,2),(1,3),(2,3),(4,5),(4,6),(5,7),(6,7)],8)
{{1,4,7},{2,5},{3,6},{8}} => {{1},{2,5,8},{3,6},{4,7}} => [1,5,6,7,8,3,4,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,7},{2,5},{4,6},{8}} => {{1},{2,6,8},{3,5},{4,7}} => [1,6,5,7,3,8,4,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,7},{2,4},{5,6},{8}} => {{1},{2,6,8},{3,4},{5,7}} => [1,6,4,3,7,8,5,2] => ([(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2,5},{3,7},{8}} => {{1},{2,6},{3,5,8},{4,7}} => [1,6,5,7,8,2,4,3] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,3,6},{2,5},{4,7},{8}} => {{1},{2,5},{3,6,8},{4,7}} => [1,5,6,7,2,8,4,3] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6},{3,5},{4,7},{8}} => {{1},{2,5},{3,7,8},{4,6}} => [1,5,7,6,2,4,8,3] => ([(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2,4},{5,7},{8}} => {{1},{2,4},{3,6,8},{5,7}} => [1,4,6,2,7,8,5,3] => ([(1,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,2,6},{3,4},{5,7},{8}} => {{1},{2,4},{3,7,8},{5,6}} => [1,4,7,2,6,5,8,3] => ([(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,6},{3,7},{8}} => {{1},{2,6},{3,7},{4,5,8}} => [1,6,7,5,8,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3,5},{2,6},{4,7},{8}} => {{1},{2,5},{3,7},{4,6,8}} => [1,5,7,6,2,8,3,4] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5},{3,6},{4,7},{8}} => {{1},{2,5},{3,6},{4,7,8}} => [1,5,6,7,2,3,8,4] => ([(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1,3,4},{2,6},{5,7},{8}} => {{1},{2,4},{3,7},{5,6,8}} => [1,4,7,2,6,8,3,5] => ([(1,2),(1,7),(2,6),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3,6},{5,7},{8}} => {{1},{2,4},{3,6},{5,7,8}} => [1,4,6,2,7,3,8,5] => ([(1,7),(2,3),(2,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,3},{4,6},{5,7},{8}} => {{1},{2,4},{3,5},{6,7,8}} => [1,4,5,2,3,7,8,6] => ([(1,7),(2,7),(3,5),(3,6),(4,5),(4,6)],8)
{{1,3,5},{2,4},{6,7},{8}} => {{1},{2,3},{4,6,8},{5,7}} => [1,3,2,6,7,8,5,4] => ([(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2,5},{6,7},{8}} => {{1},{2,3},{4,7},{5,6,8}} => [1,3,2,7,6,8,4,5] => ([(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4},{3,5},{6,7},{8}} => {{1},{2,3},{4,6},{5,7,8}} => [1,3,2,6,7,4,8,5] => ([(1,2),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,7},{2,6},{3},{5},{8}} => {{1},{2,5,8},{3,7},{4},{6}} => [1,5,7,4,8,6,3,2] => ([(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,5},{4},{6},{8}} => {{1},{2,6,8},{3},{4,7},{5}} => [1,6,3,7,5,8,4,2] => ([(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2,4},{6},{7},{8}} => {{1},{2},{3},{4,6,8},{5,7}} => [1,2,3,6,7,8,5,4] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6},{4,8},{5},{7}} => {{1,5},{2},{3,7},{4},{6,8}} => [5,2,7,4,1,8,3,6] => ([(0,4),(0,5),(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,3},{2,5},{4,8},{6},{7}} => {{1,5},{2},{3},{4,7},{6,8}} => [5,2,3,7,1,8,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
{{1,5},{2,6},{3,7},{4},{8}} => {{1},{2,6},{3,7},{4,8},{5}} => [1,6,7,8,5,2,3,4] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3},{2,5},{4,7},{6},{8}} => {{1},{2,5},{3},{4,7},{6,8}} => [1,5,3,7,2,8,4,6] => ([(1,4),(1,5),(2,3),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3},{4},{5},{6}} => {{1,7},{2,8},{3},{4},{5},{6}} => [7,8,3,4,5,6,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,8},{4},{5},{6},{7}} => {{1,7},{2},{3},{4},{5},{6,8}} => [7,2,3,4,5,8,1,6] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6},{3},{4},{7},{8}} => {{1},{2},{3,7},{4,8},{5},{6}} => [1,2,7,8,5,6,3,4] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,5},{3},{6},{7},{8}} => {{1},{2},{3},{4,7},{5,8},{6}} => [1,2,3,7,8,6,4,5] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3},{2,4},{5},{6},{7},{8}} => {{1},{2},{3},{4},{5,7},{6,8}} => [1,2,3,4,7,8,5,6] => ([(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,7},{2},{4},{6,8}} => {{1,3},{2,4,6,8},{5},{7}} => [3,4,1,6,5,8,7,2] => ([(0,5),(0,6),(1,4),(1,7),(2,3),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1,5,7},{2,4},{3},{6,8}} => {{1,3},{2,4,8},{5,7},{6}} => [3,4,1,8,7,6,5,2] => ([(0,2),(0,7),(1,2),(1,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,4},{3,6},{7}} => {{1,4,8},{2},{3,6},{5,7}} => [4,2,6,8,7,3,5,1] => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,6,8},{2,4},{3,5},{7}} => {{1,3,8},{2},{4,6},{5,7}} => [3,2,8,6,7,4,5,1] => ([(0,1),(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,5},{3},{6,8}} => {{1,3},{2,5,8},{4,7},{6}} => [3,5,1,7,8,6,4,2] => ([(0,1),(0,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3,6,7},{5,8}} => {{1,4},{2,3,6},{5,8},{7}} => [4,3,6,1,8,2,7,5] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,4},{2},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,8},{7}} => [2,4,6,1,8,3,7,5] => ([(0,7),(1,4),(1,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6)],8)
{{1,4},{2},{3,7},{5,6,8}} => {{1,3,4},{2,6},{5,8},{7}} => [3,6,4,1,8,2,7,5] => ([(0,3),(0,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)
{{1,4},{2},{3,5,8},{6,7}} => {{1,4,6},{2,3},{5,8},{7}} => [4,3,2,6,8,1,7,5] => ([(0,5),(0,6),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7)],8)
{{1,5},{2},{3,4,8},{6,7}} => {{1,5,6},{2,3},{4,8},{7}} => [5,3,2,8,6,1,7,4] => ([(0,5),(0,6),(1,2),(1,4),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,5},{3},{4,7,8},{6}} => {{1,2,5},{3},{4,7,8},{6}} => [2,5,3,7,1,6,8,4] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5,7},{3},{4,8},{6}} => {{1,5},{2,4,7,8},{3},{6}} => [5,4,3,7,1,6,8,2] => ([(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,5,7},{4},{6,8}} => {{1,3},{2,4,6,7},{5},{8}} => [3,4,1,6,5,7,2,8] => ([(1,7),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,4,7},{2},{3,5},{6,8}} => {{1,3},{2,5,8},{4,6},{7}} => [3,5,1,6,8,4,7,2] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2},{3,8},{5,7}} => {{1,6},{2,4},{3,5,8},{7}} => [6,4,5,2,8,1,7,3] => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,3,7},{4},{5,8}} => {{1,4},{2,6,7},{3,8},{5}} => [4,6,8,1,5,7,2,3] => ([(0,5),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,6,7},{4,8},{5}} => {{1,5},{2,3,6},{4},{7,8}} => [5,3,6,4,1,2,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,6},{4,7,8},{5}} => {{1,2,5},{3,6},{4},{7,8}} => [2,5,6,4,1,3,8,7] => ([(0,1),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,6},{2,3},{4},{5,7,8}} => {{1,2,4},{3,8},{5},{6,7}} => [2,4,8,1,5,7,6,3] => ([(0,5),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,7},{2,3},{4},{5,6,8}} => {{1,3,4},{2,8},{5},{6,7}} => [3,8,4,1,5,7,6,2] => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2},{3,7},{4,6,8},{5}} => {{1,3,5},{2,6},{4},{7,8}} => [3,6,5,4,1,2,8,7] => ([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,5,8},{4,7},{6}} => {{1,4,6},{2,5},{3},{7,8}} => [4,5,3,6,2,1,8,7] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,8},{4,5},{6}} => {{1,6,7},{2,8},{3},{4,5}} => [6,8,3,5,4,7,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1},{2,5},{3,4,8},{6,7}} => {{1,5,6},{2,3},{4,7},{8}} => [5,3,2,7,6,1,4,8] => ([(1,2),(1,3),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4},{3,5,8},{6,7}} => {{1,4,6},{2,3},{5,7},{8}} => [4,3,2,6,7,1,5,8] => ([(1,2),(1,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4},{3,6,7},{5,8}} => {{1,4},{2,3,6},{5,7},{8}} => [4,3,6,1,7,2,5,8] => ([(1,2),(1,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3},{2,6,7},{4},{5,8}} => {{1,4},{2,3,7},{5},{6,8}} => [4,3,7,1,5,8,2,6] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,3},{2,7},{4},{5,6,8}} => {{1,3,4},{2,7},{5},{6,8}} => [3,7,4,1,5,8,2,6] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,7,8},{4,5},{6}} => {{1,2,7},{3},{4,5},{6,8}} => [2,7,3,5,4,8,1,6] => ([(0,7),(1,2),(1,7),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2,4,7},{5},{6}} => {{1,6,8},{2,5,7},{3},{4}} => [6,5,3,4,7,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2,3,7},{5},{6}} => {{1,5,8},{2,6,7},{3},{4}} => [5,6,3,4,8,7,2,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,3,8},{5},{6}} => {{1,6,7},{2,5,8},{3},{4}} => [6,5,3,4,8,7,1,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4,6},{3,7},{5,8}} => {{1,4},{2,6},{3,5,7},{8}} => [4,6,5,1,7,2,3,8] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4,6},{3,8},{5,7}} => {{1,6},{2,4},{3,5,7},{8}} => [6,4,5,2,7,1,3,8] => ([(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1},{2,4,7},{3,5},{6,8}} => {{1,3},{2,5,7},{4,6},{8}} => [3,5,1,6,7,4,2,8] => ([(1,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,4,6},{5,7}} => {{1,7},{2,4},{3,5,6},{8}} => [7,4,5,2,6,3,1,8] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,6},{4},{5,7}} => {{1,8},{2,4},{3,6,7},{5}} => [8,4,6,2,5,7,3,1] => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,6,8},{4,7},{5}} => {{1,3,6},{2,5},{4},{7,8}} => [3,5,6,4,2,1,8,7] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5,7},{4,8},{6}} => {{1,5},{2,4,6},{3},{7,8}} => [5,4,3,6,1,2,8,7] => ([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,7},{4,5,8},{6}} => {{1,4,5},{2,6},{3},{7,8}} => [4,6,3,5,1,2,8,7] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2,7},{3},{5,6}} => {{1,5,8},{2,7},{3,4},{6}} => [5,7,4,3,8,6,2,1] => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,8},{4},{5,6}} => {{1,7},{2,6,8},{3,4},{5}} => [7,6,4,3,5,8,1,2] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,7},{2,8},{4,6},{5}} => {{1,7},{2,6,8},{3,5},{4}} => [7,6,5,4,3,8,1,2] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,7},{2},{4,5,8},{6}} => {{1,4,5},{2,6,8},{3},{7}} => [4,6,3,5,1,8,7,2] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,3,8},{4,6},{5}} => {{1,6,7},{2,8},{3,5},{4}} => [6,8,5,4,3,7,1,2] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,3,8},{4},{5,6}} => {{1,6,7},{2,8},{3,4},{5}} => [6,8,4,3,5,7,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,7,8},{2,5},{3,6},{4}} => {{1,2,8},{3,6},{4,7},{5}} => [2,8,6,7,5,3,4,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4,6,8},{3},{5}} => {{1,3,5,7},{2,8},{4},{6}} => [3,8,5,4,7,6,1,2] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,4,5},{3,8},{6}} => {{1,6},{2,8},{3},{4,5,7}} => [6,8,3,5,7,1,4,2] => ([(0,3),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4,6},{2,5},{3},{7,8}} => {{1,2},{3,5,8},{4,7},{6}} => [2,1,5,7,8,6,4,3] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7,8},{2},{3,6},{4}} => {{1,2,4,8},{3,6},{5},{7}} => [2,4,6,8,5,3,7,1] => ([(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,7},{3,6},{4}} => {{1,4,8},{2,7},{3,6},{5}} => [4,7,6,8,5,3,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5,7},{3,6},{4}} => {{1,8},{2,4,7},{3,6},{5}} => [8,4,6,7,5,3,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,6,7},{3},{4}} => {{1,4,8},{2,3,7},{5},{6}} => [4,3,7,8,5,6,2,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,7},{2},{3,8},{6}} => {{1,6},{2,4,5,8},{3},{7}} => [6,4,3,5,8,1,7,2] => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,5},{2,6},{4},{7,8}} => {{1,2},{3,7},{4,6,8},{5}} => [2,1,7,6,5,8,3,4] => ([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,6,8},{2},{3,7},{5}} => {{1,3,5,8},{2,6},{4},{7}} => [3,6,5,4,8,2,7,1] => ([(0,6),(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,6},{3,7},{5}} => {{1,8},{2,6},{3,5,7},{4}} => [8,6,5,4,7,2,3,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2,5},{3},{6,7}} => {{1,5,8},{2,3},{4,7},{6}} => [5,3,2,7,8,6,4,1] => ([(0,1),(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2,8},{4},{6,7}} => {{1,7},{2,3},{4,6,8},{5}} => [7,3,2,6,5,8,1,4] => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5},{2,3,8},{4},{6,7}} => {{1,6,7},{2,3},{4,8},{5}} => [6,3,2,8,5,7,1,4] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6},{3,4,7},{5}} => {{1,8},{2,5,6},{3,7},{4}} => [8,5,7,4,6,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,4},{3,7},{5}} => {{1,3,8},{2,6},{4},{5,7}} => [3,6,8,4,7,2,5,1] => ([(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,7,8},{4},{5}} => {{1,2,6,7},{3,8},{4},{5}} => [2,6,8,4,5,7,1,3] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5},{2,3,7},{4,8},{6}} => {{1,5},{2,6,7},{3},{4,8}} => [5,6,3,8,1,7,2,4] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2,3,6},{4},{7,8}} => {{1,2},{3,6,7},{4,8},{5}} => [2,1,6,8,5,7,3,4] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,7},{2,4},{3,8},{6}} => {{1,6},{2,4,8},{3},{5,7}} => [6,4,3,8,7,1,5,2] => ([(0,1),(0,2),(0,5),(0,7),(1,2),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6,7},{2,4,8},{3},{5}} => {{1,5,7},{2,3,8},{4},{6}} => [5,3,8,4,7,6,1,2] => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6,8},{2,5,7},{3},{4}} => {{1,3,8},{2,4,7},{5},{6}} => [3,4,8,7,5,6,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,7},{3,5},{4}} => {{1,3,8},{2,7},{4,6},{5}} => [3,7,8,6,5,4,2,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,8},{3,4},{5}} => {{1,7},{2,3,8},{4},{5,6}} => [7,3,8,4,6,5,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,7},{2,5},{3,4,8},{6}} => {{1,5,6},{2,8},{3},{4,7}} => [5,8,3,7,6,1,4,2] => ([(0,1),(0,4),(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,7},{2,6,8},{3,4},{5}} => {{1,3,7},{2,8},{4},{5,6}} => [3,8,7,4,6,5,1,2] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2,3,6},{5},{7}} => {{1,5,8},{2},{3,6,7},{4}} => [5,2,6,4,8,7,3,1] => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4,8},{3,7},{6}} => {{1,5,7},{2,6},{3},{4,8}} => [5,6,3,8,7,2,1,4] => ([(0,2),(0,3),(0,4),(0,5),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5},{3,4,8},{7}} => {{1,5,6},{2},{3,8},{4,7}} => [5,2,8,7,6,1,4,3] => ([(0,1),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)
{{1,4,8},{2,7},{3,6},{5}} => {{1,5,8},{2,7},{3,6},{4}} => [5,7,6,4,8,3,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,8},{3,6},{5}} => {{1,7},{2,5,8},{3,6},{4}} => [7,5,6,4,8,3,1,2] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4,6},{2,8},{3,7},{5}} => {{1,7},{2,6},{3,5,8},{4}} => [7,6,5,4,8,2,1,3] => ([(0,1),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3,4,7},{6}} => {{1,7},{2,5,6},{3},{4,8}} => [7,5,3,8,6,2,1,4] => ([(0,2),(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3,8},{4,7},{6}} => {{1,6,7},{2,5},{3},{4,8}} => [6,5,3,8,2,7,1,4] => ([(0,2),(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2,7},{3,5},{6}} => {{1,5,8},{2,7},{3},{4,6}} => [5,7,3,6,8,4,2,1] => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6},{3,4,8},{5}} => {{1,5,6},{2,8},{3,7},{4}} => [5,8,7,4,6,1,3,2] => ([(0,2),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,5},{4,7},{6}} => {{1,8},{2,5},{3},{4,6,7}} => [8,5,3,6,2,7,4,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5},{3,4,7},{6}} => {{1,8},{2,5,6},{3},{4,7}} => [8,5,3,7,6,2,4,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,7},{3,6},{5}} => {{1,8},{2,5,7},{3,6},{4}} => [8,5,6,4,7,3,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2,8},{4,7},{6}} => {{1,7},{2,5},{3},{4,6,8}} => [7,5,3,6,2,8,1,4] => ([(0,3),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2,7},{4,6},{5}} => {{1,6,8},{2,7},{3,5},{4}} => [6,7,5,4,3,8,2,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4,6},{3,8},{5}} => {{1,6},{2,8},{3,5,7},{4}} => [6,8,5,4,7,1,3,2] => ([(0,2),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4,8},{3,5},{6}} => {{1,5,7},{2,8},{3},{4,6}} => [5,8,3,6,7,4,1,2] => ([(0,1),(0,4),(0,5),(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,5},{4,8},{6}} => {{1,5},{2,8},{3},{4,6,7}} => [5,8,3,6,1,7,4,2] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3,8},{4,6},{5}} => {{1,6},{2,7,8},{3,5},{4}} => [6,7,5,4,3,1,8,2] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,7},{4,8},{5}} => {{1,5},{2,6,7},{3,8},{4}} => [5,6,8,4,1,7,2,3] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2},{4,6,8},{7}} => {{1,3,5},{2},{4,6,8},{7}} => [3,2,5,6,1,8,7,4] => ([(0,1),(0,7),(1,7),(2,3),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,4,6,8},{5},{7}} => {{1,3,5,7},{2},{4},{6,8}} => [3,2,5,4,7,8,1,6] => ([(0,5),(0,6),(1,4),(1,7),(2,3),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2,4,6,8},{3},{5,7}} => {{1,3,5,7},{2,4},{6},{8}} => [3,4,5,2,7,6,1,8] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,6,8},{5,7}} => {{1,3,5},{2,4},{6,8},{7}} => [3,4,5,2,1,8,7,6] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2},{4,8},{5,7}} => {{1,5},{2,4},{3,6,8},{7}} => [5,4,6,2,1,8,7,3] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)
{{1,3,6},{2},{4,7},{5,8}} => {{1,4},{2,5},{3,6,8},{7}} => [4,5,6,1,2,8,7,3] => ([(0,1),(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1,3,5},{2},{4,7},{6,8}} => {{1,3},{2,5},{4,6,8},{7}} => [3,5,1,6,2,8,7,4] => ([(0,1),(0,7),(1,7),(2,3),(2,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,3,5,7},{2},{4,6},{8}} => {{1},{2,4,6,8},{3,5},{7}} => [1,4,5,6,3,8,7,2] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2},{4,6,8},{5}} => {{1,3,5},{2,6,8},{4},{7}} => [3,6,5,4,1,8,7,2] => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2},{4,6},{5,8}} => {{1,4},{2,6,8},{3,5},{7}} => [4,6,5,1,3,8,7,2] => ([(0,1),(0,7),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,7},{2},{4,8},{6}} => {{1,5},{2,4,6,8},{3},{7}} => [5,4,3,6,1,8,7,2] => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4,8},{5,7},{6}} => {{1,5,7},{2,4},{3},{6,8}} => [5,4,3,2,7,8,1,6] => ([(0,2),(0,7),(1,2),(1,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,8},{3,5,7},{6}} => {{1,5,7},{2,4,6},{3},{8}} => [5,4,3,6,7,2,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,8},{3,5,7},{6}} => {{1,7},{2,4,6},{3},{5,8}} => [7,4,3,6,8,2,1,5] => ([(0,1),(0,4),(0,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5,7},{3,8},{6}} => {{1,6},{2,4,7},{3},{5,8}} => [6,4,3,7,8,1,2,5] => ([(0,1),(0,2),(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3},{2,5,7},{4,8},{6}} => {{1,5},{2,4,7},{3},{6,8}} => [5,4,3,7,1,8,2,6] => ([(0,1),(0,7),(1,2),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,7},{4,6,8},{5}} => {{1,3,5},{2,7},{4},{6,8}} => [3,7,5,4,1,8,2,6] => ([(0,1),(0,7),(1,6),(2,3),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,4,6},{5},{8}} => {{1},{2,6,8},{3,5,7},{4}} => [1,6,5,4,7,8,3,2] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4,6},{3},{5,8}} => {{1,4},{2,8},{3,5,7},{6}} => [4,8,5,1,7,6,3,2] => ([(0,1),(0,4),(0,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,4,8},{3},{6}} => {{1,5,7},{2,4,8},{3},{6}} => [5,4,3,8,7,6,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,8},{3,5,7},{4,6}} => {{1,7},{2,4,6},{3,5},{8}} => [7,4,5,6,3,2,1,8] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4,6},{3,5},{8}} => {{1},{2,8},{3,5,7},{4,6}} => [1,8,5,6,7,4,3,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,6},{3,5},{8}} => {{1},{2,5,8},{3,7},{4,6}} => [1,5,7,6,8,4,3,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,8},{3,7},{4,6}} => {{1,4,7},{2,6},{3,5},{8}} => [4,6,5,7,3,2,1,8] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,8},{3,6},{4,7}} => {{1,4,7},{2,5},{3,6},{8}} => [4,5,6,7,2,3,1,8] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2,4,8},{3,6},{5,7}} => {{1,5,7},{2,4},{3,6},{8}} => [5,4,6,2,7,3,1,8] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2,4,6,8},{3,5},{7}} => {{1,3,5,7},{2},{4,6},{8}} => [3,2,5,6,7,4,1,8] => ([(1,2),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,6,8},{3,5},{7}} => {{1,3,7},{2},{4,6},{5,8}} => [3,2,7,6,8,4,1,5] => ([(0,1),(0,7),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5},{3,6,8},{7}} => {{1,3,6},{2},{4,7},{5,8}} => [3,2,6,7,8,1,4,5] => ([(0,1),(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1,3},{2,5},{4,6,8},{7}} => {{1,3,5},{2},{4,7},{6,8}} => [3,2,5,7,1,8,4,6] => ([(0,1),(0,7),(1,7),(2,3),(2,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2,4,6,8},{3},{7}} => {{1,3,5,7},{2},{4,8},{6}} => [3,2,5,8,7,6,1,4] => ([(0,3),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4},{3,6,8},{7}} => {{1,3,6},{2},{4,8},{5,7}} => [3,2,6,8,7,1,5,4] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)
{{1},{2,6,8},{3,5,7},{4}} => {{1,3,7},{2,4,6},{5},{8}} => [3,4,7,6,5,2,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,8},{3,5,7},{4}} => {{1,7},{2,4,6},{3,8},{5}} => [7,4,8,6,5,2,1,3] => ([(0,2),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,4,8},{3},{5,7}} => {{1,5,7},{2,4},{3,8},{6}} => [5,4,8,2,7,6,1,3] => ([(0,1),(0,2),(0,5),(0,7),(1,2),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6},{2,4,7},{3},{5,8}} => {{1,4},{2,5,7},{3,8},{6}} => [4,5,8,1,7,6,2,3] => ([(0,1),(0,2),(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5},{2,4,7},{3},{6,8}} => {{1,3},{2,5,7},{4,8},{6}} => [3,5,1,8,7,6,2,4] => ([(0,1),(0,7),(1,2),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,7},{2,4,6},{3},{8}} => {{1},{2,4,8},{3,5,7},{6}} => [1,4,5,8,7,6,3,2] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,4},{3,6},{8}} => {{1},{2,4,8},{3,6},{5,7}} => [1,4,6,8,7,3,5,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2,6,8},{3,5},{4,7}} => {{1,3,7},{2,5},{4,6},{8}} => [3,5,7,6,2,4,1,8] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2,4,6,8},{3,7},{5}} => {{1,3,5,7},{2,6},{4},{8}} => [3,6,5,4,7,2,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,7},{3,5,8},{4}} => {{1,4,6},{2,7},{3,8},{5}} => [4,7,8,6,5,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2,7},{4},{6,8}} => {{1,3},{2,7},{4,6,8},{5}} => [3,7,1,6,5,8,2,4] => ([(0,1),(0,7),(1,6),(2,3),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,6,8},{3,5},{4}} => {{1,3,7},{2,8},{4,6},{5}} => [3,8,7,6,5,4,1,2] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,6},{3,5,8},{4}} => {{1,4,6},{2,8},{3,7},{5}} => [4,8,7,6,5,1,3,2] => ([(0,1),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,6},{5,8},{7}} => {{1,4},{2},{3,5,6},{7,8}} => [4,2,5,1,6,3,8,7] => ([(0,1),(2,5),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2},{3,5,6},{4,8},{7}} => {{1,5},{2},{3,4,6},{7,8}} => [5,2,4,6,1,3,8,7] => ([(0,1),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6},{2,3},{4,5,8},{7}} => {{1,4,5},{2},{3,8},{6,7}} => [4,2,8,5,1,7,6,3] => ([(0,4),(0,5),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,5,6},{2,3},{4,8},{7}} => {{1,5},{2},{3,4,8},{6,7}} => [5,2,4,8,1,7,6,3] => ([(0,5),(0,6),(1,2),(1,4),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5,6},{2,3,8},{4},{7}} => {{1,6,7},{2},{3,4,8},{5}} => [6,2,4,8,5,7,1,3] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5,6},{2,8},{3,4},{7}} => {{1,7},{2},{3,4,8},{5,6}} => [7,2,4,8,6,5,1,3] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5},{2,8},{3,4,6},{7}} => {{1,7},{2},{3,5,6},{4,8}} => [7,2,5,8,6,3,1,4] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3,8},{4,6},{7}} => {{1,6,7},{2},{3,5},{4,8}} => [6,2,5,8,3,7,1,4] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,6},{2,3,5,8},{4},{7}} => {{1,4,6,7},{2},{3,8},{5}} => [4,2,8,6,5,7,1,3] => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2,4},{3,6},{5},{7,8}} => {{1,2},{3,6},{4},{5,7,8}} => [2,1,6,4,7,3,8,5] => ([(0,1),(2,5),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2,4,6},{3},{5,8},{7}} => {{1,4},{2},{3,5,7,8},{6}} => [4,2,5,1,7,6,8,3] => ([(0,7),(1,2),(1,7),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,2,4},{3,8},{5},{6,7}} => {{1,6},{2,3},{4},{5,7,8}} => [6,3,2,4,7,1,8,5] => ([(0,5),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4},{2,3,8},{5},{6,7}} => {{1,6,7},{2,3},{4},{5,8}} => [6,3,2,4,8,7,1,5] => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2,8},{5},{6,7}} => {{1,7},{2,3},{4},{5,6,8}} => [7,3,2,4,6,8,1,5] => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4},{2,3,8},{5,7},{6}} => {{1,6,7},{2,4},{3},{5,8}} => [6,4,3,2,8,7,1,5] => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2,3},{5,8},{7}} => {{1,4},{2},{3,5,8},{6,7}} => [4,2,5,1,8,7,6,3] => ([(0,5),(0,6),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7)],8)
{{1,4},{2,3,6,8},{5},{7}} => {{1,3,6,7},{2},{4},{5,8}} => [3,2,6,4,8,7,1,5] => ([(0,6),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4},{2,3,6},{5,8},{7}} => {{1,4},{2},{3,6,7},{5,8}} => [4,2,6,1,8,7,3,5] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,3,8},{2,6},{4,5},{7}} => {{1,6,8},{2},{3,7},{4,5}} => [6,2,7,5,4,8,3,1] => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2,6},{5},{7,8}} => {{1,2},{3,7},{4},{5,6,8}} => [2,1,7,4,6,8,3,5] => ([(0,1),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6},{2,5,8},{3,4},{7}} => {{1,4,7},{2},{3,8},{5,6}} => [4,2,8,7,6,5,1,3] => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,8},{2,5,6},{4},{7}} => {{1,6,8},{2},{3,4,7},{5}} => [6,2,4,7,5,8,3,1] => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2,5},{4},{6,7}} => {{1,6,8},{2,3},{4,7},{5}} => [6,3,2,7,5,8,4,1] => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4},{3,7,8},{6}} => {{1,2,6},{3},{4,8},{5,7}} => [2,6,3,8,7,1,5,4] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,5,6},{2,4},{3,8},{7}} => {{1,6},{2},{3,4,8},{5,7}} => [6,2,4,8,7,1,5,3] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4},{2,8},{3,5,6},{7}} => {{1,7},{2},{3,4,6},{5,8}} => [7,2,4,6,8,3,1,5] => ([(0,6),(0,7),(1,3),(1,5),(1,6),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,3,8},{4},{6}} => {{1,6,7},{2,4,8},{3},{5}} => [6,4,3,8,5,7,1,2] => ([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5},{3,7},{4},{6,8}} => {{1,3},{2,6},{4,7,8},{5}} => [3,6,1,7,5,2,8,4] => ([(0,7),(1,2),(1,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,7},{3},{5,6,8}} => {{1,3,4},{2,7},{5,8},{6}} => [3,7,4,1,8,6,2,5] => ([(0,4),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(4,6),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5,7,8},{3},{4}} => {{1,2,4,7},{3,8},{5},{6}} => [2,4,8,7,5,6,1,3] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6,7},{2,5,8},{3},{4}} => {{1,4,7},{2,3,8},{5},{6}} => [4,3,8,7,5,6,1,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,5,6,8},{3},{4}} => {{1,3,4,7},{2,8},{5},{6}} => [3,8,4,7,5,6,1,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,6,8},{3},{4,5}} => {{1,3,7},{2,8},{4,5},{6}} => [3,8,7,5,4,6,1,2] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,8},{2,6},{3},{4,5,7}} => {{1,8},{2,4,5},{3,7},{6}} => [8,4,7,5,2,6,3,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5,6},{3},{4,7}} => {{1,8},{2,5},{3,4,7},{6}} => [8,5,4,7,2,6,3,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5},{3},{4,6,7}} => {{1,8},{2,3,5},{4,7},{6}} => [8,3,5,7,2,6,4,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,5},{3},{4,6}} => {{1,2,8},{3,5},{4,7},{6}} => [2,8,5,7,3,6,4,1] => ([(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4},{3,6,7},{5}} => {{1,8},{2,3,6},{4},{5,7}} => [8,3,6,4,7,2,5,1] => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7,8},{2,4},{3,6},{5}} => {{1,2,8},{3,6},{4},{5,7}} => [2,8,6,4,7,3,5,1] => ([(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,7},{4,5,8},{6}} => {{1,4,5},{2,7},{3},{6,8}} => [4,7,3,5,1,8,2,6] => ([(0,1),(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3},{2,6},{4,7,8},{5}} => {{1,2,5},{3,7},{4},{6,8}} => [2,5,7,4,1,8,3,6] => ([(0,7),(1,2),(1,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,4,7,8},{3},{5}} => {{1,2,5,7},{3,8},{4},{6}} => [2,5,8,4,7,6,1,3] => ([(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,4,8},{3},{5,6}} => {{1,5,7},{2,8},{3,4},{6}} => [5,8,4,3,7,6,1,2] => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,7},{2,5,8},{3,4},{6}} => {{1,4,7},{2,8},{3},{5,6}} => [4,8,3,7,6,5,1,2] => ([(0,1),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,3,5,8},{4},{6}} => {{1,4,6,7},{2,8},{3},{5}} => [4,8,3,6,5,7,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,7},{3},{4,6},{5,8}} => {{1,4},{2,7,8},{3,5},{6}} => [4,7,5,1,3,6,8,2] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3,6},{4,5,8}} => {{1,4,5},{2,8},{3,6},{7}} => [4,8,6,5,1,3,7,2] => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3,5,6},{4,8}} => {{1,5},{2,8},{3,4,6},{7}} => [5,8,4,6,1,3,7,2] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2},{3,5},{4,8}} => {{1,5},{2,3,8},{4,6},{7}} => [5,3,8,6,1,4,7,2] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,6},{2},{3,5},{4,7,8}} => {{1,2,5},{3,8},{4,6},{7}} => [2,5,8,6,1,4,7,3] => ([(0,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5},{2},{3,7,8},{4,6}} => {{1,2,6},{3,5},{4,8},{7}} => [2,6,5,8,3,1,7,4] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2},{3,8},{4,6,7}} => {{1,6},{2,3,5},{4,8},{7}} => [6,3,5,8,2,1,7,4] => ([(0,3),(0,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2},{3,8},{4,7}} => {{1,6},{2,5},{3,4,8},{7}} => [6,5,4,8,2,1,7,3] => ([(0,1),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)
{{1,6},{2},{3,8},{4,5,7}} => {{1,6},{2,4,5},{3,8},{7}} => [6,4,8,5,2,1,7,3] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,6},{2},{3,4,8},{5,7}} => {{1,5,6},{2,4},{3,8},{7}} => [5,4,8,2,6,1,7,3] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,2,6,8},{3},{4,7},{5}} => {{1,3,7,8},{2,5},{4},{6}} => [3,5,7,4,2,6,8,1] => ([(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2},{3,7},{4,5}} => {{1,3,8},{2,6},{4,5},{7}} => [3,6,8,5,4,2,7,1] => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,8},{2},{3,7},{4}} => {{1,3,4,8},{2,6},{5},{7}} => [3,6,4,8,5,2,7,1] => ([(0,5),(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2},{3,6,7},{4}} => {{1,4,8},{2,3,6},{5},{7}} => [4,3,6,8,5,2,7,1] => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{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] => ([],9)
{{1},{2},{3},{4},{5},{6},{7},{8,9}} => {{1,2},{3},{4},{5},{6},{7},{8},{9}} => [2,1,3,4,5,6,7,8,9] => ([(7,8)],9)
{{1},{2},{3},{4},{5},{6},{7,9},{8}} => {{1,3},{2},{4},{5},{6},{7},{8},{9}} => [3,2,1,4,5,6,7,8,9] => ([(6,7),(6,8),(7,8)],9)
{{1},{2},{3},{4},{5},{6,9},{7},{8}} => {{1,4},{2},{3},{5},{6},{7},{8},{9}} => [4,2,3,1,5,6,7,8,9] => ([(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2},{3},{4},{5,9},{6},{7},{8}} => {{1,5},{2},{3},{4},{6},{7},{8},{9}} => [5,2,3,4,1,6,7,8,9] => ([(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2},{3},{4,9},{5},{6},{7},{8}} => {{1,6},{2},{3},{4},{5},{7},{8},{9}} => [6,2,3,4,5,1,7,8,9] => ([(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2},{3,9},{4},{5},{6},{7},{8}} => {{1,7},{2},{3},{4},{5},{6},{8},{9}} => [7,2,3,4,5,6,1,8,9] => ([(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2,9},{3},{4},{5},{6},{7},{8}} => {{1,8},{2},{3},{4},{5},{6},{7},{9}} => [8,2,3,4,5,6,7,1,9] => ([(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,9},{2},{3},{4},{5},{6},{7},{8}} => {{1,9},{2},{3},{4},{5},{6},{7},{8}} => [9,2,3,4,5,6,7,8,1] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],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] => ([],10)
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => [2,1,3,4,5,6,7,8,9,10] => ([(8,9)],10)
{{1},{2},{3},{4},{5},{6},{7,8,9}} => {{1,2,3},{4},{5},{6},{7},{8},{9}} => [2,3,1,4,5,6,7,8,9] => ([(6,8),(7,8)],9)
{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => {{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => [3,2,1,4,5,6,7,8,9,10] => ([(7,8),(7,9),(8,9)],10)
{{1},{2},{3},{4},{5},{6,9},{7,8}} => {{1,4},{2,3},{5},{6},{7},{8},{9}} => [4,3,2,1,5,6,7,8,9] => ([(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => [9,2,3,4,5,6,7,8,1,10] => ([(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => [10,2,3,4,5,6,7,8,9,1] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,2,3,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,7,8,9}} => [1,3,4,5,6,7,8,9,2] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
{{1},{2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8},{9}} => [2,3,4,5,6,7,8,1,9] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
{{1,2,3,4,5,6,7,8,9},{10}} => {{1},{2,3,4,5,6,7,8,9,10}} => [1,3,4,5,6,7,8,9,10,2] => ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1,2,3,4,5,6,8},{7},{9}} => {{1},{2,4,5,6,7,8,9},{3}} => [1,4,3,5,6,7,8,9,2] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2,3,4,5,6,7,9},{8}} => {{1,3,4,5,6,7,8},{2},{9}} => [3,2,4,5,6,7,8,1,9] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9},{10}} => [2,3,4,5,6,7,8,9,1,10] => ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1,2,3,4,5,6,7,8,9,10},{11}} => {{1},{2,3,4,5,6,7,8,9,10,11}} => [1,3,4,5,6,7,8,9,10,11,2] => ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
{{1},{2,3,4,5,6,7,8,9,10,11}} => {{1,2,3,4,5,6,7,8,9,10},{11}} => [2,3,4,5,6,7,8,9,10,1,11] => ([(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
{{1,3,6,8},{2},{4},{5,7}} => {{1,3,6,8},{2,4},{5},{7}} => [3,4,6,2,5,8,7,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,8},{2},{3,5},{7}} => {{1,3,5,8},{2},{4,6},{7}} => [3,2,5,6,8,4,7,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,3},{4,8},{6}} => {{1,5},{2,4,8},{3},{6,7}} => [5,4,3,8,1,7,6,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4,8},{2},{3,6},{5,7}} => {{1,5,8},{2,4},{3,6},{7}} => [5,4,6,2,8,3,7,1] => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,8},{2},{4,6},{5,7}} => {{1,6,8},{2,4},{3,5},{7}} => [6,4,5,2,3,8,7,1] => ([(0,1),(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7,8},{2},{3,6},{5}} => {{1,2,5,8},{3,6},{4},{7}} => [2,5,6,4,8,3,7,1] => ([(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,7},{2},{3,5},{8}} => {{1},{2,3,5,8},{4,6},{7}} => [1,3,5,6,8,4,7,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2},{3,7},{5,6}} => {{1,5,8},{2,6},{3,4},{7}} => [5,6,4,3,8,2,7,1] => ([(0,1),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2},{3,7},{4,6}} => {{1,4,8},{2,6},{3,5},{7}} => [4,6,5,8,3,2,7,1] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2},{3,6},{4,7}} => {{1,4,8},{2,5},{3,6},{7}} => [4,5,6,8,2,3,7,1] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4,7},{2,3},{5,8},{6}} => {{1,4},{2,5,8},{3},{6,7}} => [4,5,3,1,8,7,6,2] => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,5,8},{4,7},{6}} => {{1,4,7},{2,5},{3},{6,8}} => [4,5,3,7,2,8,1,6] => ([(0,1),(0,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4,7,8},{3},{6}} => {{1,2,5,7},{3},{4,8},{6}} => [2,5,3,8,7,6,1,4] => ([(0,7),(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,4,6,7},{5},{8}} => {{1},{2,3,5,7},{4},{6,8}} => [1,3,5,4,7,8,2,6] => ([(1,7),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3},{2,4,8},{5,6},{7}} => {{1,5,7},{2},{3,4},{6,8}} => [5,2,4,3,7,8,1,6] => ([(0,1),(0,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,5,8},{4,6},{7}} => {{1,4,7},{2},{3,5},{6,8}} => [4,2,5,7,3,8,1,6] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,4},{5,8},{7}} => {{1,4},{2},{3,8},{5,6,7}} => [4,2,8,1,6,7,5,3] => ([(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,6},{2,4},{3,5,8},{7}} => {{1,4,6},{2},{3,8},{5,7}} => [4,2,8,6,7,1,5,3] => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,6},{3,5,8},{7}} => {{1,4,6},{2},{3,7},{5,8}} => [4,2,7,6,8,1,3,5] => ([(0,3),(0,7),(1,2),(1,4),(1,7),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5,6},{3,7},{8}} => {{1},{2,6},{3,4,7},{5,8}} => [1,6,4,7,8,2,3,5] => ([(1,2),(1,3),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4},{2,6,7},{3,8},{5}} => {{1,6},{2,3,7},{4},{5,8}} => [6,3,7,4,8,1,2,5] => ([(0,5),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5},{3,6},{4},{7,8}} => {{1,2},{3,6},{4,7,8},{5}} => [2,1,6,7,5,3,8,4] => ([(0,1),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,4},{3,7},{5,6},{8}} => {{1},{2,6},{3,4},{5,7,8}} => [1,6,4,3,7,2,8,5] => ([(1,5),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,4},{2,7},{5,6},{8}} => {{1},{2,7},{3,4},{5,6,8}} => [1,7,4,3,6,8,2,5] => ([(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6,7},{2,8},{3},{4,5}} => {{1,7},{2,3,8},{4,5},{6}} => [7,3,8,5,4,6,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,5,6},{2,3},{4,7},{8}} => {{1},{2,5},{3,4,8},{6,7}} => [1,5,4,8,2,7,6,3] => ([(1,2),(1,3),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2,3},{5,7},{8}} => {{1},{2,4},{3,5,8},{6,7}} => [1,4,5,2,8,7,6,3] => ([(1,2),(1,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3,6},{5,7},{8}} => {{1},{2,4},{3,6,7},{5,8}} => [1,4,6,2,8,7,3,5] => ([(1,2),(1,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4},{2,3,7},{5},{6,8}} => {{1,3},{2,6,7},{4},{5,8}} => [3,6,1,4,8,7,2,5] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,4},{3,7},{5},{6,8}} => {{1,3},{2,6},{4},{5,7,8}} => [3,6,1,4,7,2,8,5] => ([(0,5),(1,2),(1,7),(2,6),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,3,4},{2,7},{5},{6,8}} => {{1,3},{2,7},{4},{5,6,8}} => [3,7,1,4,6,8,2,5] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3},{4,5},{6,8}} => {{1,3},{2,7,8},{4,5},{6}} => [3,7,1,5,4,6,8,2] => ([(0,7),(1,2),(1,7),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6},{3},{4},{5,7,8}} => {{1,2,4},{3,7,8},{5},{6}} => [2,4,7,1,5,6,8,3] => ([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,7},{2,3,4},{5},{6,8}} => {{1,3},{2,8},{4},{5,6,7}} => [3,8,1,4,6,7,5,2] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4},{3,6,8},{5}} => {{1,3,6},{2,8},{4},{5,7}} => [3,8,6,4,7,1,5,2] => ([(0,5),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4},{2,7},{3,6,8},{5}} => {{1,3,6},{2,7},{4},{5,8}} => [3,7,6,4,8,1,2,5] => ([(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,6},{3,5,7},{8}} => {{1},{2,4,6},{3,7},{5,8}} => [1,4,7,6,8,2,3,5] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,4},{3,5,7},{8}} => {{1},{2,4,6},{3,8},{5,7}} => [1,4,8,6,7,2,5,3] => ([(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6},{2,3,4},{5,7},{8}} => {{1},{2,4},{3,8},{5,6,7}} => [1,4,8,2,6,7,5,3] => ([(1,2),(1,7),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,5,7},{4,6},{8}} => {{1},{2,4,7},{3,5},{6,8}} => [1,4,5,7,3,8,2,6] => ([(1,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4,7},{5,6},{8}} => {{1},{2,5,7},{3,4},{6,8}} => [1,5,4,3,7,8,2,6] => ([(1,2),(1,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,7,8},{3},{4,6}} => {{1,2,7},{3,5},{4,8},{6}} => [2,7,5,8,3,6,1,4] => ([(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4},{3,5,6},{8}} => {{1},{2,8},{3,4,6},{5,7}} => [1,8,4,6,7,3,5,2] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5},{3,7,8},{4}} => {{1,2,6},{3,8},{4,7},{5}} => [2,6,8,7,5,1,4,3] => ([(0,6),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1,5},{2,6},{3,7,8},{4}} => {{1,2,6},{3,7},{4,8},{5}} => [2,6,7,8,5,1,3,4] => ([(0,6),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,8},{3,6,7},{5}} => {{1,7},{2,3,6},{4},{5,8}} => [7,3,6,4,8,2,1,5] => ([(0,2),(0,5),(0,6),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,7},{3,5,6},{8}} => {{1},{2,7},{3,4,6},{5,8}} => [1,7,4,6,8,3,2,5] => ([(1,3),(1,5),(1,6),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4,5,6},{7,8}} => {{1,2},{3,4,5,7},{6,8}} => [2,1,4,5,7,8,3,6] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,3,5,6},{7,8}} => {{1,2},{3,4,6,7},{5,8}} => [2,1,4,6,8,7,3,5] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,3,5,7},{6,8}} => {{1,3},{2,4,6,7},{5,8}} => [3,4,1,6,8,7,2,5] => ([(0,1),(0,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4,5,7},{6,8}} => {{1,3},{2,4,5,7},{6,8}} => [3,4,1,5,7,8,2,6] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,2},{3,4,5,7},{6,8}} => {{1,3},{2,4,5,6},{7,8}} => [3,4,1,5,6,2,8,7] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,4,5,6,7,8}} => {{1,2,3,4,5,7},{6,8}} => [2,3,4,5,7,8,1,6] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,3,5,6,7,8}} => {{1,2,3,4,6,7},{5,8}} => [2,3,4,6,8,7,1,5] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2,3,4,6,7,8}} => {{1,2,3,5,6,7},{4,8}} => [2,3,5,8,6,7,1,4] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,4,6,7},{5,8}} => {{1,4},{2,3,5,6},{7,8}} => [4,3,5,1,6,2,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,4,6,7},{5,8}} => {{1,4},{2,3,5,7},{6,8}} => [4,3,5,1,7,8,2,6] => ([(0,1),(0,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3,6,7},{4,8}} => {{1,5},{2,3,6,7},{4,8}} => [5,3,6,8,1,7,2,4] => ([(0,4),(0,6),(0,7),(1,3),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,3},{2,4},{5,6,7,8}} => {{1,2,3,4},{5,7},{6,8}} => [2,3,4,1,7,8,5,6] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6)],8)
{{1,4},{2,5},{3,6,7,8}} => {{1,2,3,6},{4,7},{5,8}} => [2,3,6,7,8,1,4,5] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1,3},{2,5},{4,6,7,8}} => {{1,2,3,5},{4,7},{6,8}} => [2,3,5,7,1,8,4,6] => ([(0,7),(1,7),(2,3),(2,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7,8}} => [2,3,5,6,1,4,8,7] => ([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2,4,6,8},{3,7}} => {{1,3,5,7},{2,6},{4,8}} => [3,6,5,8,7,2,1,4] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,8},{2,3,6,7}} => {{1,4,5,8},{2,3,6,7}} => [4,3,6,5,8,7,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3,5,6},{7,8}} => {{1,2},{3,4,6},{5,8},{7}} => [2,1,4,6,8,3,7,5] => ([(0,1),(2,5),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,5},{2},{3,6},{7,8}} => {{1,2},{3,6},{4,5,8},{7}} => [2,1,6,5,8,3,7,4] => ([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,5},{2},{3,4,6},{7,8}} => {{1,2},{3,5,6},{4,8},{7}} => [2,1,5,8,6,3,7,4] => ([(0,1),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6},{2},{3,4,7,8},{5}} => {{1,2,5,6},{3,8},{4},{7}} => [2,5,8,4,6,1,7,3] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2},{3,4,7,8},{6}} => {{1,2,5,6},{3},{4,8},{7}} => [2,5,3,8,6,1,7,4] => ([(0,7),(1,5),(1,6),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2},{3,7,8},{6}} => {{1,2,6},{3},{4,5,8},{7}} => [2,6,3,5,8,1,7,4] => ([(0,7),(1,5),(1,7),(2,3),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2},{3,8},{6,7}} => {{1,6},{2,3},{4,5,8},{7}} => [6,3,2,5,8,1,7,4] => ([(0,4),(0,5),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,6,7},{2},{3,4,8},{5}} => {{1,5,6},{2,3,8},{4},{7}} => [5,3,8,4,6,1,7,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,7},{2},{3,4,8},{5,6}} => {{1,5,6},{2,8},{3,4},{7}} => [5,8,4,3,6,1,7,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,6,7},{2},{3,8},{5}} => {{1,6},{2,3,5,8},{4},{7}} => [6,3,5,4,8,1,7,2] => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,6},{2},{3,7,8},{5}} => {{1,2,6},{3,5,8},{4},{7}} => [2,6,5,4,8,1,7,3] => ([(0,7),(1,2),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6},{2},{4},{5,7,8}} => {{1,2,4},{3,6,8},{5},{7}} => [2,4,6,1,5,8,7,3] => ([(0,6),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,2},{3,6},{4},{5,7,8}} => {{1,2,4},{3,6},{5},{7,8}} => [2,4,6,1,5,3,8,7] => ([(0,1),(2,5),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4},{2},{3,5,7,8},{6}} => {{1,2,4,6},{3},{5,8},{7}} => [2,4,3,6,8,1,7,5] => ([(0,7),(1,2),(1,7),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,6},{2,4},{3},{5,7,8}} => {{1,2,4},{3,8},{5,7},{6}} => [2,4,8,1,7,6,5,3] => ([(0,2),(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,3},{4},{5,8}} => {{1,4},{2,3,8},{5},{6,7}} => [4,3,8,1,5,7,6,2] => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4},{3},{5,6,8}} => {{1,3,4},{2,8},{5,7},{6}} => [3,8,4,1,7,6,5,2] => ([(0,2),(0,7),(1,2),(1,6),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,4},{3},{5,8}} => {{1,4},{2,3,8},{5,7},{6}} => [4,3,8,1,7,6,5,2] => ([(0,1),(0,2),(0,7),(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,6,7},{4},{5,8}} => {{1,4},{2,3,6},{5},{7,8}} => [4,3,6,1,5,2,8,7] => ([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,6,7},{2},{4},{5,8}} => {{1,4},{2,3,6,8},{5},{7}} => [4,3,6,1,5,8,7,2] => ([(0,6),(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,3,7},{2},{4},{5,6,8}} => {{1,3,4},{2,6,8},{5},{7}} => [3,6,4,1,5,8,7,2] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,2},{3,7},{4},{5,6,8}} => {{1,3,4},{2,6},{5},{7,8}} => [3,6,4,1,5,2,8,7] => ([(0,1),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,7},{2},{3,8},{5,6}} => {{1,6},{2,5,8},{3,4},{7}} => [6,5,4,3,8,1,7,2] => ([(0,1),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,4,5},{3},{6,8}} => {{1,3},{2,8},{4,5,7},{6}} => [3,8,1,5,7,6,4,2] => ([(0,1),(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,3},{4,6},{7}} => {{1,4,8},{2},{3,5},{6,7}} => [4,2,5,8,3,7,6,1] => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,8},{2},{3,5,6},{7}} => {{1,5,8},{2},{3,4,6},{7}} => [5,2,4,6,8,3,7,1] => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,3},{4},{6,8}} => {{1,3},{2,4,8},{5},{6,7}} => [3,4,1,8,5,7,6,2] => ([(0,1),(0,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,6},{3,7},{4,8}} => {{1,5},{2,6},{3,4,7},{8}} => [5,6,4,7,1,2,3,8] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2},{3,6,7},{4,5,8}} => {{1,4,5},{2,3,6},{7},{8}} => [4,3,6,5,1,2,7,8] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,6,7},{4},{5,8}} => {{1,4},{2,3,6,7},{5},{8}} => [4,3,6,1,5,7,2,8] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1},{2},{3,4,6,8},{5,7}} => {{1,3,5,6},{2,4},{7},{8}} => [3,4,5,2,6,1,7,8] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5},{3,6,7},{4,8}} => {{1,5},{2,3,6},{4,7},{8}} => [5,3,6,7,1,2,4,8] => ([(1,2),(1,3),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2},{3,5,6},{4,7,8}} => {{1,2,5},{3,4,6},{7},{8}} => [2,5,4,6,1,3,7,8] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2},{3,5},{4,6,7,8}} => {{1,2,3,5},{4,6},{7},{8}} => [2,3,5,6,1,4,7,8] => ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1},{2,4,8},{3,5},{6,7}} => {{1,5,7},{2,3},{4,6},{8}} => [5,3,2,6,7,4,1,8] => ([(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4},{3,6,8},{5,7}} => {{1,3,6},{2,4},{5,7},{8}} => [3,4,6,2,7,1,5,8] => ([(1,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1},{2,4,7},{3,6},{5,8}} => {{1,4},{2,5,7},{3,6},{8}} => [4,5,6,1,7,3,2,8] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,8},{4,5,7},{6}} => {{1,7},{2,4,5},{3},{6,8}} => [7,4,3,5,2,8,1,6] => ([(0,1),(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3,4,5},{6,8}} => {{1,3},{2,8},{4,5,6},{7}} => [3,8,1,5,6,4,7,2] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,5,7},{4,6,8}} => {{1,3,5},{2,4,6},{7},{8}} => [3,4,5,6,1,2,7,8] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2},{3,6,7},{4,8}} => {{1,5},{2,3,6},{4,8},{7}} => [5,3,6,8,1,2,7,4] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
{{1,5},{2},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,8},{7}} => [2,5,6,8,1,3,7,4] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2},{3},{4,6,7,8}} => {{1,2,3,5},{4,8},{6},{7}} => [2,3,5,8,1,6,7,4] => ([(0,7),(1,7),(2,5),(2,7),(3,5),(3,6),(4,5),(4,6),(5,6),(6,7)],8)
{{1},{2,6},{3},{4,5,7,8}} => {{1,2,4,5},{3,7},{6},{8}} => [2,4,7,5,1,6,3,8] => ([(1,7),(2,5),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2},{3,4},{5,7,8}} => {{1,2,4},{3,8},{5,6},{7}} => [2,4,8,1,6,5,7,3] => ([(0,5),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2,6},{3},{4,7,8},{5}} => {{1,2,5},{3,7,8},{4},{6}} => [2,5,7,4,1,6,8,3] => ([(0,6),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2},{3,4,7},{5,8}} => {{1,4},{2,5,6},{3,8},{7}} => [4,5,8,1,6,2,7,3] => ([(0,6),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1,5},{2},{3,7},{4,6,8}} => {{1,3,5},{2,6},{4,8},{7}} => [3,6,5,8,1,2,7,4] => ([(0,5),(0,6),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,5},{2,6},{3},{4,7,8}} => {{1,2,5},{3,7},{4,8},{6}} => [2,5,7,8,1,6,3,4] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,3,6},{2,5},{4},{7,8}} => {{1,2},{3,6,8},{4,7},{5}} => [2,1,6,7,5,8,4,3] => ([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4,6},{3},{7,8}} => {{1,2},{3,5,7},{4,8},{6}} => [2,1,5,8,7,6,3,4] => ([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2,6},{3},{7,8}} => {{1,2},{3,7},{4,5,8},{6}} => [2,1,7,5,8,6,3,4] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,8},{2,7},{3,4},{6}} => {{1,4,8},{2,7},{3},{5,6}} => [4,7,3,8,6,5,2,1] => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,8},{3},{6,7}} => {{1,7},{2,3},{4,5,8},{6}} => [7,3,2,5,8,6,1,4] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,8},{3,5},{4}} => {{1,7},{2,3,8},{4,6},{5}} => [7,3,8,6,5,4,1,2] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,8},{3},{4,5,7}} => {{1,7},{2,4,5},{3,8},{6}} => [7,4,8,5,2,6,1,3] => ([(0,3),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,7),(6,7)],8)
{{1,6},{2,5,8},{3},{4,7}} => {{1,4,7},{2,5},{3,8},{6}} => [4,5,8,7,2,6,1,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)
{{1,6},{2,4,5,8},{3},{7}} => {{1,4,5,7},{2},{3,8},{6}} => [4,2,8,5,7,6,1,3] => ([(0,2),(0,7),(1,5),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5},{2,7},{3},{4,6,8}} => {{1,3,5},{2,7},{4,8},{6}} => [3,7,5,8,1,6,2,4] => ([(0,5),(0,7),(1,2),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,7},{2,5},{3,6,8},{4}} => {{1,3,6},{2,8},{4,7},{5}} => [3,8,6,7,5,1,4,2] => ([(0,4),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,8},{2,6},{3,5,7},{4}} => {{1,8},{2,4,6},{3,7},{5}} => [8,4,7,6,5,2,3,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,3},{4,7},{6}} => {{1,4,8},{2,5},{3},{6,7}} => [4,5,3,8,2,7,6,1] => ([(0,1),(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3},{4,6,8},{5}} => {{1,3,5},{2,8},{4},{6,7}} => [3,8,5,4,1,7,6,2] => ([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6,7},{2,3},{4,8},{5}} => {{1,5},{2,3,8},{4},{6,7}} => [5,3,8,4,1,7,6,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5,6},{3,7},{4}} => {{1,8},{2,6},{3,4,7},{5}} => [8,6,4,7,5,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2,6},{4},{5,7}} => {{1,6,8},{2,4},{3,7},{5}} => [6,4,7,2,5,8,3,1] => ([(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,5},{3,8},{4}} => {{1,6},{2,3,8},{4,7},{5}} => [6,3,8,7,5,1,4,2] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6,7},{3},{4,8}} => {{1,5},{2,3,7},{4,8},{6}} => [5,3,7,8,1,6,2,4] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,3,8},{2,7},{4,5},{6}} => {{1,6,8},{2,7},{3},{4,5}} => [6,7,3,5,4,8,2,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2,4,8},{3},{7}} => {{1,5,7},{2},{3,4,8},{6}} => [5,2,4,8,7,6,1,3] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,6},{2,8},{3},{4,7}} => {{1,7},{2,5},{3,4,8},{6}} => [7,5,4,8,2,6,1,3] => ([(0,1),(0,4),(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5,7},{2},{3,6,8},{4}} => {{1,3,6},{2,4,8},{5},{7}} => [3,4,6,8,5,1,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2},{3,6,8},{4,7}} => {{1,3,6},{2,5},{4,8},{7}} => [3,5,6,8,2,1,7,4] => ([(0,6),(0,7),(1,4),(1,5),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,6,8},{2,5},{3},{4,7}} => {{1,3,8},{2,5},{4,7},{6}} => [3,5,8,7,2,6,4,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5},{2,6,8},{3},{4,7}} => {{1,3,7},{2,5},{4,8},{6}} => [3,5,7,8,2,6,1,4] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,5,7},{2,6},{3},{4,8}} => {{1,5},{2,4,8},{3,7},{6}} => [5,4,7,8,1,6,3,2] => ([(0,2),(0,3),(0,4),(0,5),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5,7},{3},{4,8}} => {{1,5},{2,4,7},{3,8},{6}} => [5,4,8,7,1,6,2,3] => ([(0,1),(0,2),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2},{3,6},{4,8}} => {{1,5},{2,4,8},{3,6},{7}} => [5,4,6,8,1,3,7,2] => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2},{3,8},{4,6}} => {{1,6},{2,4,8},{3,5},{7}} => [6,4,5,8,3,1,7,2] => ([(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5,6},{2},{3,7},{4,8}} => {{1,5},{2,6},{3,4,8},{7}} => [5,6,4,8,1,2,7,3] => ([(0,5),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1,5,8},{2,6},{3},{4,7}} => {{1,4,8},{2,5},{3,7},{6}} => [4,5,7,8,2,6,3,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,7},{2,5,8},{3,6},{4}} => {{1,4,7},{2,8},{3,6},{5}} => [4,8,6,7,5,3,1,2] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,7},{2,5,8},{3},{4,6}} => {{1,4,7},{2,8},{3,5},{6}} => [4,8,5,7,3,6,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,5,6},{3},{4,8}} => {{1,5},{2,8},{3,4,7},{6}} => [5,8,4,7,1,6,3,2] => ([(0,2),(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,5},{3},{4,8}} => {{1,5},{2,3,8},{4,7},{6}} => [5,3,8,7,1,6,4,2] => ([(0,2),(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5},{3},{4,7,8}} => {{1,2,5},{3,8},{4,7},{6}} => [2,5,8,7,1,6,4,3] => ([(0,3),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2,7},{3},{4,8}} => {{1,5},{2,7},{3,4,8},{6}} => [5,7,4,8,1,6,2,3] => ([(0,1),(0,2),(0,4),(0,5),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,7},{3},{4,6}} => {{1,4,8},{2,7},{3,5},{6}} => [4,7,5,8,3,6,2,1] => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5,8},{3,7},{4}} => {{1,4,7},{2,6},{3,8},{5}} => [4,6,8,7,5,2,1,3] => ([(0,4),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2,8},{3,7},{4}} => {{1,7},{2,6},{3,4,8},{5}} => [7,6,4,8,5,2,1,3] => ([(0,2),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3,6,7},{4}} => {{1,7},{2,3,6},{4,8},{5}} => [7,3,6,8,5,2,1,4] => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,7,8},{3,6},{4}} => {{1,2,7},{3,6},{4,8},{5}} => [2,7,6,8,5,3,1,4] => ([(0,7),(1,2),(1,3),(1,4),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5},{3,6,7},{4}} => {{1,8},{2,3,6},{4,7},{5}} => [8,3,6,7,5,2,4,1] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,5,7},{3},{4,6}} => {{1,8},{2,4,7},{3,5},{6}} => [8,4,5,7,3,6,2,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,8},{3,6},{4}} => {{1,7},{2,4,8},{3,6},{5}} => [7,4,6,8,5,3,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5},{2,7},{3,6,8},{4}} => {{1,3,6},{2,7},{4,8},{5}} => [3,7,6,8,5,1,2,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,7},{2,5},{3},{4,6,8}} => {{1,3,5},{2,8},{4,7},{6}} => [3,8,5,7,1,6,4,2] => ([(0,3),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,5},{3,7},{4}} => {{1,3,8},{2,6},{4,7},{5}} => [3,6,8,7,5,2,4,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6,8},{3,7},{4}} => {{1,3,7},{2,6},{4,8},{5}} => [3,6,7,8,5,2,1,4] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5,7},{3,8},{4}} => {{1,6},{2,4,7},{3,8},{5}} => [6,4,8,7,5,1,2,3] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
{{1,5,7},{2,8},{3},{4,6}} => {{1,7},{2,4,8},{3,5},{6}} => [7,4,5,8,3,6,1,2] => ([(0,1),(0,4),(0,5),(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3},{4,6,7}} => {{1,7},{2,3,5},{4,8},{6}} => [7,3,5,8,2,6,1,4] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,7,8},{3,5},{4}} => {{1,2,7},{3,8},{4,6},{5}} => [2,7,8,6,5,4,1,3] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3,5,6},{4}} => {{1,7},{2,8},{3,4,6},{5}} => [7,8,4,6,5,3,1,2] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,7},{2,5,6},{3,8},{4}} => {{1,6},{2,8},{3,4,7},{5}} => [6,8,4,7,5,1,3,2] => ([(0,1),(0,2),(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6,7},{3,8},{4}} => {{1,6},{2,3,7},{4,8},{5}} => [6,3,7,8,5,1,2,4] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,3,5},{4,6},{7}} => {{1,8},{2},{3,5},{4,6,7}} => [8,2,5,6,3,7,4,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,4,6},{3,5},{7}} => {{1,8},{2},{3,5,7},{4,6}} => [8,2,5,6,7,4,3,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3,4,5},{6}} => {{1,7},{2,8},{3},{4,5,6}} => [7,8,3,5,6,4,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2},{4,6},{7,8}} => {{1,2},{3,5},{4,6,8},{7}} => [2,1,5,6,3,8,7,4] => ([(0,1),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3,6,7},{2},{4,8},{5}} => {{1,5},{2,3,6,8},{4},{7}} => [5,3,6,4,1,8,7,2] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2},{3,6,7},{5}} => {{1,5,8},{2,3,6},{4},{7}} => [5,3,6,4,8,2,7,1] => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2},{3,4,8},{7}} => {{1,5,6},{2},{3,4,8},{7}} => [5,2,4,8,6,1,7,3] => ([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2},{3,5,7,8},{4}} => {{1,2,4,6},{3,8},{5},{7}} => [2,4,8,6,5,1,7,3] => ([(0,7),(1,5),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,8},{2,4,6},{3},{5,7}} => {{1,8},{2,4},{3,5,7},{6}} => [8,4,5,2,7,6,3,1] => ([(0,3),(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2},{3,5,7},{4}} => {{1,3,8},{2,4,6},{5},{7}} => [3,4,8,6,5,2,7,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2},{3,4,7},{6}} => {{1,4,8},{2,5,6},{3},{7}} => [4,5,3,8,6,2,7,1] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,7},{5},{6,8}} => {{1,3},{2,5,6},{4},{7,8}} => [3,5,1,4,6,2,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,5},{3},{4,7},{6,8}} => {{1,3},{2,5},{4,7,8},{6}} => [3,5,1,7,2,6,8,4] => ([(0,7),(1,2),(1,4),(2,6),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,6},{3},{4,7},{5,8}} => {{1,4},{2,5},{3,7,8},{6}} => [4,5,7,1,2,6,8,3] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
{{1,3,7},{2,6},{4},{5,8}} => {{1,4},{2,6,8},{3,7},{5}} => [4,6,7,1,5,8,3,2] => ([(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5},{3},{4,6,8},{7}} => {{1,3,5},{2},{4,7,8},{6}} => [3,2,5,7,1,6,8,4] => ([(0,7),(1,2),(1,6),(2,6),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,2,5},{3},{4,6},{7,8}} => {{1,2},{3,5},{4,7,8},{6}} => [2,1,5,7,3,6,8,4] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,3},{2,5,6},{4,8},{7}} => {{1,5},{2},{3,4,7},{6,8}} => [5,2,4,7,1,8,3,6] => ([(0,5),(0,6),(1,2),(1,7),(2,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,8},{4,5,6},{7}} => {{1,7},{2},{3,4,5},{6,8}} => [7,2,4,5,3,8,1,6] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2,8},{4,6},{7}} => {{1,7},{2},{3,5},{4,6,8}} => [7,2,5,6,3,8,1,4] => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2,6},{3,8},{4,5},{7}} => {{1,6},{2},{3,7,8},{4,5}} => [6,2,7,5,4,1,8,3] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,7},{3},{5,8},{6}} => {{1,4},{2,5,7,8},{3},{6}} => [4,5,3,1,7,6,8,2] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,7},{3},{5},{6,8}} => {{1,3},{2,5,7,8},{4},{6}} => [3,5,1,4,7,6,8,2] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3},{5,7},{6,8}} => {{1,3},{2,4},{5,7,8},{6}} => [3,4,1,2,7,6,8,5] => ([(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4},{5,6,8},{7}} => {{1,3,4},{2},{5,7},{6,8}} => [3,2,4,1,7,8,5,6] => ([(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5,8},{3,7},{6}} => {{1,4,7},{2,6},{3},{5,8}} => [4,6,3,7,8,2,1,5] => ([(0,2),(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4,7},{5,8},{6}} => {{1,4},{2,5,7},{3},{6,8}} => [4,5,3,1,7,8,2,6] => ([(0,1),(0,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4},{2,5,6},{3,8},{7}} => {{1,6},{2},{3,4,7},{5,8}} => [6,2,4,7,8,1,3,5] => ([(0,6),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1,4,6},{2,8},{3,5},{7}} => {{1,7},{2},{3,5,8},{4,6}} => [7,2,5,6,8,4,1,3] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,2,5,8},{3},{4,6},{7}} => {{1,4,7,8},{2},{3,5},{6}} => [4,2,5,7,3,6,8,1] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2},{3,5},{7,8}} => {{1,2},{3,5,8},{4,6},{7}} => [2,1,5,6,8,4,7,3] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5,8},{4,6},{7}} => {{1,4,6},{2},{3,5},{7,8}} => [4,2,5,6,3,1,8,7] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3,5},{4},{6,8}} => {{1,3},{2,7,8},{4,6},{5}} => [3,7,1,6,5,4,8,2] => ([(0,7),(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,4},{5},{6,8}} => {{1,3},{2,6,8},{4},{5,7}} => [3,6,1,4,7,8,5,2] => ([(0,1),(0,7),(1,6),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,4,7},{5},{6,8}} => {{1,3},{2,5,6,7},{4},{8}} => [3,5,1,4,6,7,2,8] => ([(1,7),(2,7),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5,7},{3},{6,8}} => {{1,3},{2,4,7},{5,8},{6}} => [3,4,1,7,8,6,2,5] => ([(0,1),(0,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3},{2,4,6},{5,8},{7}} => {{1,4},{2},{3,5,7},{6,8}} => [4,2,5,1,7,8,3,6] => ([(0,1),(0,2),(1,7),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1},{2,3,5},{4,7},{6,8}} => {{1,3},{2,5},{4,6,7},{8}} => [3,5,1,6,2,7,4,8] => ([(1,7),(2,3),(2,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,4},{2,5,8},{3,6},{7}} => {{1,4,7},{2},{3,6},{5,8}} => [4,2,6,7,8,3,1,5] => ([(0,5),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,7,9},{2,4,6,8,10}} => {{1,3,5,7,9},{2,4,6,8,10}} => [3,4,5,6,7,8,9,10,1,2] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
{{1,3,4,5,6},{2,7,8,9,10}} => {{1,2,3,4,9},{5,6,7,8,10}} => [2,3,4,9,6,7,8,10,1,5] => ([(0,9),(1,9),(2,9),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9)],10)
{{1,2,3,4,5},{6,7,8,9,10}} => {{1,2,3,4,5},{6,7,8,9,10}} => [2,3,4,5,1,7,8,9,10,6] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8)],10)
{{1,3,5,7,9,11},{2,4,6,8,10,12}} => {{1,3,5,7,9,11},{2,4,6,8,10,12}} => [3,4,5,6,7,8,9,10,11,12,1,2] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],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}} => [2,3,4,5,6,1,8,9,10,11,12,7] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,10),(6,10),(7,10),(8,10),(9,10)],12)
{{1,4,6,7},{2,3,5,8}} => {{1,4,6,7},{2,3,5,8}} => [4,3,5,6,8,7,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,4},{3,7,8},{5}} => {{1,2,6},{3,8},{4},{5,7}} => [2,6,8,4,7,1,5,3] => ([(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6},{2,4},{3,7},{5},{8}} => {{1},{2,6},{3,8},{4},{5,7}} => [1,6,8,4,7,2,5,3] => ([(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7},{2,3,4,8}} => {{1,5,6,7},{2,3,4,8}} => [5,3,4,8,6,7,1,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,8},{3,4},{5},{6}} => {{1,7},{2,8},{3},{4},{5,6}} => [7,8,3,4,6,5,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,6,7},{2,4,8},{3}} => {{1,5,7},{2,3,4,8},{6}} => [5,3,4,8,7,6,1,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,7},{2,4,6,8},{3}} => {{1,3,5,7},{2,4,8},{6}} => [3,4,5,8,7,6,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2,3},{4,6,7},{8}} => {{1},{2,3,5},{4,8},{6,7}} => [1,3,5,8,2,7,6,4] => ([(1,5),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5},{2,3},{4,6,8},{7}} => {{1,3,5},{2},{4,8},{6,7}} => [3,2,5,8,1,7,6,4] => ([(0,1),(0,5),(1,5),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5,6},{2,3,4,8},{7}} => {{1,5,6,7},{2},{3,4,8}} => [5,2,4,8,6,7,1,3] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,4},{3,8},{5},{7}} => {{1,6},{2},{3,8},{4},{5,7}} => [6,2,8,4,7,1,5,3] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1,5},{2,3},{4,6},{7},{8}} => {{1},{2},{3,5},{4,8},{6,7}} => [1,2,5,8,3,7,6,4] => ([(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3},{4,7,8},{6}} => {{1,2,5},{3},{4,8},{6,7}} => [2,5,3,8,1,7,6,4] => ([(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2,3},{4,8},{6},{7}} => {{1,5},{2},{3},{4,8},{6,7}} => [5,2,3,8,1,7,6,4] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5},{2,3},{4,7},{6},{8}} => {{1},{2,5},{3},{4,8},{6,7}} => [1,5,3,8,2,7,6,4] => ([(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,3,6},{2},{4,7},{5},{8}} => {{1},{2,5},{3,6,8},{4},{7}} => [1,5,6,4,2,8,7,3] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,7},{5,8},{6}} => {{1,4},{2,5},{3},{6,8},{7}} => [4,5,3,1,2,8,7,6] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2,4,7},{3},{5,8},{6}} => {{1,4},{2,5,7},{3},{6},{8}} => [4,5,3,1,7,6,2,8] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,4,7},{5},{8}} => {{1},{2,5,6,7},{3,8},{4}} => [1,5,8,4,6,7,2,3] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4,8},{2,6,7},{3},{5}} => {{1,5,8},{2,3,7},{4},{6}} => [5,3,7,4,8,6,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,4},{3,5,8},{6}} => {{1,4,6},{2,8},{3},{5,7}} => [4,8,3,6,7,1,5,2] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5,8},{2,3,7},{4},{6}} => {{1,4,8},{2,6,7},{3},{5}} => [4,6,3,8,5,7,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,8},{3,7},{4},{6}} => {{1,4,7},{2,6},{3},{5},{8}} => [4,6,3,7,5,2,1,8] => ([(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,4,7},{3,5},{8}} => {{1},{2,5,7},{3,8},{4,6}} => [1,5,8,6,7,4,2,3] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,6},{2,3,7},{4,5},{8}} => {{1},{2,6,7},{3,8},{4,5}} => [1,6,8,5,4,7,2,3] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,5,7},{3},{6},{8}} => {{1},{2,4,7},{3},{5,8},{6}} => [1,4,3,7,8,6,2,5] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5},{3},{6,8},{7}} => {{1,3},{2},{4,7},{5,8},{6}} => [3,2,1,7,8,6,4,5] => ([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5},{2,3,6,8},{4},{7}} => {{1,3,6,7},{2},{4,8},{5}} => [3,2,6,8,5,7,1,4] => ([(0,1),(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,5},{3,6,8},{4},{7}} => {{1,3,6},{2},{4,7},{5},{8}} => [3,2,6,7,5,1,4,8] => ([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6},{3,7},{4,8},{5}} => {{1,5},{2,6},{3,7},{4},{8}} => [5,6,7,4,1,2,3,8] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2,6},{3,7},{4},{5},{8}} => {{1},{2,6},{3,7},{4},{5},{8}} => [1,6,7,4,5,2,3,8] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,5,6},{3,4,7},{8}} => {{1},{2,5,6},{3,4,7},{8}} => [1,5,4,7,6,2,3,8] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6,7},{2,3,8},{4},{5}} => {{1,6,7},{2,3,8},{4},{5}} => [6,3,8,4,5,7,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4,6},{3,5,7},{8}} => {{1},{2,4,6},{3,5,7},{8}} => [1,4,5,6,7,2,3,8] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6,7},{8}} => [1,3,5,6,2,7,4,8] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,6},{2},{3,5,8},{7}} => {{1,4,6},{2},{3,5,8},{7}} => [4,2,5,6,8,1,7,3] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2},{3,8},{4},{5},{7}} => {{1,6},{2},{3,8},{4},{5},{7}} => [6,2,8,4,5,1,7,3] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1},{2},{3,5},{4,6},{7},{8}} => {{1},{2},{3,5},{4,6},{7},{8}} => [1,2,5,6,3,4,7,8] => ([(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2},{3},{4,8},{6},{7}} => {{1,5},{2},{3},{4,8},{6},{7}} => [5,2,3,8,1,6,7,4] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1},{2,5},{3},{4,7},{6},{8}} => {{1},{2,5},{3},{4,7},{6},{8}} => [1,5,3,7,2,6,4,8] => ([(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)
{{1,6,8},{2},{3,4},{5,7}} => {{1,3,8},{2,4},{5,6},{7}} => [3,4,8,2,6,5,7,1] => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2},{3,4},{5,8}} => {{1,4},{2,3,8},{5,6},{7}} => [4,3,8,1,6,5,7,2] => ([(0,6),(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2},{3,4,6},{5,7}} => {{1,8},{2,4},{3,5,6},{7}} => [8,4,5,2,6,3,7,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,8},{3,7},{5,6}} => {{1,5,7},{2,6},{3,4},{8}} => [5,6,4,3,7,2,1,8] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,7,8},{4},{5,6}} => {{1,2,7},{3,4},{5},{6,8}} => [2,7,4,3,5,8,1,6] => ([(0,7),(1,2),(1,7),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6,8},{4},{5,7}} => {{1,3,7},{2,4},{5},{6,8}} => [3,4,7,2,5,8,1,6] => ([(0,1),(0,7),(1,6),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,3},{4},{5,7}} => {{1,3,8},{2,4},{5},{6,7}} => [3,4,8,2,5,7,6,1] => ([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6,8},{4,7},{5}} => {{1,3,7},{2,5},{4},{6,8}} => [3,5,7,4,2,8,1,6] => ([(0,2),(0,7),(1,6),(1,7),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,8},{2},{4,7},{5}} => {{1,3,6,8},{2,5},{4},{7}} => [3,5,6,4,2,8,7,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,4,7},{3},{5}} => {{1,3,8},{2,5,7},{4},{6}} => [3,5,8,4,7,6,2,1] => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2},{5,7},{6,8}} => {{1,3},{2,4},{5,6,8},{7}} => [3,4,1,2,6,8,7,5] => ([(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4},{5,7,8},{6}} => {{1,2,4},{3},{5,7},{6,8}} => [2,4,3,1,7,8,5,6] => ([(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5,6},{3},{7,8}} => {{1,2},{3,4,7},{5,8},{6}} => [2,1,4,7,8,6,3,5] => ([(0,1),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5},{2},{3,6,7,8},{4}} => {{1,2,3,6},{4,8},{5},{7}} => [2,3,6,8,5,1,7,4] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,8},{2},{3,7},{6}} => {{1,4,5,8},{2,6},{3},{7}} => [4,6,3,5,8,2,7,1] => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4,6},{3,8},{7}} => {{1,6},{2},{3,5,7},{4,8}} => [6,2,5,8,7,1,3,4] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,7},{3,8},{5,6}} => {{1,6},{2,5,7},{3,4},{8}} => [6,5,4,3,7,1,2,8] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,3,8},{4},{5,7}} => {{1,6,7},{2,4},{3,8},{5}} => [6,4,8,2,5,7,1,3] => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1},{2,6},{3,4,8},{5,7}} => {{1,5,6},{2,4},{3,7},{8}} => [5,4,7,2,6,1,3,8] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1},{2,3},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6,7},{8}} => [3,4,1,5,2,7,6,8] => ([(1,2),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,5,6},{4,7},{8}} => {{1},{2,5},{3,4,6,7},{8}} => [1,5,4,6,2,7,3,8] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,5,7},{4,8},{6}} => {{1,5},{2,4,6,7},{3},{8}} => [5,4,3,6,1,7,2,8] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2},{3,4,6,7},{8}} => {{1},{2,3,5,6},{4,8},{7}} => [1,3,5,8,6,2,7,4] => ([(1,7),(2,5),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,7},{2},{3,6},{8}} => {{1},{2,4,5,8},{3,6},{7}} => [1,4,6,5,8,3,7,2] => ([(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,4},{3},{5,7}} => {{1,3,8},{2,4},{5,7},{6}} => [3,4,8,2,7,6,5,1] => ([(0,5),(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2},{3,4,5,7},{8}} => {{1},{2,4,5,6},{3,8},{7}} => [1,4,8,5,6,2,7,3] => ([(1,6),(1,7),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,6},{2,7},{3,4,5},{8}} => {{1},{2,7},{3,8},{4,5,6}} => [1,7,8,5,6,4,2,3] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4,8},{2,6},{3,5,7}} => {{1,5,8},{2,4,6},{3,7}} => [5,4,7,6,8,2,3,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,8},{2,5,7},{4,6}} => {{1,6,8},{2,4,7},{3,5}} => [6,4,5,7,3,8,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,7},{3,4,6},{8}} => {{1},{2,7},{3,5,6},{4,8}} => [1,7,5,8,6,3,2,4] => ([(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,5,6},{3},{8}} => {{1},{2,5,8},{3,4,7},{6}} => [1,5,4,7,8,6,3,2] => ([(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,3,6},{4},{8}} => {{1},{2,4,8},{3,6,7},{5}} => [1,4,6,8,5,7,3,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6},{4,5,8},{7}} => {{1,4,5},{2},{3,7},{6,8}} => [4,2,7,5,1,8,3,6] => ([(0,1),(0,5),(1,6),(2,4),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,6},{2,3,8},{5},{7}} => {{1,6,7},{2},{3,5,8},{4}} => [6,2,5,4,8,7,1,3] => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2,6},{3,8},{4},{5,7}} => {{1,6},{2,4},{3,7,8},{5}} => [6,4,7,2,5,1,8,3] => ([(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1},{2,6},{3,8},{4},{5,7}} => {{1,6},{2,4},{3,7},{5},{8}} => [6,4,7,2,5,1,3,8] => ([(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3},{4},{5,6}} => {{1,7},{2,8},{3,4},{5},{6}} => [7,8,4,3,5,6,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2},{3,8},{4},{5,7}} => {{1,6},{2,4},{3,8},{5},{7}} => [6,4,8,2,5,1,7,3] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1},{2},{3,5},{4,8},{6,7}} => {{1,5},{2,3},{4,6},{7},{8}} => [5,3,2,6,1,4,7,8] => ([(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5},{3},{4,8},{6,7}} => {{1,5},{2,3},{4,7,8},{6}} => [5,3,2,7,1,6,8,4] => ([(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,4,6},{3,8},{5,7}} => {{1,6},{2,4},{3,5,7,8}} => [6,4,5,2,7,1,8,3] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,7},{3,5,8},{6}} => {{1,4,6},{2,7},{3},{5,8}} => [4,7,3,6,8,1,2,5] => ([(0,1),(0,5),(0,6),(1,3),(1,7),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,5},{2,4,6},{3,7},{8}} => {{1},{2,6},{3,5,7},{4,8}} => [1,6,5,8,7,2,3,4] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,6},{2,3,5},{4,7},{8}} => {{1},{2,5},{3,8},{4,6,7}} => [1,5,8,6,2,7,4,3] => ([(1,3),(1,5),(1,6),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5},{3,8},{4,6,7}} => {{1,6},{2,3,5},{4,7},{8}} => [6,3,5,7,2,1,4,8] => ([(1,3),(1,5),(1,6),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,7},{3,4,8},{6}} => {{1,5,6},{2,4,7},{3},{8}} => [5,4,3,7,6,1,2,8] => ([(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,8},{2,4},{3,5,7},{6}} => {{1,8},{2,4,6},{3},{5,7}} => [8,4,3,6,7,2,5,1] => ([(0,3),(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,4},{3,5},{8}} => {{1},{2,3,8},{4,6},{5,7}} => [1,3,8,6,7,4,5,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5},{3,6},{4,7},{8}} => {{1},{2,5},{3,6},{4,7},{8}} => [1,5,6,7,2,3,4,8] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,3,5,8},{2},{4,7},{6}} => {{1,4,6,8},{2,5},{3},{7}} => [4,5,3,6,2,8,7,1] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2},{3,7,8},{4}} => {{1,2,6},{3,4,8},{5},{7}} => [2,6,4,8,5,1,7,3] => ([(0,7),(1,5),(1,6),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,7},{2},{3,5,8},{6}} => {{1,4,6},{2,5,8},{3},{7}} => [4,5,3,6,8,1,7,2] => ([(0,4),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,5,6,8},{3},{4,7}} => {{1,3,4,7},{2,5},{6},{8}} => [3,5,4,7,2,6,1,8] => ([(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,4,6,7},{5,8}} => {{1,4},{2,3,5,6},{7},{8}} => [4,3,5,1,6,2,7,8] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,6},{3,7,8},{4,5}} => {{1,2,6},{3,7},{4,5},{8}} => [2,6,7,5,4,1,3,8] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,6,7},{3,5},{4,8}} => {{1,5},{2,3,7},{4,6},{8}} => [5,3,7,6,1,4,2,8] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1},{2,4,6},{3,7,8},{5}} => {{1,2,6},{3,5,7},{4},{8}} => [2,6,5,4,7,1,3,8] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,4,5},{6,8},{7}} => {{1,3},{2},{4,5,7},{6,8}} => [3,2,1,5,7,8,4,6] => ([(0,7),(1,2),(1,3),(2,3),(4,5),(4,6),(5,7),(6,7)],8)
{{1,3},{2,4,5},{6,7},{8}} => {{1},{2,3},{4,5,7},{6,8}} => [1,3,2,5,7,8,4,6] => ([(1,2),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,4,5},{3,6},{8}} => {{1},{2,8},{3,6},{4,5,7}} => [1,8,6,5,7,3,4,2] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7},{2},{3},{4,8}} => {{1,5},{2,3,4,8},{6},{7}} => [5,3,4,8,1,6,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,5,7},{2,6},{3,4},{8}} => {{1},{2,4,8},{3,7},{5,6}} => [1,4,7,8,6,5,3,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,6,7},{5,8}} => {{1,4},{2,3,5},{6,8},{7}} => [4,3,5,1,2,8,7,6] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,7},{2,4,5,8}} => {{1,4,5,7},{2,3,6,8}} => [4,3,6,5,7,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,8},{3,5,6},{4,7}} => {{1,7},{2,5},{3,4,6},{8}} => [7,5,4,6,2,3,1,8] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3,8},{4,5,6}} => {{1,6},{2,8},{3,4,5},{7}} => [6,8,4,5,3,1,7,2] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5},{3,7,8},{6}} => {{1,2,6},{3},{4,5,7},{8}} => [2,6,3,5,7,1,4,8] => ([(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1},{2,6},{3,8},{4,5,7}} => {{1,6},{2,4,5},{3,7},{8}} => [6,4,7,5,2,1,3,8] => ([(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,6,7},{3,8},{5}} => {{1,6},{2,3,5,7},{4},{8}} => [6,3,5,4,7,1,2,8] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2},{4,7,8},{6}} => {{1,2,5},{3},{4,6,8},{7}} => [2,5,3,6,1,8,7,4] => ([(0,7),(1,2),(1,6),(2,6),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,3},{2,5},{4,7,8},{6}} => {{1,2,5},{3},{4,7},{6,8}} => [2,5,3,7,1,8,4,6] => ([(0,7),(1,2),(1,4),(2,6),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2,6},{3},{4,5,8}} => {{1,4,5},{2,8},{3,7},{6}} => [4,8,7,5,1,6,3,2] => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,7,8},{4,6},{5}} => {{1,2,7},{3,5},{4},{6,8}} => [2,7,5,4,3,8,1,6] => ([(0,7),(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,8},{3,7},{6}} => {{1,7},{2,6},{3},{4,5,8}} => [7,6,3,5,8,2,1,4] => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2,4},{5},{7,8}} => {{1,2},{3,6,8},{4},{5,7}} => [2,1,6,4,7,8,5,3] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2},{4,5,8},{7}} => {{1,4,5},{2},{3,6,8},{7}} => [4,2,6,5,1,8,7,3] => ([(0,1),(0,7),(1,7),(2,3),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2,5,7},{3},{6}} => {{1,5,8},{2,4,7},{3},{6}} => [5,4,3,7,8,6,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5,8},{3,6},{7}} => {{1,4,5,7},{2},{3,6},{8}} => [4,2,6,5,7,3,1,8] => ([(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,6},{5,8},{7}} => {{1,4},{2},{3,5},{6,8},{7}} => [4,2,5,1,3,8,7,6] => ([(0,1),(0,2),(1,2),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3},{2,5},{4},{6,8},{7}} => {{1,3},{2},{4,7},{5},{6,8}} => [3,2,1,7,5,8,4,6] => ([(0,1),(0,2),(1,2),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1},{2,6},{3,5},{4,8},{7}} => {{1,5},{2},{3,7},{4,6},{8}} => [5,2,7,6,1,4,3,8] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,5},{2,4},{3,7},{6},{8}} => {{1},{2,6},{3},{4,8},{5,7}} => [1,6,3,8,7,2,5,4] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,5},{2,4,6,7},{3},{8}} => {{1},{2,3,5,7},{4,8},{6}} => [1,3,5,8,7,6,2,4] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,8},{3,5},{4,7},{6}} => {{1,7},{2,5},{3},{4,6},{8}} => [7,5,3,6,2,4,1,8] => ([(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,7,8},{3,6},{4}} => {{1,2,4,7},{3,6},{5},{8}} => [2,4,6,7,5,3,1,8] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2,4,7},{3},{8}} => {{1},{2,5,7},{3,4,8},{6}} => [1,5,4,8,7,6,2,3] => ([(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,5,6,7},{4},{8}} => {{1},{2,3,4,7},{5},{6,8}} => [1,3,4,7,5,8,2,6] => ([(1,7),(2,7),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1},{2,4},{3,8},{5,7},{6}} => {{1,6},{2,4},{3},{5,7},{8}} => [6,4,3,2,7,1,5,8] => ([(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,7},{4,6},{5},{8}} => {{1},{2,7},{3,5},{4},{6,8}} => [1,7,5,4,3,8,2,6] => ([(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,3,5},{6},{8}} => {{1},{2,5,8},{3},{4,6,7}} => [1,5,3,6,8,7,4,2] => ([(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,3,6,7},{4},{8}} => {{1},{2,3,6,7},{4,8},{5}} => [1,3,6,8,5,7,2,4] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,6},{4,5,7},{8}} => {{1},{2,4,5},{3,6,7},{8}} => [1,4,6,5,2,7,3,8] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6},{2},{4,5,7},{8}} => {{1},{2,4,5},{3,6,8},{7}} => [1,4,6,5,2,8,7,3] => ([(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3,5},{6,7},{8}} => {{1},{2,3},{4,6,7},{5,8}} => [1,3,2,6,8,7,4,5] => ([(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,6},{4,5,8},{7}} => {{1,4,5},{2},{3,6,7},{8}} => [4,2,6,5,1,7,3,8] => ([(1,7),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,7},{4,6,8},{5}} => {{1,3,5},{2,6,7},{4},{8}} => [3,6,5,4,1,7,2,8] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2},{3,5},{6,7}} => {{1,5,8},{2,3},{4,6},{7}} => [5,3,2,6,8,4,7,1] => ([(0,6),(0,7),(1,4),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2},{3,5},{4,7}} => {{1,3,8},{2,5},{4,6},{7}} => [3,5,8,6,2,4,7,1] => ([(0,6),(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3,5,8},{6},{7}} => {{1,4,6,7},{2},{3},{5,8}} => [4,2,3,6,8,7,1,5] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(6,7)],8)
{{1,2},{3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7},{8,9}} => [1,2,3,4,5,6,7,9,8] => ([(7,8)],9)
{{1,3},{2},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,9},{8}} => [1,2,3,4,5,6,9,8,7] => ([(6,7),(6,8),(7,8)],9)
{{1,4},{2},{3},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,9},{7},{8}} => [1,2,3,4,5,9,7,8,6] => ([(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,5},{2},{3},{4},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,9},{6},{7},{8}} => [1,2,3,4,9,6,7,8,5] => ([(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,6},{2},{3},{4},{5},{7},{8},{9}} => {{1},{2},{3},{4,9},{5},{6},{7},{8}} => [1,2,3,9,5,6,7,8,4] => ([(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,7},{2},{3},{4},{5},{6},{8},{9}} => {{1},{2},{3,9},{4},{5},{6},{7},{8}} => [1,2,9,4,5,6,7,8,3] => ([(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,8},{2},{3},{4},{5},{6},{7},{9}} => {{1},{2,9},{3},{4},{5},{6},{7},{8}} => [1,9,3,4,5,6,7,8,2] => ([(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => [1,2,3,4,5,6,7,8,10,9] => ([(8,9)],10)
{{1,2,3},{4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6},{7,8,9}} => [1,2,3,4,5,6,8,9,7] => ([(6,8),(7,8)],9)
{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => [1,2,3,4,5,6,7,10,9,8] => ([(7,8),(7,9),(8,9)],10)
{{1,3,4},{2},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,7,9},{8}} => [1,2,3,4,5,7,9,8,6] => ([(5,8),(6,7),(6,8),(7,8)],9)
{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => [1,2,3,4,5,6,10,8,9,7] => ([(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => [1,2,3,4,5,10,7,8,9,6] => ([(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}} => {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => [1,2,3,4,10,6,7,8,9,5] => ([(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}} => {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => [1,2,3,10,5,6,7,8,9,4] => ([(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,7,8},{2},{3},{4},{5},{6},{9}} => {{1},{2,3,9},{4},{5},{6},{7},{8}} => [1,3,9,4,5,6,7,8,2] => ([(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}} => {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => [1,2,10,4,5,6,7,8,9,3] => ([(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,8,9},{2},{3},{4},{5},{6},{7}} => {{1,2,9},{3},{4},{5},{6},{7},{8}} => [2,9,3,4,5,6,7,8,1] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}} => {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => [1,10,3,4,5,6,7,8,9,2] => ([(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,5},{2,6},{3,4,7},{8}} => {{1},{2,5,6},{3,7},{4,8}} => [1,5,7,8,6,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
{{1,4,5},{2,3,6},{7},{8}} => {{1},{2},{3,6,7},{4,5,8}} => [1,2,6,5,8,7,3,4] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2,4},{3,6,7},{8}} => {{1},{2,3,6},{4,8},{5,7}} => [1,3,6,8,7,2,5,4] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)
{{1,5},{2,3,4,6},{7},{8}} => {{1},{2},{3,5,6,7},{4,8}} => [1,2,5,8,6,7,3,4] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,5,7},{3,6},{8}} => {{1},{2,4,7},{3,6},{5,8}} => [1,4,6,7,8,3,2,5] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7,8,9}} => [2,3,4,5,6,7,8,9,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
{{1,2,3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8,9,10}} => [2,3,4,5,6,7,8,9,10,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1,9},{2},{3},{4},{5},{6},{7,8}} => {{1,9},{2,3},{4},{5},{6},{7},{8}} => [9,3,2,4,5,6,7,8,1] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,5},{3,8},{4},{6,7}} => {{1,6},{2,3},{4,7,8},{5}} => [6,3,2,7,5,1,8,4] => ([(0,5),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4},{2,5,7,8},{3},{6}} => {{1,2,4,7},{3},{5,8},{6}} => [2,4,3,7,8,6,1,5] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5,6},{3},{4,7},{8}} => {{1},{2,5},{3,4,7,8},{6}} => [1,5,4,7,2,6,8,3] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1},{2,3},{4,6,7},{5,8}} => {{1,4},{2,3,5},{6,7},{8}} => [4,3,5,1,2,7,6,8] => ([(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,6},{3,7,8},{5}} => {{1,2,6},{3,7},{4},{5,8}} => [2,6,7,4,8,1,3,5] => ([(0,7),(1,2),(1,5),(1,6),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1},{2,3,5,6},{4,8},{7}} => {{1,5},{2},{3,4,6,7},{8}} => [5,2,4,6,1,7,3,8] => ([(1,7),(2,5),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,5},{4,7,8},{6}} => {{1,2,5},{3},{4,6,7},{8}} => [2,5,3,6,1,7,4,8] => ([(1,7),(2,5),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1},{2,4,8},{3,6,7},{5}} => {{1,5,7},{2,3,6},{4},{8}} => [5,3,6,4,7,2,1,8] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,6},{4,7,8},{5}} => {{1,2,5},{3,6,7},{4},{8}} => [2,5,6,4,1,7,3,8] => ([(1,7),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,7},{2,3,6,8}} => {{1,3,6,7},{2,4,5,8}} => [3,4,6,5,8,7,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,7},{2,6},{3,4,8}} => {{1,5,6},{2,4,8},{3,7}} => [5,4,7,8,6,1,3,2] => ([(0,1),(0,4),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,6},{2,5,7},{3,4,8}} => {{1,5,6},{2,4,7},{3,8}} => [5,4,8,7,6,1,2,3] => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,6},{2,5},{3,4,7},{8}} => {{1},{2,5,6},{3,8},{4,7}} => [1,5,8,7,6,2,4,3] => ([(1,2),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5,7},{3,6},{8}} => {{1},{2,4,5,7},{3,6},{8}} => [1,4,6,5,7,3,2,8] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,7},{3,6,8}} => {{1,3,6},{2,7},{4,5,8}} => [3,7,6,5,8,1,2,4] => ([(0,6),(0,7),(1,2),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,4,5,7},{3,8}} => {{1,6},{2,4,5,7},{3,8}} => [6,4,8,5,7,1,2,3] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,3,6},{2,7},{4,5},{8}} => {{1},{2,7},{3,6,8},{4,5}} => [1,7,6,5,4,8,2,3] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2},{4,7},{5},{6,8}} => {{1,3},{2,5},{4},{6,8},{7}} => [3,5,1,4,2,8,7,6] => ([(0,1),(0,2),(1,2),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3,5},{6,8},{7}} => {{1,3},{2},{4,6},{5,8},{7}} => [3,2,1,6,8,4,7,5] => ([(0,1),(0,2),(1,2),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,6},{4},{5,7}} => {{1,7},{2,4},{3,6},{5},{8}} => [7,4,6,2,5,3,1,8] => ([(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,5},{3},{4,6},{8}} => {{1},{2,8},{3,5},{4,7},{6}} => [1,8,5,7,3,6,4,2] => ([(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,5,7},{4},{8}} => {{1},{2,4,6,7},{3,8},{5}} => [1,4,8,6,5,7,2,3] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,8},{2},{3,6},{7}} => {{1,4,5,8},{2},{3,6},{7}} => [4,2,6,5,8,3,7,1] => ([(0,5),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2},{5,8},{7}} => {{1,4},{2},{3,5,6,8},{7}} => [4,2,5,1,6,8,7,3] => ([(0,7),(1,2),(1,7),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,5},{2},{3,7},{4,6},{8}} => {{1},{2,6},{3,5},{4,8},{7}} => [1,6,5,8,3,2,7,4] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,5},{2,4,7},{3,6},{8}} => {{1},{2,5,7},{3,6},{4,8}} => [1,5,6,8,7,3,2,4] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,4},{2,3,5,7},{6},{8}} => {{1},{2,4,6,7},{3},{5,8}} => [1,4,3,6,8,7,2,5] => ([(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1},{2,5,6,8},{3,7},{4}} => {{1,3,4,7},{2,6},{5},{8}} => [3,6,4,7,5,2,1,8] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,3,6},{4},{7}} => {{1,4,8},{2},{3,6,7},{5}} => [4,2,6,8,5,7,3,1] => ([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,3,7},{4},{5}} => {{1,3,8},{2,6,7},{4},{5}} => [3,6,8,4,5,7,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3},{4,7,8},{5}} => {{1,2,5},{3,8},{4},{6,7}} => [2,5,8,4,1,7,6,3] => ([(0,5),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2,4,7},{3,5,6},{8}} => {{1},{2,5,7},{3,4,6},{8}} => [1,5,4,6,7,3,2,8] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5},{3,8},{6,7}} => {{1,6},{2,3},{4,5,7},{8}} => [6,3,2,5,7,1,4,8] => ([(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,7},{2},{4,5},{6,8}} => {{1,3},{2,6,8},{4,5},{7}} => [3,6,1,5,4,8,7,2] => ([(0,1),(0,7),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,5,7,8},{4,6}} => {{1,2,4,6},{3,5},{7},{8}} => [2,4,5,6,3,1,7,8] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7,8},{2},{3},{4,6}} => {{1,2,4,8},{3,5},{6},{7}} => [2,4,5,8,3,6,7,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5,7,8},{3},{4,6}} => {{1,2,4,7},{3,5},{6},{8}} => [2,4,5,7,3,6,1,8] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,7},{2},{3,8},{4}} => {{1,6},{2,3,4,8},{5},{7}} => [6,3,4,8,5,1,7,2] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,7,8},{2},{3,5},{4,6}} => {{1,2,8},{3,5},{4,6},{7}} => [2,8,5,6,3,4,7,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5,6,7,8,9},{3}} => {{1,2,3,4,5,6,8},{7},{9}} => [2,3,4,5,6,8,7,1,9] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
{{1,3,4,5,6,7,8},{2},{9}} => {{1},{2,3,4,5,6,7,9},{8}} => [1,3,4,5,6,7,9,8,2] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
{{1},{2,4,5,6,7,8,9,10},{3}} => {{1,2,3,4,5,6,7,9},{8},{10}} => [2,3,4,5,6,7,9,8,1,10] => ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,3,5,6,7,8,9},{4}} => {{1,2,3,4,5,7,8},{6},{9}} => [2,3,4,5,7,6,8,1,9] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,4,5,6,7,8},{3},{9}} => {{1},{2,3,4,5,6,8,9},{7}} => [1,3,4,5,6,8,7,9,2] => ([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
{{1,3,4,5,6,7,8,9},{2},{10}} => {{1},{2,3,4,5,6,7,8,10},{9}} => [1,3,4,5,6,7,8,10,9,2] => ([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3,7},{2,5,6,8},{4}} => {{1,3,4,7},{2,6,8},{5}} => [3,6,4,7,5,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2},{3,5,6,7,8}} => {{1,2,3,4,6},{5,8},{7}} => [2,3,4,6,8,1,7,5] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7)],8)
{{1,2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9,10}} => [2,3,4,5,6,7,8,1,10,9] => ([(0,1),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1,2,3,4},{5,6,7,8,9,10}} => {{1,2,3,4,5,6},{7,8,9,10}} => [2,3,4,5,6,1,8,9,10,7] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8)],10)
{{1,4},{2,5},{3,7,8},{6}} => {{1,2,6},{3},{4,7},{5,8}} => [2,6,3,7,8,1,4,5] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
{{1,7},{2},{3,5},{4,6,8}} => {{1,3,5},{2,8},{4,6},{7}} => [3,8,5,6,1,4,7,2] => ([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3},{2,5,7,8},{4},{6}} => {{1,2,4,7},{3},{5},{6,8}} => [2,4,3,7,5,8,1,6] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3,5,8},{4,6}} => {{1,4,6},{2,8},{3,5},{7}} => [4,8,5,6,3,1,7,2] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,6},{2},{3,5,7},{4,8}} => {{1,5},{2,4,6},{3,8},{7}} => [5,4,8,6,1,2,7,3] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6},{2,3,5},{7},{8}} => {{1},{2},{3,5,8},{4,6,7}} => [1,2,5,6,8,7,4,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2,4,5},{7},{8}} => {{1},{2},{3,6,8},{4,5,7}} => [1,2,6,5,7,8,4,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,3,5,7,8},{4}} => {{1,2,4,6,7},{3,8},{5}} => [2,4,8,6,5,7,1,3] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,6},{2,3,7,8},{5}} => {{1,2,6,7},{3,5,8},{4}} => [2,6,5,4,8,7,1,3] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,8},{2,7},{3,6}} => {{1,4,5,8},{2,7},{3,6}} => [4,7,6,5,8,3,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,6,8},{3,5,7}} => {{1,3,5,7},{2,4,6},{8}} => [3,4,5,6,7,2,1,8] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,4,7},{3,6,8}} => {{1,3,6},{2,5,7},{4,8}} => [3,5,6,8,7,1,2,4] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,3,5,7},{2},{4,6,8}} => {{1,3,5},{2,4,6,8},{7}} => [3,4,5,6,1,8,7,2] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4,6,7},{3},{5,8}} => {{1,4},{2,3,5,7,8},{6}} => [4,3,5,1,7,6,8,2] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2,4,6,8},{7}} => {{1,3,5,7},{2},{4,6,8}} => [3,2,5,6,7,8,1,4] => ([(0,1),(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,4,6,7},{2},{5,8}} => {{1,4},{2,3,5,6,8},{7}} => [4,3,5,1,6,8,7,2] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5,6,8},{4,7}} => {{1,3,4,6,7},{2,5},{8}} => [3,5,4,6,2,7,1,8] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,3,5,7,8},{6}} => {{1,2,4,6,7},{3},{5,8}} => [2,4,3,6,8,7,1,5] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1},{2},{3},{4},{5},{6,7},{8,9}} => {{1,2},{3,4},{5},{6},{7},{8},{9}} => [2,1,4,3,5,6,7,8,9] => ([(5,8),(6,7)],9)
{{1},{2},{3},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7},{8},{9}} => [2,1,4,3,6,5,7,8,9] => ([(3,8),(4,7),(5,6)],9)
{{1},{2,3},{4,5},{6,7},{8,9}} => {{1,2},{3,4},{5,6},{7,8},{9}} => [2,1,4,3,6,5,8,7,9] => ([(1,8),(2,7),(3,6),(4,5)],9)
{{1},{2},{3},{4},{5},{6},{7,8},{9,10}} => {{1,2},{3,4},{5},{6},{7},{8},{9},{10}} => [2,1,4,3,5,6,7,8,9,10] => ([(6,9),(7,8)],10)
{{1},{2},{3},{4},{5,6},{7,8},{9,10}} => {{1,2},{3,4},{5,6},{7},{8},{9},{10}} => [2,1,4,3,6,5,7,8,9,10] => ([(4,9),(5,8),(6,7)],10)
{{1},{2,3,7},{4,5},{6,8}} => {{1,3},{2,6,7},{4,5},{8}} => [3,6,1,5,4,7,2,8] => ([(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2},{4,5,7},{6,8}} => {{1,3},{2,4,5},{6,8},{7}} => [3,4,1,5,2,8,7,6] => ([(0,7),(1,2),(1,3),(2,3),(4,5),(4,6),(5,7),(6,7)],8)
{{1,2},{3},{4,6,8},{5,7}} => {{1,3,5},{2,4},{6},{7,8}} => [3,4,5,2,1,6,8,7] => ([(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,5},{3},{6,7,8}} => {{1,2,3},{4,7},{5,8},{6}} => [2,3,1,7,8,6,4,5] => ([(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,7},{2,8},{3},{4,5,6}} => {{1,7},{2,8},{3,4,5},{6}} => [7,8,4,5,3,6,1,2] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2,5,6},{3},{7}} => {{1,5,8},{2},{3,4,7},{6}} => [5,2,4,7,8,6,3,1] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2},{5,7},{8}} => {{1},{2,4},{3,5,6,8},{7}} => [1,4,5,2,6,8,7,3] => ([(1,7),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,2,6},{3,7},{4,5},{8}} => {{1},{2,6},{3,7,8},{4,5}} => [1,6,7,5,4,2,8,3] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,4},{3,8},{5}} => {{1,6},{2,3,8},{4},{5,7}} => [6,3,8,4,7,1,5,2] => ([(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,4},{2},{3,5},{6,7,8}} => {{1,2,3},{4,6},{5,8},{7}} => [2,3,1,6,8,4,7,5] => ([(0,5),(1,5),(2,3),(2,7),(3,6),(4,6),(4,7),(6,7)],8)
{{1,6},{2,7},{3},{4,5,8}} => {{1,4,5},{2,7},{3,8},{6}} => [4,7,8,5,1,6,2,3] => ([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,7,8},{3},{4,5}} => {{1,2,7},{3,8},{4,5},{6}} => [2,7,8,5,4,6,1,3] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,6},{2},{3,5,8},{4,7}} => {{1,4,6},{2,5},{3,8},{7}} => [4,5,8,6,2,1,7,3] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1,9},{2,3,4,5,6,7,8}} => {{1,9},{2,3,4,5,6,7,8}} => [9,3,4,5,6,7,8,2,1] => ([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,3,8},{2,6,7},{4},{5}} => {{1,6,8},{2,3,7},{4},{5}} => [6,3,7,4,5,8,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3,6},{4},{5,8}} => {{1,4},{2,7,8},{3,6},{5}} => [4,7,6,1,5,3,8,2] => ([(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,8},{3},{4,6},{5,7}} => {{1,7,8},{2,4},{3,5},{6}} => [7,4,5,2,3,6,8,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,10},{2,3,4,5,6,7,8,9}} => {{1,10},{2,3,4,5,6,7,8,9}} => [10,3,4,5,6,7,8,9,2,1] => ([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}} => {{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}} => [2,1,3,4,5,6,7,8,9,10,11] => ([(9,10)],11)
{{1,3},{2,5,6},{4,7},{8}} => {{1},{2,5},{3,4,7},{6,8}} => [1,5,4,7,2,8,3,6] => ([(1,2),(1,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)
{{1,4},{2,6,7},{3,5},{8}} => {{1},{2,3,7},{4,6},{5,8}} => [1,3,7,6,8,4,2,5] => ([(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2,7,8},{3,6},{5}} => {{1,2,7},{3,6},{4},{5,8}} => [2,7,6,4,8,3,1,5] => ([(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5},{3,6,7},{8}} => {{1},{2,3,6},{4,5,7},{8}} => [1,3,6,5,7,2,4,8] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4,5},{3,6,8},{7}} => {{1,3,6},{2},{4,5,7},{8}} => [3,2,6,5,7,1,4,8] => ([(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6},{4,5,7},{8}} => {{1},{2,4,5},{3,7},{6,8}} => [1,4,7,5,2,8,3,6] => ([(1,2),(1,7),(2,6),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,9},{2,8},{3,7},{4,6},{5},{10}} => {{1},{2,10},{3,9},{4,8},{5,7},{6}} => [1,10,9,8,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,10},{3,9},{4,8},{5,7},{6}} => {{1,9},{2,8},{3,7},{4,6},{5},{10}} => [9,8,7,6,5,4,3,2,1,10] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,4,6},{2,3,5,7,8}} => {{1,2,4,6,7},{3,5,8}} => [2,4,5,6,8,7,1,3] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,6},{2,4,7},{3,8}} => {{1,6},{2,5,7},{3,4,8}} => [6,5,4,8,7,1,2,3] => ([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,2,7},{3,6},{4,5,8}} => {{1,4,5},{2,7,8},{3,6}} => [4,7,6,5,1,3,8,2] => ([(0,7),(1,2),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,6,7,8},{3,5}} => {{1,2,3,5,7},{4,6},{8}} => [2,3,5,6,7,4,1,8] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,3,5,8},{4,7},{6}} => {{1,4,6,7},{2,5},{3},{8}} => [4,5,3,6,2,7,1,8] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2,3,5,6,8}} => {{1,3,4,6,7},{2,5,8}} => [3,5,4,6,8,7,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3,4,5,6,7,9},{8}} => {{1,3,4,5,6,7,8,9},{2}} => [3,2,4,5,6,7,8,9,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,3,4,5,6,7,8,10},{9}} => {{1,3,4,5,6,7,8,9,10},{2}} => [3,2,4,5,6,7,8,9,10,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(7,9),(8,9)],10)
{{1,2,3,4,5,6,7,8,9,11},{10}} => {{1,3,4,5,6,7,8,9,10,11},{2}} => [3,2,4,5,6,7,8,9,10,11,1] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(8,10),(9,10)],11)
{{1,3,7,8},{2,4,5,6}} => {{1,2,6,8},{3,4,5,7}} => [2,6,4,5,7,8,3,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6,8},{2,4,5,7}} => {{1,3,6,8},{2,4,5,7}} => [3,4,6,5,7,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3},{4,7},{6}} => {{1,7},{2,5},{3},{4,8},{6}} => [7,5,3,8,2,6,1,4] => ([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,6},{3,4,5,8},{7}} => {{1,4,5,6},{2},{3,7,8}} => [4,2,7,5,6,1,8,3] => ([(0,7),(1,4),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2,3,5,6},{7}} => {{1,5,8},{2},{3,4,6,7}} => [5,2,4,6,8,7,3,1] => ([(0,6),(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4},{2,5,6,7,8}} => {{1,2,3,4,7},{5,6,8}} => [2,3,4,7,6,8,1,5] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5},{2,8},{4,6,7}} => {{1,7},{2,3,5},{4,6,8}} => [7,3,5,6,2,8,1,4] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4,7,8},{2,3,6},{5}} => {{1,2,5,8},{3,6,7},{4}} => [2,5,6,4,8,7,3,1] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,5},{3,6},{4,7,8}} => {{1,2,5},{3,6},{4,7,8}} => [2,5,6,7,1,3,8,4] => ([(0,7),(1,6),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6,7},{2},{3,8},{4},{5}} => {{1,6},{2,3,8},{4},{5},{7}} => [6,3,8,4,5,1,7,2] => ([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}} => {{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}} => [7,8,9,10,11,12,1,2,3,4,5,6] => ([(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)],12)
{{1,2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8,9}} => [2,3,4,5,6,7,1,9,8] => ([(0,1),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
{{1,2,3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7,8,9}} => [2,3,4,5,6,1,8,9,7] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7)],9)
{{1,2,3,4},{5,6,7,8,9}} => {{1,2,3,4,5},{6,7,8,9}} => [2,3,4,5,1,7,8,9,6] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7)],9)
{{1},{2},{3,4,5,6,7,8,9}} => {{1,2,3,4,5,6,7},{8},{9}} => [2,3,4,5,6,7,1,8,9] => ([(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
{{1,2,3},{4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7},{8,9,10}} => [2,3,4,5,6,7,1,9,10,8] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8)],10)
{{1},{2},{3},{4},{5,7},{6,8}} => {{1,3},{2,4},{5},{6},{7},{8}} => [3,4,1,2,5,6,7,8] => ([(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2},{3,5},{4,8},{6},{7}} => {{1,5},{2},{3},{4,6},{7},{8}} => [5,2,3,6,1,4,7,8] => ([(2,3),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,5},{3,8},{4},{6},{7}} => {{1,6},{2},{3},{4,7},{5},{8}} => [6,2,3,7,5,1,4,8] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4,6,7,8},{2,3,5}} => {{1,2,3,5,8},{4,6,7}} => [2,3,5,6,8,7,4,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,7,8},{2,3,6}} => {{1,2,4,5,8},{3,6,7}} => [2,4,6,5,8,7,3,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2,3,6,8},{4}} => {{1,3,6,7},{2,4,8},{5}} => [3,4,6,8,5,7,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,8},{2,4,6},{3,7}} => {{1,4,8},{2,6},{3,5,7}} => [4,6,5,8,7,2,3,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3},{2,4},{5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5},{6,8},{7,9}} => [1,2,3,4,5,8,9,6,7] => ([(5,7),(5,8),(6,7),(6,8)],9)
{{1},{2,3,5},{4,7},{6},{8}} => {{1},{2,5},{3},{4,6,7},{8}} => [1,5,3,6,2,7,4,8] => ([(2,7),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,4,5,7},{6,8}} => {{1,3},{2,4,5,6,7},{8}} => [3,4,1,5,6,7,2,8] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,6,8},{4,5},{7}} => {{1,3,7},{2},{4,5},{6,8}} => [3,2,7,5,4,8,1,6] => ([(0,1),(0,7),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,7},{2},{3},{5,8}} => {{1,4},{2,3,5,8},{6},{7}} => [4,3,5,1,8,6,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(6,7)],8)
{{1,4,7,8},{2},{3,5},{6}} => {{1,2,5,8},{3},{4,6},{7}} => [2,5,3,6,8,4,7,1] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,7,8},{3,6},{5}} => {{1,2,5,7},{3,6},{4},{8}} => [2,5,6,4,7,3,1,8] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3,7,8},{5,6}} => {{1,2,6},{3,4},{5,8},{7}} => [2,6,4,3,8,1,7,5] => ([(0,7),(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5,6,8},{2,3,7},{4}} => {{1,3,4,8},{2,6,7},{5}} => [3,6,4,8,5,7,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6},{2,3},{4,7,8}} => {{1,2,5},{3,4,8},{6,7}} => [2,5,4,8,1,7,6,3] => ([(0,6),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,6},{2},{3,7},{4},{5,8}} => {{1,4},{2,6},{3,8},{5},{7}} => [4,6,8,1,5,2,7,3] => ([(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,7},{2},{3,8},{4},{5},{6}} => {{1,6},{2,8},{3},{4},{5},{7}} => [6,8,3,4,5,1,7,2] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,3,4,5,6,9},{7},{8}} => {{1,4,5,6,7,8,9},{2},{3}} => [4,2,3,5,6,7,8,9,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,6,7,8,9},{2,3,4,5}} => {{1,2,3,4,9},{5,6,7,8}} => [2,3,4,9,6,7,8,5,1] => ([(0,8),(1,8),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,9},{3},{4},{5},{6},{7},{8}} => {{1,8,9},{2},{3},{4},{5},{6},{7}} => [8,2,3,4,5,6,7,9,1] => ([(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,8},{2},{3,9},{4},{5},{6},{7}} => {{1,7},{2,9},{3},{4},{5},{6},{8}} => [7,9,3,4,5,6,1,8,2] => ([(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,8),(6,7),(7,8)],9)
{{1,2,3,4,5,6,7,10},{8},{9}} => {{1,4,5,6,7,8,9,10},{2},{3}} => [4,2,3,5,6,7,8,9,10,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,2,3,4,5,10},{6},{7},{8},{9}} => {{1,6,7,8,9,10},{2},{3},{4},{5}} => [6,2,3,4,5,7,8,9,10,1] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,2,10},{3},{4},{5},{6},{7},{8},{9}} => {{1,9,10},{2},{3},{4},{5},{6},{7},{8}} => [9,2,3,4,5,6,7,8,10,1] => ([(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,4,6,8},{2,3,5,7}} => {{1,3,5,8},{2,4,6,7}} => [3,4,5,6,8,7,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,6},{4,5,8}} => {{1,4,5},{2,6,8},{3,7}} => [4,6,7,5,1,8,3,2] => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,6},{5,7,8}} => {{1,2,4},{3,5,6},{7,8}} => [2,4,5,1,6,3,8,7] => ([(0,1),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7,8},{2,4},{3,5,6}} => {{1,2,8},{3,4,6},{5,7}} => [2,8,4,6,7,3,5,1] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => {{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [11,2,3,4,5,6,7,8,9,10,1] => ([(0,9),(0,10),(1,9),(1,10),(2,9),(2,10),(3,9),(3,10),(4,9),(4,10),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,10)],11)
{{1,3},{2,5,8},{4},{6,7}} => {{1,4,7},{2,3},{5},{6,8}} => [4,3,2,7,5,8,1,6] => ([(0,6),(0,7),(1,2),(1,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
{{1},{2},{3},{4},{5},{6,7,8,9}} => {{1,2,3,4},{5},{6},{7},{8},{9}} => [2,3,4,1,5,6,7,8,9] => ([(5,8),(6,8),(7,8)],9)
{{1},{2},{3},{4},{5,6,7,8,9}} => {{1,2,3,4,5},{6},{7},{8},{9}} => [2,3,4,5,1,6,7,8,9] => ([(4,8),(5,8),(6,8),(7,8)],9)
{{1},{2},{3},{4,5,6,7,8,9}} => {{1,2,3,4,5,6},{7},{8},{9}} => [2,3,4,5,6,1,7,8,9] => ([(3,8),(4,8),(5,8),(6,8),(7,8)],9)
{{1},{2},{3},{4},{5},{6},{7},{8,9,10}} => {{1,2,3},{4},{5},{6},{7},{8},{9},{10}} => [2,3,1,4,5,6,7,8,9,10] => ([(7,9),(8,9)],10)
{{1},{2},{3},{4},{5},{6},{7,8,9,10}} => {{1,2,3,4},{5},{6},{7},{8},{9},{10}} => [2,3,4,1,5,6,7,8,9,10] => ([(6,9),(7,9),(8,9)],10)
{{1},{2},{3},{4},{5},{6,7,8,9,10}} => {{1,2,3,4,5},{6},{7},{8},{9},{10}} => [2,3,4,5,1,6,7,8,9,10] => ([(5,9),(6,9),(7,9),(8,9)],10)
{{1},{2},{3},{4},{5,6,7,8,9,10}} => {{1,2,3,4,5,6},{7},{8},{9},{10}} => [2,3,4,5,6,1,7,8,9,10] => ([(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1},{2,4},{3,5,6,7,8}} => {{1,2,3,4,6},{5,7},{8}} => [2,3,4,6,7,1,5,8] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2},{3},{4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7},{8},{9},{10}} => [2,3,4,5,6,7,1,8,9,10] => ([(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1},{2},{3,4,5,6,7,8,9,10}} => {{1,2,3,4,5,6,7,8},{9},{10}} => [2,3,4,5,6,7,8,1,9,10] => ([(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1},{2},{3,7},{4,8},{5},{6}} => {{1,5},{2,6},{3},{4},{7},{8}} => [5,6,3,4,1,2,7,8] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,7},{2},{3},{4},{5},{6,8}} => {{1,3},{2,8},{4},{5},{6},{7}} => [3,8,1,4,5,6,7,2] => ([(0,1),(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6},{3},{4,8},{7}} => {{1,5},{2},{3,7},{4,8},{6}} => [5,2,7,8,1,6,3,4] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
{{1,5},{2},{3},{4,6},{7},{8}} => {{1},{2},{3,5},{4,8},{6},{7}} => [1,2,5,8,3,6,7,4] => ([(2,3),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2},{3},{4,7},{5},{8}} => {{1},{2,5},{3,8},{4},{6},{7}} => [1,5,8,4,2,6,7,3] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,5,7},{2},{3},{4,6},{8}} => {{1},{2,4,8},{3,5},{6},{7}} => [1,4,5,8,3,6,7,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7},{2},{3,6},{5},{8}} => {{1},{2,5,8},{3,6},{4},{7}} => [1,5,6,4,8,3,7,2] => ([(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2},{3,7},{4,8},{6}} => {{1,5},{2,6},{3},{4,8},{7}} => [5,6,3,8,1,2,7,4] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
{{1,5},{2},{3,7},{4},{6},{8}} => {{1},{2,6},{3},{4,8},{5},{7}} => [1,6,3,8,5,2,7,4] => ([(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1},{2,6},{3},{4,8},{5},{7}} => {{1,5},{2},{3,7},{4},{6},{8}} => [5,2,7,4,1,6,3,8] => ([(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,2,3,7},{4},{5},{6,8}} => {{1,3},{2,6,7,8},{4},{5}} => [3,6,1,4,5,7,8,2] => ([(0,7),(1,7),(2,3),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,5},{4,6,7},{8}} => {{1},{2,3,5},{4,7},{6,8}} => [1,3,5,7,2,8,4,6] => ([(1,7),(2,3),(2,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5,7,8},{2,3},{4,6}} => {{1,2,4,8},{3,5},{6,7}} => [2,4,5,8,3,7,6,1] => ([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,6,8},{2,4},{3,7}} => {{1,3,4,8},{2,6},{5,7}} => [3,6,4,8,7,2,5,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2},{3,4,6,8},{7}} => {{1,3,5,6},{2},{4,8},{7}} => [3,2,5,8,6,1,7,4] => ([(0,1),(0,7),(1,7),(2,5),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6},{2},{3},{4,5,7,8}} => {{1,2,4,5},{3,8},{6},{7}} => [2,4,8,5,1,6,7,3] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,4,7},{2},{5,8},{6}} => {{1,4},{2,5,6,8},{3},{7}} => [4,5,3,1,6,8,7,2] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,8},{2,3,4,5,7}} => {{1,3,8},{2,4,5,6,7}} => [3,4,8,5,6,7,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2,3,5},{4,6,8}} => {{1,3,5},{2,8},{4,6,7}} => [3,8,5,6,1,7,4,2] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3,5},{6},{7},{8}} => {{1},{2},{3},{4,6},{5,8},{7}} => [1,2,3,6,8,4,7,5] => ([(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,4},{2},{3,5},{6},{7},{8},{9}} => {{1},{2},{3},{4},{5,7},{6,9},{8}} => [1,2,3,4,7,9,5,8,6] => ([(4,7),(4,8),(5,6),(5,8),(6,7),(7,8)],9)
{{1,5,9},{2},{3},{4},{6},{7},{8}} => {{1,5,9},{2},{3},{4},{6},{7},{8}} => [5,2,3,4,9,6,7,8,1] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,6),(3,8),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)
{{1,3},{2,4,5,6,7},{8}} => {{1},{2,3,4,5,7},{6,8}} => [1,3,4,5,7,8,2,6] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7,8}} => [1,3,4,6,7,2,8,5] => ([(1,7),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,4,5,6,7,8},{9}} => {{1},{2,3,4,5,6,8},{7,9}} => [1,3,4,5,6,8,9,2,7] => ([(1,8),(2,8),(3,8),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
{{1,3,4,5,7},{2},{6,8}} => {{1,3},{2,4,5,6,8},{7}} => [3,4,1,5,6,8,7,2] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,4,5,7,8},{2},{3,6}} => {{1,2,4,5,8},{3,6},{7}} => [2,4,6,5,8,3,7,1] => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,8},{2,9},{3},{4},{5},{6},{7}} => {{1,8},{2,9},{3},{4},{5},{6},{7}} => [8,9,3,4,5,6,7,1,2] => ([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
{{1,3,4,7},{2,8},{5,6}} => {{1,7},{2,5,6,8},{3,4}} => [7,5,4,3,6,8,1,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,5,8},{3,7},{4,6}} => {{1,4,7,8},{2,6},{3,5}} => [4,6,5,7,3,2,8,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6},{2,8},{3,7}} => {{1,7},{2,6},{3,4,5,8}} => [7,6,4,5,8,2,1,3] => ([(0,3),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,3,4,5,6,9},{7,8}} => {{1,4,5,6,7,8,9},{2,3}} => [4,3,2,5,6,7,8,9,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,3,4,5,6,7,10},{8,9}} => {{1,4,5,6,7,8,9,10},{2,3}} => [4,3,2,5,6,7,8,9,10,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2},{3},{4,6,8},{5,7}} => {{1,3,5},{2,4},{6},{7},{8}} => [3,4,5,2,1,6,7,8] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5},{4,6,7},{8}} => {{1},{2,3,5},{4,6},{7,8}} => [1,3,5,6,2,4,8,7] => ([(1,2),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,7},{2},{3},{4,6,8}} => {{1,3,5},{2,4,8},{6},{7}} => [3,4,5,8,1,6,7,2] => ([(0,5),(0,7),(1,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1,2,7},{3},{4,5,6,8}} => {{1,3,4,5},{2,7,8},{6}} => [3,7,4,5,1,6,8,2] => ([(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,5},{2,4,6,7,8}} => {{1,2,3,5,7},{4,6,8}} => [2,3,5,6,7,8,1,4] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5,6},{2,4,8},{3,7}} => {{1,5,7},{2,6},{3,4,8}} => [5,6,4,8,7,2,1,3] => ([(0,1),(0,4),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,2,7},{3,8},{4},{5,6}} => {{1,6},{2,7,8},{3,4},{5}} => [6,7,4,3,5,1,8,2] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,6,8},{2,3,5,7},{4}} => {{1,3,8},{2,4,6,7},{5}} => [3,4,8,6,5,7,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,5,6,7},{2,3,8}} => {{1,6,7},{2,3,4,5,8}} => [6,3,4,5,8,7,1,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,6,7},{3},{4,8},{5}} => {{1,5},{2,3,7,8},{4},{6}} => [5,3,7,4,1,6,8,2] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,3,8},{2,4,5,6,7}} => {{1,6,8},{2,3,4,5,7}} => [6,3,4,5,7,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2,8},{5,7}} => {{1,7},{2,4},{3,5,6,8}} => [7,4,5,2,6,8,1,3] => ([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1},{2,7},{3},{4,5,6,8}} => {{1,3,4,5},{2,7},{6},{8}} => [3,7,4,5,1,6,2,8] => ([(1,6),(1,7),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,2,4},{3,6},{5,7,8}} => {{1,2,4},{3,6},{5,7,8}} => [2,4,6,1,7,3,8,5] => ([(0,7),(1,6),(2,5),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7)],8)
{{1,2,5,6,8},{3},{4,7}} => {{1,3,4,7,8},{2,5},{6}} => [3,5,4,7,2,6,8,1] => ([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,6},{2,5,7,8},{4}} => {{1,2,4,7},{3,6,8},{5}} => [2,4,6,7,5,8,1,3] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2},{3,6},{5,7},{8}} => {{1},{2,4},{3,6},{5,8},{7}} => [1,4,6,2,8,3,7,5] => ([(1,4),(1,5),(2,3),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
{{1,2},{3,4,7},{5,6,8}} => {{1,3,4},{2,5,6},{7,8}} => [3,5,4,1,6,2,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,7},{2,4},{5,6,8}} => {{1,3,4},{2,6,8},{5,7}} => [3,6,4,1,7,8,5,2] => ([(0,5),(0,7),(1,5),(1,7),(2,3),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,6,8},{4,5}} => {{1,3,7},{2,6,8},{4,5}} => [3,6,7,5,4,8,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,7},{2,3,8},{6}} => {{1,6,7},{2,4,5,8},{3}} => [6,4,3,5,8,7,1,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,6,7},{3},{4},{5,8}} => {{1,4},{2,3,7,8},{5},{6}} => [4,3,7,1,5,6,8,2] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,3,5},{2,4,6,7},{8}} => {{1},{2,3,5,7},{4,6,8}} => [1,3,5,6,7,8,2,4] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4,8},{3,6},{5},{7}} => {{1,5,7},{2},{3,6},{4},{8}} => [5,2,6,4,7,3,1,8] => ([(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5,6},{2,8},{4,7}} => {{1,7},{2,5},{3,4,6,8}} => [7,5,4,6,2,8,1,3] => ([(0,5),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
{{1},{2,7},{3,5,8},{4},{6}} => {{1,4,6},{2,7},{3},{5},{8}} => [4,7,3,6,5,1,2,8] => ([(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,6},{2,4,7},{3},{5},{8}} => {{1},{2,5,7},{3,8},{4},{6}} => [1,5,8,4,7,6,2,3] => ([(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,5,6,8},{3},{7}} => {{1,3,4,7},{2},{5,8},{6}} => [3,2,4,7,8,6,1,5] => ([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5,6},{4,7,8}} => {{1,2,5},{3,4,6},{7,8}} => [2,5,4,6,1,3,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,3},{4},{5,7},{6,8}} => {{1,3},{2,4},{5},{6,7,8}} => [3,4,1,2,5,7,8,6] => ([(1,7),(2,7),(3,5),(3,6),(4,5),(4,6)],8)
{{1,7},{2},{3,4,5,8},{6}} => {{1,4,5,6},{2,8},{3},{7}} => [4,8,3,5,6,1,7,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,3,6},{2,5},{4,7,8}} => {{1,2,5},{3,6,8},{4,7}} => [2,5,6,7,1,8,4,3] => ([(0,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,6},{2,4,7,8},{3,5}} => {{1,2,5,7},{3,8},{4,6}} => [2,5,8,6,7,4,1,3] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,6,7},{2,8},{3,5}} => {{1,7},{2,3,5,8},{4,6}} => [7,3,5,6,8,4,1,2] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,7},{2,5,6},{3,8}} => {{1,6},{2,5,8},{3,4,7}} => [6,5,4,7,8,1,3,2] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
{{1,3,7},{2,5,6},{4,8}} => {{1,5},{2,6,8},{3,4,7}} => [5,6,4,7,1,8,3,2] => ([(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,4,8},{3,5}} => {{1,5,7},{2,3,8},{4,6}} => [5,3,8,6,7,4,1,2] => ([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,3,5},{6},{7,8}} => {{1,2},{3},{4,6,7},{5,8}} => [2,1,3,6,8,7,4,5] => ([(1,2),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2,5},{3,6,7},{8}} => {{1},{2,3,6},{4,7},{5,8}} => [1,3,6,7,8,2,4,5] => ([(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
{{1},{2,4,5,6},{3,7},{8}} => {{1},{2,6},{3,4,5,7},{8}} => [1,6,4,5,7,2,3,8] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4},{3,5,6,7},{8}} => {{1},{2,3,4,6},{5,7},{8}} => [1,3,4,6,7,2,5,8] => ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,4,5},{2},{3,6,8},{7}} => {{1,3,6},{2},{4,5,8},{7}} => [3,2,6,5,8,1,7,4] => ([(0,1),(0,7),(1,7),(2,3),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,4},{3,5},{6},{7,8}} => {{1,2},{3},{4,6},{5,7,8}} => [2,1,3,6,7,4,8,5] => ([(1,2),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2,6},{3},{4,5,7,8}} => {{1,2,4,5},{3,7,8},{6}} => [2,4,7,5,1,6,8,3] => ([(0,7),(1,5),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,5,8},{2},{3,6,7}} => {{1,4,5,8},{2,3,6},{7}} => [4,3,6,5,8,2,7,1] => ([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,4,6,8},{5,7}} => {{1,3,5,6},{2,4},{7,8}} => [3,4,5,2,6,1,8,7] => ([(0,1),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2,6,7},{3},{4},{8}} => {{1},{2,3,7},{4,8},{5},{6}} => [1,3,7,8,5,6,2,4] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1},{2,3},{4,6},{5,7},{8}} => {{1},{2,4},{3,5},{6,7},{8}} => [1,4,5,2,3,7,6,8] => ([(2,3),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,6,7},{4,5},{8}} => {{1},{2,3,7},{4,5},{6,8}} => [1,3,7,5,4,8,2,6] => ([(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,4,5},{6},{8}} => {{1},{2,6,8},{3},{4,5,7}} => [1,6,3,5,7,8,4,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,6,7},{2,3,5},{8}} => {{1},{2,3,5,8},{4,6,7}} => [1,3,5,6,8,7,4,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2},{3,6},{4},{7},{8}} => {{1},{2},{3,6},{4,8},{5},{7}} => [1,2,6,8,5,3,7,4] => ([(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,4,5},{2,3,6,7,8}} => {{1,2,3,6,7},{4,5,8}} => [2,3,6,5,8,7,1,4] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2,3,6},{7,8}} => {{1,2},{3,6,7},{4,5,8}} => [2,1,6,5,8,7,3,4] => ([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5},{2,3,8},{6,7}} => {{1,6,7},{2,3},{4,5,8}} => [6,3,2,5,8,7,1,4] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,4,7},{2,3,8},{5,6}} => {{1,6,7},{2,5,8},{3,4}} => [6,5,4,3,8,7,1,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6,8},{2,7},{4,5}} => {{1,3,6,8},{2,7},{4,5}} => [3,7,6,5,4,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2,3},{4,5,8}} => {{1,4,5},{2,3,8},{6,7}} => [4,3,8,5,1,7,6,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,6,7},{2,5,8},{3,4}} => {{1,4,7},{2,3,8},{5,6}} => [4,3,8,7,6,5,1,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4,6,8,10},{3},{5},{7},{9}} => {{1,3,5,7,9},{2},{4},{6},{8},{10}} => [3,2,5,4,7,6,9,8,1,10] => ([(1,8),(1,9),(2,7),(2,9),(3,6),(3,9),(4,5),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1},{2,4,6,10},{3},{5},{7,9},{8}} => {{1,5,7,9},{2,4},{3},{6},{8},{10}} => [5,4,3,2,7,6,9,8,1,10] => ([(1,4),(1,9),(2,3),(2,9),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,4,8,10},{3},{5,7},{6},{9}} => {{1,3,7,9},{2},{4,6},{5},{8},{10}} => [3,2,7,6,5,4,9,8,1,10] => ([(1,4),(1,9),(2,3),(2,9),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,4,10},{3},{5,7,9},{6},{8}} => {{1,7,9},{2,4,6},{3},{5},{8},{10}} => [7,4,3,6,5,2,9,8,1,10] => ([(1,2),(1,9),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,4,10},{3},{5,9},{6,8},{7}} => {{1,7,9},{2,6},{3,5},{4},{8},{10}} => [7,6,5,4,3,2,9,8,1,10] => ([(1,2),(1,9),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,6,8,10},{3,5},{4},{7},{9}} => {{1,3,5,9},{2},{4},{6,8},{7},{10}} => [3,2,5,4,9,8,7,6,1,10] => ([(1,4),(1,9),(2,3),(2,9),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,6,10},{3,5},{4},{7,9},{8}} => {{1,5,9},{2,4},{3},{6,8},{7},{10}} => [5,4,3,2,9,8,7,6,1,10] => ([(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,9),(3,4),(3,5),(3,9),(4,5),(4,9),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,8,10},{3,5,7},{4},{6},{9}} => {{1,3,9},{2},{4,6,8},{5},{7},{10}} => [3,2,9,6,5,8,7,4,1,10] => ([(1,2),(1,9),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,8,10},{3,7},{4,6},{5},{9}} => {{1,3,9},{2},{4,8},{5,7},{6},{10}} => [3,2,9,8,7,6,5,4,1,10] => ([(1,2),(1,9),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,10},{3,5,7,9},{4},{6},{8}} => {{1,9},{2,4,6,8},{3},{5},{7},{10}} => [9,4,3,6,5,8,7,2,1,10] => ([(1,6),(1,7),(1,8),(1,9),(2,5),(2,7),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,10},{3,5,9},{4},{6,8},{7}} => {{1,9},{2,6,8},{3,5},{4},{7},{10}} => [9,6,5,4,3,8,7,2,1,10] => ([(1,2),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,10},{3,7,9},{4,6},{5},{8}} => {{1,9},{2,4,8},{3},{5,7},{6},{10}} => [9,4,3,8,7,6,5,2,1,10] => ([(1,2),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,10},{3,9},{4,6,8},{5},{7}} => {{1,9},{2,8},{3,5,7},{4},{6},{10}} => [9,8,5,4,7,6,3,2,1,10] => ([(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3},{2},{4,6,8,10},{5},{7},{9}} => {{1,3,5,7},{2},{4},{6},{8,10},{9}} => [3,2,5,4,7,6,1,10,9,8] => ([(0,1),(0,2),(1,2),(3,8),(3,9),(4,7),(4,9),(5,6),(5,9),(6,9),(7,9),(8,9)],10)
{{1,3},{2},{4,6,10},{5},{7,9},{8}} => {{1,5,7},{2,4},{3},{6},{8,10},{9}} => [5,4,3,2,7,6,1,10,9,8] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3},{2},{4,8,10},{5,7},{6},{9}} => {{1,3,7},{2},{4,6},{5},{8,10},{9}} => [3,2,7,6,5,4,1,10,9,8] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3},{2},{4,10},{5,7,9},{6},{8}} => {{1,7},{2,4,6},{3},{5},{8,10},{9}} => [7,4,3,6,5,2,1,10,9,8] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3},{2},{4,10},{5,9},{6,8},{7}} => {{1,7},{2,6},{3,5},{4},{8,10},{9}} => [7,6,5,4,3,2,1,10,9,8] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3,5},{2},{4},{6,8,10},{7},{9}} => {{1,3,5},{2},{4},{6,8,10},{7},{9}} => [3,2,5,4,1,8,7,10,9,6] => ([(0,3),(0,9),(1,2),(1,9),(2,9),(3,9),(4,7),(4,8),(5,6),(5,8),(6,8),(7,8)],10)
{{1,3,5},{2},{4},{6,10},{7,9},{8}} => {{1,5},{2,4},{3},{6,8,10},{7},{9}} => [5,4,3,2,1,8,7,10,9,6] => ([(0,3),(0,9),(1,2),(1,9),(2,9),(3,9),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],10)
{{1,5},{2,4},{3},{6,8,10},{7},{9}} => {{1,3,5},{2},{4},{6,10},{7,9},{8}} => [3,2,5,4,1,10,9,8,7,6] => ([(0,3),(0,9),(1,2),(1,9),(2,9),(3,9),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],10)
{{1,5},{2,4},{3},{6,10},{7,9},{8}} => {{1,5},{2,4},{3},{6,10},{7,9},{8}} => [5,4,3,2,1,10,9,8,7,6] => ([(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3,5,7},{2},{4},{6},{8,10},{9}} => {{1,3},{2},{4,6,8,10},{5},{7},{9}} => [3,2,1,6,5,8,7,10,9,4] => ([(0,1),(0,2),(1,2),(3,8),(3,9),(4,7),(4,9),(5,6),(5,9),(6,9),(7,9),(8,9)],10)
{{1,3,7},{2},{4,6},{5},{8,10},{9}} => {{1,3},{2},{4,8,10},{5,7},{6},{9}} => [3,2,1,8,7,6,5,10,9,4] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,5,7},{2,4},{3},{6},{8,10},{9}} => {{1,3},{2},{4,6,10},{5},{7,9},{8}} => [3,2,1,6,5,10,9,8,7,4] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,7},{2,4,6},{3},{5},{8,10},{9}} => {{1,3},{2},{4,10},{5,7,9},{6},{8}} => [3,2,1,10,7,6,9,8,5,4] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,7},{2,6},{3,5},{4},{8,10},{9}} => {{1,3},{2},{4,10},{5,9},{6,8},{7}} => [3,2,1,10,9,8,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3,5,7,9},{2},{4},{6},{8},{10}} => {{1},{2,4,6,8,10},{3},{5},{7},{9}} => [1,4,3,6,5,8,7,10,9,2] => ([(1,8),(1,9),(2,7),(2,9),(3,6),(3,9),(4,5),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
{{1,3,5,9},{2},{4},{6,8},{7},{10}} => {{1},{2,6,8,10},{3,5},{4},{7},{9}} => [1,6,5,4,3,8,7,10,9,2] => ([(1,4),(1,9),(2,3),(2,9),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3,7,9},{2},{4,6},{5},{8},{10}} => {{1},{2,4,8,10},{3},{5,7},{6},{9}} => [1,4,3,8,7,6,5,10,9,2] => ([(1,4),(1,9),(2,3),(2,9),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3,9},{2},{4,6,8},{5},{7},{10}} => {{1},{2,8,10},{3,5,7},{4},{6},{9}} => [1,8,5,4,7,6,3,10,9,2] => ([(1,2),(1,9),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,3,9},{2},{4,8},{5,7},{6},{10}} => {{1},{2,8,10},{3,7},{4,6},{5},{9}} => [1,8,7,6,5,4,3,10,9,2] => ([(1,2),(1,9),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,5,7,9},{2,4},{3},{6},{8},{10}} => {{1},{2,4,6,10},{3},{5},{7,9},{8}} => [1,4,3,6,5,10,9,8,7,2] => ([(1,4),(1,9),(2,3),(2,9),(3,9),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,5,9},{2,4},{3},{6,8},{7},{10}} => {{1},{2,6,10},{3,5},{4},{7,9},{8}} => [1,6,5,4,3,10,9,8,7,2] => ([(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,9),(3,4),(3,5),(3,9),(4,5),(4,9),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,7,9},{2,4,6},{3},{5},{8},{10}} => {{1},{2,4,10},{3},{5,7,9},{6},{8}} => [1,4,3,10,7,6,9,8,5,2] => ([(1,2),(1,9),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,7,9},{2,6},{3,5},{4},{8},{10}} => {{1},{2,4,10},{3},{5,9},{6,8},{7}} => [1,4,3,10,9,8,7,6,5,2] => ([(1,2),(1,9),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,9},{2,4,6,8},{3},{5},{7},{10}} => {{1},{2,10},{3,5,7,9},{4},{6},{8}} => [1,10,5,4,7,6,9,8,3,2] => ([(1,6),(1,7),(1,8),(1,9),(2,5),(2,7),(2,8),(2,9),(3,4),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,9},{2,4,8},{3},{5,7},{6},{10}} => {{1},{2,10},{3,7,9},{4,6},{5},{8}} => [1,10,7,6,5,4,9,8,3,2] => ([(1,2),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,9},{2,6,8},{3,5},{4},{7},{10}} => {{1},{2,10},{3,5,9},{4},{6,8},{7}} => [1,10,5,4,9,8,7,6,3,2] => ([(1,2),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1,9},{2,8},{3,5,7},{4},{6},{10}} => {{1},{2,10},{3,9},{4,6,8},{5},{7}} => [1,10,9,6,5,8,7,4,3,2] => ([(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
{{1},{2,4,6,8,10,12},{3},{5},{7},{9},{11}} => {{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}} => [3,2,5,4,7,6,9,8,11,10,1,12] => ([(1,10),(1,11),(2,9),(2,11),(3,8),(3,11),(4,7),(4,11),(5,6),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
{{1},{2,4,6,8,12},{3},{5},{7},{9,11},{10}} => {{1,5,7,9,11},{2,4},{3},{6},{8},{10},{12}} => [5,4,3,2,7,6,9,8,11,10,1,12] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,6,10,12},{3},{5},{7,9},{8},{11}} => {{1,3,7,9,11},{2},{4,6},{5},{8},{10},{12}} => [3,2,7,6,5,4,9,8,11,10,1,12] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,6,12},{3},{5},{7,9,11},{8},{10}} => {{1,7,9,11},{2,4,6},{3},{5},{8},{10},{12}} => [7,4,3,6,5,2,9,8,11,10,1,12] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,6,12},{3},{5},{7,11},{8,10},{9}} => {{1,7,9,11},{2,6},{3,5},{4},{8},{10},{12}} => [7,6,5,4,3,2,9,8,11,10,1,12] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,8,10,12},{3},{5,7},{6},{9},{11}} => {{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}} => [3,2,5,4,9,8,7,6,11,10,1,12] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,8,12},{3},{5,7},{6},{9,11},{10}} => {{1,5,9,11},{2,4},{3},{6,8},{7},{10},{12}} => [5,4,3,2,9,8,7,6,11,10,1,12] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,10,12},{3},{5,7,9},{6},{8},{11}} => {{1,3,9,11},{2},{4,6,8},{5},{7},{10},{12}} => [3,2,9,6,5,8,7,4,11,10,1,12] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,10,12},{3},{5,9},{6,8},{7},{11}} => {{1,3,9,11},{2},{4,8},{5,7},{6},{10},{12}} => [3,2,9,8,7,6,5,4,11,10,1,12] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,12},{3},{5,7,9,11},{6},{8},{10}} => {{1,9,11},{2,4,6,8},{3},{5},{7},{10},{12}} => [9,4,3,6,5,8,7,2,11,10,1,12] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,12},{3},{5,7,11},{6},{8,10},{9}} => {{1,9,11},{2,6,8},{3,5},{4},{7},{10},{12}} => [9,6,5,4,3,8,7,2,11,10,1,12] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,12},{3},{5,9,11},{6,8},{7},{10}} => {{1,9,11},{2,4,8},{3},{5,7},{6},{10},{12}} => [9,4,3,8,7,6,5,2,11,10,1,12] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,12},{3},{5,11},{6,8,10},{7},{9}} => {{1,9,11},{2,8},{3,5,7},{4},{6},{10},{12}} => [9,8,5,4,7,6,3,2,11,10,1,12] => ([(1,2),(1,11),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,4,12},{3},{5,11},{6,10},{7,9},{8}} => {{1,9,11},{2,8},{3,7},{4,6},{5},{10},{12}} => [9,8,7,6,5,4,3,2,11,10,1,12] => ([(1,2),(1,11),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,6,8,10,12},{3,5},{4},{7},{9},{11}} => {{1,3,5,7,11},{2},{4},{6},{8,10},{9},{12}} => [3,2,5,4,7,6,11,10,9,8,1,12] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,6,8,12},{3,5},{4},{7},{9,11},{10}} => {{1,5,7,11},{2,4},{3},{6},{8,10},{9},{12}} => [5,4,3,2,7,6,11,10,9,8,1,12] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,6,10,12},{3,5},{4},{7,9},{8},{11}} => {{1,3,7,11},{2},{4,6},{5},{8,10},{9},{12}} => [3,2,7,6,5,4,11,10,9,8,1,12] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,6,12},{3,5},{4},{7,9,11},{8},{10}} => {{1,7,11},{2,4,6},{3},{5},{8,10},{9},{12}} => [7,4,3,6,5,2,11,10,9,8,1,12] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}} => {{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}} => [7,6,5,4,3,2,11,10,9,8,1,12] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,8,10,12},{3,5,7},{4},{6},{9},{11}} => {{1,3,5,11},{2},{4},{6,8,10},{7},{9},{12}} => [3,2,5,4,11,8,7,10,9,6,1,12] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,8,12},{3,5,7},{4},{6},{9,11},{10}} => {{1,5,11},{2,4},{3},{6,8,10},{7},{9},{12}} => [5,4,3,2,11,8,7,10,9,6,1,12] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,8,10,12},{3,7},{4,6},{5},{9},{11}} => {{1,3,5,11},{2},{4},{6,10},{7,9},{8},{12}} => [3,2,5,4,11,10,9,8,7,6,1,12] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}} => {{1,5,11},{2,4},{3},{6,10},{7,9},{8},{12}} => [5,4,3,2,11,10,9,8,7,6,1,12] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,10,12},{3,5,7,9},{4},{6},{8},{11}} => {{1,3,11},{2},{4,6,8,10},{5},{7},{9},{12}} => [3,2,11,6,5,8,7,10,9,4,1,12] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,10,12},{3,5,9},{4},{6,8},{7},{11}} => {{1,3,11},{2},{4,8,10},{5,7},{6},{9},{12}} => [3,2,11,8,7,6,5,10,9,4,1,12] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,10,12},{3,7,9},{4,6},{5},{8},{11}} => {{1,3,11},{2},{4,6,10},{5},{7,9},{8},{12}} => [3,2,11,6,5,10,9,8,7,4,1,12] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,10,12},{3,9},{4,6,8},{5},{7},{11}} => {{1,3,11},{2},{4,10},{5,7,9},{6},{8},{12}} => [3,2,11,10,7,6,9,8,5,4,1,12] => ([(1,2),(1,11),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}} => {{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}} => [3,2,11,10,9,8,7,6,5,4,1,12] => ([(1,2),(1,11),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,5,7,9,11},{4},{6},{8},{10}} => {{1,11},{2,4,6,8,10},{3},{5},{7},{9},{12}} => [11,4,3,6,5,8,7,10,9,2,1,12] => ([(1,8),(1,9),(1,10),(1,11),(2,7),(2,9),(2,10),(2,11),(3,6),(3,9),(3,10),(3,11),(4,5),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,5,7,11},{4},{6},{8,10},{9}} => {{1,11},{2,6,8,10},{3,5},{4},{7},{9},{12}} => [11,6,5,4,3,8,7,10,9,2,1,12] => ([(1,4),(1,9),(1,10),(1,11),(2,3),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,5,9,11},{4},{6,8},{7},{10}} => {{1,11},{2,4,8,10},{3},{5,7},{6},{9},{12}} => [11,4,3,8,7,6,5,10,9,2,1,12] => ([(1,4),(1,9),(1,10),(1,11),(2,3),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,5,11},{4},{6,8,10},{7},{9}} => {{1,11},{2,8,10},{3,5,7},{4},{6},{9},{12}} => [11,8,5,4,7,6,3,10,9,2,1,12] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,5,11},{4},{6,10},{7,9},{8}} => {{1,11},{2,8,10},{3,7},{4,6},{5},{9},{12}} => [11,8,7,6,5,4,3,10,9,2,1,12] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,7,9,11},{4,6},{5},{8},{10}} => {{1,11},{2,4,6,10},{3},{5},{7,9},{8},{12}} => [11,4,3,6,5,10,9,8,7,2,1,12] => ([(1,4),(1,9),(1,10),(1,11),(2,3),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}} => {{1,11},{2,6,10},{3,5},{4},{7,9},{8},{12}} => [11,6,5,4,3,10,9,8,7,2,1,12] => ([(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,9),(2,10),(2,11),(3,4),(3,5),(3,9),(3,10),(3,11),(4,5),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,9,11},{4,6,8},{5},{7},{10}} => {{1,11},{2,4,10},{3},{5,7,9},{6},{8},{12}} => [11,4,3,10,7,6,9,8,5,2,1,12] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,9,11},{4,8},{5,7},{6},{10}} => {{1,11},{2,4,10},{3},{5,9},{6,8},{7},{12}} => [11,4,3,10,9,8,7,6,5,2,1,12] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,11},{4,6,8,10},{5},{7},{9}} => {{1,11},{2,10},{3,5,7,9},{4},{6},{8},{12}} => [11,10,5,4,7,6,9,8,3,2,1,12] => ([(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}} => {{1,11},{2,10},{3,7,9},{4,6},{5},{8},{12}} => [11,10,7,6,5,4,9,8,3,2,1,12] => ([(1,2),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}} => {{1,11},{2,10},{3,5,9},{4},{6,8},{7},{12}} => [11,10,5,4,9,8,7,6,3,2,1,12] => ([(1,2),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,11},{4,10},{5,7,9},{6},{8}} => {{1,11},{2,10},{3,9},{4,6,8},{5},{7},{12}} => [11,10,9,6,5,8,7,4,3,2,1,12] => ([(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}} => {{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}} => [11,10,9,8,7,6,5,4,3,2,1,12] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,6,8,10,12},{5},{7},{9},{11}} => {{1,3,5,7,9},{2},{4},{6},{8},{10,12},{11}} => [3,2,5,4,7,6,9,8,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,10),(3,11),(4,9),(4,11),(5,8),(5,11),(6,7),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
{{1,3},{2},{4,6,8,12},{5},{7},{9,11},{10}} => {{1,5,7,9},{2,4},{3},{6},{8},{10,12},{11}} => [5,4,3,2,7,6,9,8,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,6),(3,11),(4,5),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,6,10,12},{5},{7,9},{8},{11}} => {{1,3,7,9},{2},{4,6},{5},{8},{10,12},{11}} => [3,2,7,6,5,4,9,8,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,6),(3,11),(4,5),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,6,12},{5},{7,9,11},{8},{10}} => {{1,7,9},{2,4,6},{3},{5},{8},{10,12},{11}} => [7,4,3,6,5,2,9,8,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,6,12},{5},{7,11},{8,10},{9}} => {{1,7,9},{2,6},{3,5},{4},{8},{10,12},{11}} => [7,6,5,4,3,2,9,8,1,12,11,10] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,8,10,12},{5,7},{6},{9},{11}} => {{1,3,5,9},{2},{4},{6,8},{7},{10,12},{11}} => [3,2,5,4,9,8,7,6,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,6),(3,11),(4,5),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}} => {{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}} => [5,4,3,2,9,8,7,6,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,10,12},{5,7,9},{6},{8},{11}} => {{1,3,9},{2},{4,6,8},{5},{7},{10,12},{11}} => [3,2,9,6,5,8,7,4,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,10,12},{5,9},{6,8},{7},{11}} => {{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}} => [3,2,9,8,7,6,5,4,1,12,11,10] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,12},{5,7,9,11},{6},{8},{10}} => {{1,9},{2,4,6,8},{3},{5},{7},{10,12},{11}} => [9,4,3,6,5,8,7,2,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,8),(3,9),(3,10),(3,11),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}} => {{1,9},{2,6,8},{3,5},{4},{7},{10,12},{11}} => [9,6,5,4,3,8,7,2,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,12},{5,9,11},{6,8},{7},{10}} => {{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}} => [9,4,3,8,7,6,5,2,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,12},{5,11},{6,8,10},{7},{9}} => {{1,9},{2,8},{3,5,7},{4},{6},{10,12},{11}} => [9,8,5,4,7,6,3,2,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}} => {{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}} => [9,8,7,6,5,4,3,2,1,12,11,10] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5},{2},{4},{6,8,10,12},{7},{9},{11}} => {{1,3,5,7},{2},{4},{6},{8,10,12},{9},{11}} => [3,2,5,4,7,6,1,10,9,12,11,8] => ([(0,5),(0,11),(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,11),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],12)
{{1,3,5},{2},{4},{6,8,12},{7},{9,11},{10}} => {{1,5,7},{2,4},{3},{6},{8,10,12},{9},{11}} => [5,4,3,2,7,6,1,10,9,12,11,8] => ([(0,1),(0,11),(1,11),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5},{2},{4},{6,10,12},{7,9},{8},{11}} => {{1,3,7},{2},{4,6},{5},{8,10,12},{9},{11}} => [3,2,7,6,5,4,1,10,9,12,11,8] => ([(0,1),(0,11),(1,11),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5},{2},{4},{6,12},{7,9,11},{8},{10}} => {{1,7},{2,4,6},{3},{5},{8,10,12},{9},{11}} => [7,4,3,6,5,2,1,10,9,12,11,8] => ([(0,3),(0,8),(1,2),(1,8),(2,8),(3,8),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(9,10),(9,11),(10,11)],12)
{{1,3,5},{2},{4},{6,12},{7,11},{8,10},{9}} => {{1,7},{2,6},{3,5},{4},{8,10,12},{9},{11}} => [7,6,5,4,3,2,1,10,9,12,11,8] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5},{2,4},{3},{6,8,10,12},{7},{9},{11}} => {{1,3,5,7},{2},{4},{6},{8,12},{9,11},{10}} => [3,2,5,4,7,6,1,12,11,10,9,8] => ([(0,5),(0,11),(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,11),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],12)
{{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}} => {{1,5,7},{2,4},{3},{6},{8,12},{9,11},{10}} => [5,4,3,2,7,6,1,12,11,10,9,8] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5},{2,4},{3},{6,10,12},{7,9},{8},{11}} => {{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}} => [3,2,7,6,5,4,1,12,11,10,9,8] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5},{2,4},{3},{6,12},{7,9,11},{8},{10}} => {{1,7},{2,4,6},{3},{5},{8,12},{9,11},{10}} => [7,4,3,6,5,2,1,12,11,10,9,8] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}} => {{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}} => [7,6,5,4,3,2,1,12,11,10,9,8] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5,7},{2},{4},{6},{8,10,12},{9},{11}} => {{1,3,5},{2},{4},{6,8,10,12},{7},{9},{11}} => [3,2,5,4,1,8,7,10,9,12,11,6] => ([(0,5),(0,11),(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,11),(6,9),(6,10),(7,8),(7,10),(8,10),(9,10)],12)
{{1,3,5,7},{2},{4},{6},{8,12},{9,11},{10}} => {{1,5},{2,4},{3},{6,8,10,12},{7},{9},{11}} => [5,4,3,2,1,8,7,10,9,12,11,6] => ([(0,5),(0,11),(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,11),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],12)
{{1,3,7},{2},{4,6},{5},{8,10,12},{9},{11}} => {{1,3,5},{2},{4},{6,10,12},{7,9},{8},{11}} => [3,2,5,4,1,10,9,8,7,12,11,6] => ([(0,1),(0,11),(1,11),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}} => {{1,5},{2,4},{3},{6,10,12},{7,9},{8},{11}} => [5,4,3,2,1,10,9,8,7,12,11,6] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,7},{2,4},{3},{6},{8,10,12},{9},{11}} => {{1,3,5},{2},{4},{6,8,12},{7},{9,11},{10}} => [3,2,5,4,1,8,7,12,11,10,9,6] => ([(0,1),(0,11),(1,11),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,7},{2,4},{3},{6},{8,12},{9,11},{10}} => {{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}} => [5,4,3,2,1,8,7,12,11,10,9,6] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7},{2,4,6},{3},{5},{8,10,12},{9},{11}} => {{1,3,5},{2},{4},{6,12},{7,9,11},{8},{10}} => [3,2,5,4,1,12,9,8,11,10,7,6] => ([(0,3),(0,8),(1,2),(1,8),(2,8),(3,8),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(9,10),(9,11),(10,11)],12)
{{1,7},{2,4,6},{3},{5},{8,12},{9,11},{10}} => {{1,5},{2,4},{3},{6,12},{7,9,11},{8},{10}} => [5,4,3,2,1,12,9,8,11,10,7,6] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7},{2,6},{3,5},{4},{8,10,12},{9},{11}} => {{1,3,5},{2},{4},{6,12},{7,11},{8,10},{9}} => [3,2,5,4,1,12,11,10,9,8,7,6] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}} => {{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}} => [5,4,3,2,1,12,11,10,9,8,7,6] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5,7,9},{2},{4},{6},{8},{10,12},{11}} => {{1,3},{2},{4,6,8,10,12},{5},{7},{9},{11}} => [3,2,1,6,5,8,7,10,9,12,11,4] => ([(0,1),(0,2),(1,2),(3,10),(3,11),(4,9),(4,11),(5,8),(5,11),(6,7),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
{{1,3,5,9},{2},{4},{6,8},{7},{10,12},{11}} => {{1,3},{2},{4,8,10,12},{5,7},{6},{9},{11}} => [3,2,1,8,7,6,5,10,9,12,11,4] => ([(0,1),(0,2),(1,2),(3,6),(3,11),(4,5),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,7,9},{2},{4,6},{5},{8},{10,12},{11}} => {{1,3},{2},{4,6,10,12},{5},{7,9},{8},{11}} => [3,2,1,6,5,10,9,8,7,12,11,4] => ([(0,1),(0,2),(1,2),(3,6),(3,11),(4,5),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,9},{2},{4,6,8},{5},{7},{10,12},{11}} => {{1,3},{2},{4,10,12},{5,7,9},{6},{8},{11}} => [3,2,1,10,7,6,9,8,5,12,11,4] => ([(0,1),(0,2),(1,2),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}} => {{1,3},{2},{4,10,12},{5,9},{6,8},{7},{11}} => [3,2,1,10,9,8,7,6,5,12,11,4] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,7,9},{2,4},{3},{6},{8},{10,12},{11}} => {{1,3},{2},{4,6,8,12},{5},{7},{9,11},{10}} => [3,2,1,6,5,8,7,12,11,10,9,4] => ([(0,1),(0,2),(1,2),(3,6),(3,11),(4,5),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}} => {{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}} => [3,2,1,8,7,6,5,12,11,10,9,4] => ([(0,1),(0,2),(1,2),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7,9},{2,4,6},{3},{5},{8},{10,12},{11}} => {{1,3},{2},{4,6,12},{5},{7,9,11},{8},{10}} => [3,2,1,6,5,12,9,8,11,10,7,4] => ([(0,1),(0,2),(1,2),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7,9},{2,6},{3,5},{4},{8},{10,12},{11}} => {{1,3},{2},{4,6,12},{5},{7,11},{8,10},{9}} => [3,2,1,6,5,12,11,10,9,8,7,4] => ([(0,1),(0,11),(1,11),(2,3),(2,4),(3,4),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9},{2,4,6,8},{3},{5},{7},{10,12},{11}} => {{1,3},{2},{4,12},{5,7,9,11},{6},{8},{10}} => [3,2,1,12,7,6,9,8,11,10,5,4] => ([(0,1),(0,2),(1,2),(3,8),(3,9),(3,10),(3,11),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}} => {{1,3},{2},{4,12},{5,9,11},{6,8},{7},{10}} => [3,2,1,12,9,8,7,6,11,10,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9},{2,6,8},{3,5},{4},{7},{10,12},{11}} => {{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}} => [3,2,1,12,7,6,11,10,9,8,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9},{2,8},{3,5,7},{4},{6},{10,12},{11}} => {{1,3},{2},{4,12},{5,11},{6,8,10},{7},{9}} => [3,2,1,12,11,8,7,10,9,6,5,4] => ([(0,1),(0,2),(1,2),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}} => {{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}} => [3,2,1,12,11,10,9,8,7,6,5,4] => ([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5,7,9,11},{2},{4},{6},{8},{10},{12}} => {{1},{2,4,6,8,10,12},{3},{5},{7},{9},{11}} => [1,4,3,6,5,8,7,10,9,12,11,2] => ([(1,10),(1,11),(2,9),(2,11),(3,8),(3,11),(4,7),(4,11),(5,6),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
{{1,3,5,7,11},{2},{4},{6},{8,10},{9},{12}} => {{1},{2,6,8,10,12},{3,5},{4},{7},{9},{11}} => [1,6,5,4,3,8,7,10,9,12,11,2] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5,9,11},{2},{4},{6,8},{7},{10},{12}} => {{1},{2,4,8,10,12},{3},{5,7},{6},{9},{11}} => [1,4,3,8,7,6,5,10,9,12,11,2] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5,11},{2},{4},{6,8,10},{7},{9},{12}} => {{1},{2,8,10,12},{3,5,7},{4},{6},{9},{11}} => [1,8,5,4,7,6,3,10,9,12,11,2] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,5,11},{2},{4},{6,10},{7,9},{8},{12}} => {{1},{2,8,10,12},{3,7},{4,6},{5},{9},{11}} => [1,8,7,6,5,4,3,10,9,12,11,2] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,7,9,11},{2},{4,6},{5},{8},{10},{12}} => {{1},{2,4,6,10,12},{3},{5},{7,9},{8},{11}} => [1,4,3,6,5,10,9,8,7,12,11,2] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,7,11},{2},{4,6},{5},{8,10},{9},{12}} => {{1},{2,6,10,12},{3,5},{4},{7,9},{8},{11}} => [1,6,5,4,3,10,9,8,7,12,11,2] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,9,11},{2},{4,6,8},{5},{7},{10},{12}} => {{1},{2,4,10,12},{3},{5,7,9},{6},{8},{11}} => [1,4,3,10,7,6,9,8,5,12,11,2] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,9,11},{2},{4,8},{5,7},{6},{10},{12}} => {{1},{2,4,10,12},{3},{5,9},{6,8},{7},{11}} => [1,4,3,10,9,8,7,6,5,12,11,2] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,11},{2},{4,6,8,10},{5},{7},{9},{12}} => {{1},{2,10,12},{3,5,7,9},{4},{6},{8},{11}} => [1,10,5,4,7,6,9,8,3,12,11,2] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,11},{2},{4,6,10},{5},{7,9},{8},{12}} => {{1},{2,10,12},{3,7,9},{4,6},{5},{8},{11}} => [1,10,7,6,5,4,9,8,3,12,11,2] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,11},{2},{4,8,10},{5,7},{6},{9},{12}} => {{1},{2,10,12},{3,5,9},{4},{6,8},{7},{11}} => [1,10,5,4,9,8,7,6,3,12,11,2] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,11},{2},{4,10},{5,7,9},{6},{8},{12}} => {{1},{2,10,12},{3,9},{4,6,8},{5},{7},{11}} => [1,10,9,6,5,8,7,4,3,12,11,2] => ([(1,2),(1,11),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}} => {{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}} => [1,10,9,8,7,6,5,4,3,12,11,2] => ([(1,2),(1,11),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,7,9,11},{2,4},{3},{6},{8},{10},{12}} => {{1},{2,4,6,8,12},{3},{5},{7},{9,11},{10}} => [1,4,3,6,5,8,7,12,11,10,9,2] => ([(1,6),(1,11),(2,5),(2,11),(3,4),(3,11),(4,11),(5,11),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,7,11},{2,4},{3},{6},{8,10},{9},{12}} => {{1},{2,6,8,12},{3,5},{4},{7},{9,11},{10}} => [1,6,5,4,3,8,7,12,11,10,9,2] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,9,11},{2,4},{3},{6,8},{7},{10},{12}} => {{1},{2,4,8,12},{3},{5,7},{6},{9,11},{10}} => [1,4,3,8,7,6,5,12,11,10,9,2] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,7),(6,11),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,11},{2,4},{3},{6,8,10},{7},{9},{12}} => {{1},{2,8,12},{3,5,7},{4},{6},{9,11},{10}} => [1,8,5,4,7,6,3,12,11,10,9,2] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,5,11},{2,4},{3},{6,10},{7,9},{8},{12}} => {{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}} => [1,8,7,6,5,4,3,12,11,10,9,2] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7,9,11},{2,4,6},{3},{5},{8},{10},{12}} => {{1},{2,4,6,12},{3},{5},{7,9,11},{8},{10}} => [1,4,3,6,5,12,9,8,11,10,7,2] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7,11},{2,4,6},{3},{5},{8,10},{9},{12}} => {{1},{2,6,12},{3,5},{4},{7,9,11},{8},{10}} => [1,6,5,4,3,12,9,8,11,10,7,2] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,8),(5,9),(5,10),(5,11),(6,7),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7,9,11},{2,6},{3,5},{4},{8},{10},{12}} => {{1},{2,4,6,12},{3},{5},{7,11},{8,10},{9}} => [1,4,3,6,5,12,11,10,9,8,7,2] => ([(1,4),(1,11),(2,3),(2,11),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}} => {{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}} => [1,6,5,4,3,12,11,10,9,8,7,2] => ([(1,2),(1,3),(1,4),(1,11),(2,3),(2,4),(2,11),(3,4),(3,11),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9,11},{2,4,6,8},{3},{5},{7},{10},{12}} => {{1},{2,4,12},{3},{5,7,9,11},{6},{8},{10}} => [1,4,3,12,7,6,9,8,11,10,5,2] => ([(1,2),(1,11),(2,11),(3,8),(3,9),(3,10),(3,11),(4,7),(4,9),(4,10),(4,11),(5,6),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9,11},{2,4,8},{3},{5,7},{6},{10},{12}} => {{1},{2,4,12},{3},{5,9,11},{6,8},{7},{10}} => [1,4,3,12,9,8,7,6,11,10,5,2] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9,11},{2,6,8},{3,5},{4},{7},{10},{12}} => {{1},{2,4,12},{3},{5,7,11},{6},{8,10},{9}} => [1,4,3,12,7,6,11,10,9,8,5,2] => ([(1,2),(1,11),(2,11),(3,4),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9,11},{2,8},{3,5,7},{4},{6},{10},{12}} => {{1},{2,4,12},{3},{5,11},{6,8,10},{7},{9}} => [1,4,3,12,11,8,7,10,9,6,5,2] => ([(1,2),(1,11),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9,11},{2,8},{3,7},{4,6},{5},{10},{12}} => {{1},{2,4,12},{3},{5,11},{6,10},{7,9},{8}} => [1,4,3,12,11,10,9,8,7,6,5,2] => ([(1,2),(1,11),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,4,6,8,10},{3},{5},{7},{9},{12}} => {{1},{2,12},{3,5,7,9,11},{4},{6},{8},{10}} => [1,12,5,4,7,6,9,8,11,10,3,2] => ([(1,8),(1,9),(1,10),(1,11),(2,7),(2,9),(2,10),(2,11),(3,6),(3,9),(3,10),(3,11),(4,5),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,4,6,10},{3},{5},{7,9},{8},{12}} => {{1},{2,12},{3,7,9,11},{4,6},{5},{8},{10}} => [1,12,7,6,5,4,9,8,11,10,3,2] => ([(1,4),(1,9),(1,10),(1,11),(2,3),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,4,8,10},{3},{5,7},{6},{9},{12}} => {{1},{2,12},{3,5,9,11},{4},{6,8},{7},{10}} => [1,12,5,4,9,8,7,6,11,10,3,2] => ([(1,4),(1,9),(1,10),(1,11),(2,3),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,4,10},{3},{5,7,9},{6},{8},{12}} => {{1},{2,12},{3,9,11},{4,6,8},{5},{7},{10}} => [1,12,9,6,5,8,7,4,11,10,3,2] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,4,10},{3},{5,9},{6,8},{7},{12}} => {{1},{2,12},{3,9,11},{4,8},{5,7},{6},{10}} => [1,12,9,8,7,6,5,4,11,10,3,2] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,6,8,10},{3,5},{4},{7},{9},{12}} => {{1},{2,12},{3,5,7,11},{4},{6},{8,10},{9}} => [1,12,5,4,7,6,11,10,9,8,3,2] => ([(1,4),(1,9),(1,10),(1,11),(2,3),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,6,10},{3,5},{4},{7,9},{8},{12}} => {{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}} => [1,12,7,6,5,4,11,10,9,8,3,2] => ([(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,9),(2,10),(2,11),(3,4),(3,5),(3,9),(3,10),(3,11),(4,5),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,8,10},{3,5,7},{4},{6},{9},{12}} => {{1},{2,12},{3,5,11},{4},{6,8,10},{7},{9}} => [1,12,5,4,11,8,7,10,9,6,3,2] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,8,10},{3,7},{4,6},{5},{9},{12}} => {{1},{2,12},{3,5,11},{4},{6,10},{7,9},{8}} => [1,12,5,4,11,10,9,8,7,6,3,2] => ([(1,2),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,10},{3,5,7,9},{4},{6},{8},{12}} => {{1},{2,12},{3,11},{4,6,8,10},{5},{7},{9}} => [1,12,11,6,5,8,7,10,9,4,3,2] => ([(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,7),(3,8),(3,9),(3,10),(3,11),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,10},{3,5,9},{4},{6,8},{7},{12}} => {{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}} => [1,12,11,8,7,6,5,10,9,4,3,2] => ([(1,2),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,10},{3,7,9},{4,6},{5},{8},{12}} => {{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}} => [1,12,11,6,5,10,9,8,7,4,3,2] => ([(1,2),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,10},{3,9},{4,6,8},{5},{7},{12}} => {{1},{2,12},{3,11},{4,10},{5,7,9},{6},{8}} => [1,12,11,10,7,6,9,8,5,4,3,2] => ([(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}} => {{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}} => [1,12,11,10,9,8,7,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
{{1,9},{2},{3},{4},{5},{6,8},{7}} => {{1,9},{2,4},{3},{5},{6},{7},{8}} => [9,4,3,2,5,6,7,8,1] => ([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,3,6},{4},{5,8},{7}} => {{1,4},{2},{3,6,7,8},{5}} => [4,2,6,1,5,7,8,3] => ([(0,7),(1,7),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,3},{2,4,5,7},{6},{8}} => {{1},{2,4,5,7},{3},{6,8}} => [1,4,3,5,7,8,2,6] => ([(1,7),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3},{2,4,6},{5,7},{8}} => {{1},{2,4},{3,5,7},{6,8}} => [1,4,5,2,7,8,3,6] => ([(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1,3},{2,4},{5,6,7},{8}} => {{1},{2,3,4},{5,7},{6,8}} => [1,3,4,2,7,8,5,6] => ([(1,7),(2,7),(3,5),(3,6),(4,5),(4,6)],8)
{{1,6,7},{2,3,5,8},{4}} => {{1,4,6,7},{2,3,8},{5}} => [4,3,8,6,5,7,1,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,5,8},{2,4,6,7}} => {{1,4,6,8},{2,3,5,7}} => [4,3,5,6,7,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,4,6},{2},{5,7,8}} => {{1,2,4},{3,5,6,8},{7}} => [2,4,5,1,6,8,7,3] => ([(0,7),(1,6),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,6,7},{3},{4,8},{5}} => {{1,5},{2,3,7},{4},{6},{8}} => [5,3,7,4,1,6,2,8] => ([(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,6,7},{2},{3},{4,8},{5}} => {{1,5},{2,3,8},{4},{6},{7}} => [5,3,8,4,1,6,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,5,7},{2},{3,8},{4},{6}} => {{1,6},{2,4,8},{3},{5},{7}} => [6,4,3,8,5,1,7,2] => ([(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1},{2,5},{3,8},{4},{6,7}} => {{1,6},{2,3},{4,7},{5},{8}} => [6,3,2,7,5,1,4,8] => ([(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,5},{2,8},{3},{4},{6,7}} => {{1,7},{2,3},{4,8},{5},{6}} => [7,3,2,8,5,6,1,4] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2,8},{3},{4},{5,7}} => {{1,7},{2,4},{3,8},{5},{6}} => [7,4,8,2,5,6,1,3] => ([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,2,7},{3,5},{4,6,8}} => {{1,3,5},{2,7,8},{4,6}} => [3,7,5,6,1,4,8,2] => ([(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,3,6},{2,4,5,7,8}} => {{1,2,4,5,7},{3,6,8}} => [2,4,6,5,7,8,1,3] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,5,6},{2},{3,7,8}} => {{1,2,6},{3,4,5,8},{7}} => [2,6,4,5,8,1,7,3] => ([(0,7),(1,4),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,3,6,8},{4,7},{5}} => {{1,3,6,7},{2,5},{4},{8}} => [3,5,6,4,2,7,1,8] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,5,7},{3,6,8}} => {{1,3,6},{2,4,5,7},{8}} => [3,4,6,5,7,1,2,8] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,7},{2,5},{3,6,8}} => {{1,3,6},{2,5,8},{4,7}} => [3,5,6,7,8,1,4,2] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)
{{1,5},{2,8},{3,4,6,7}} => {{1,7},{2,3,5,6},{4,8}} => [7,3,5,8,6,2,1,4] => ([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4},{3,5,7,8},{6}} => {{1,2,4,6},{3},{5,7},{8}} => [2,4,3,6,7,1,5,8] => ([(1,7),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
{{1},{2,5,8},{3,6},{4},{7}} => {{1,4,7},{2},{3,6},{5},{8}} => [4,2,6,7,5,3,1,8] => ([(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,4,6,7},{3,5},{8}} => {{1},{2,3,5,7},{4,6},{8}} => [1,3,5,6,7,4,2,8] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6,7},{2},{3},{4,5,8}} => {{1,4,5},{2,3,8},{6},{7}} => [4,3,8,5,1,6,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
{{1,5,7},{2,3,4,6},{8}} => {{1},{2,4,8},{3,5,6,7}} => [1,4,5,8,6,7,3,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4,5,6},{7},{8}} => {{1},{2},{3,4,5,7},{6,8}} => [1,2,4,5,7,8,3,6] => ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,2,5,7},{3},{4,6},{8}} => {{1},{2,4,7,8},{3,5},{6}} => [1,4,5,7,3,6,8,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3},{2,6},{4},{5,7},{8}} => {{1},{2,4},{3,7},{5},{6,8}} => [1,4,7,2,5,8,3,6] => ([(1,4),(1,7),(2,3),(2,7),(3,6),(4,6),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3},{4,5,6,8}} => {{1,3,4,5},{2,8},{6},{7}} => [3,8,4,5,1,6,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,6},{2},{3,4,8},{5},{7}} => {{1,5,6},{2},{3,8},{4},{7}} => [5,2,8,4,6,1,7,3] => ([(0,5),(0,6),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,2},{3,4,6},{5,7},{8}} => {{1},{2,4},{3,5,6},{7,8}} => [1,4,5,2,6,3,8,7] => ([(1,2),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,5},{2,4,7},{3},{6},{8}} => {{1},{2,5,7},{3},{4,8},{6}} => [1,5,3,8,7,6,2,4] => ([(1,2),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,6,7},{2},{3,5,8}} => {{1,4,6},{2,3,5,8},{7}} => [4,3,5,6,8,1,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3,6},{2,4,5},{7,8}} => {{1,2},{3,6,8},{4,5,7}} => [2,1,6,5,7,8,4,3] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,8},{2,4,7},{5,6}} => {{1,6,8},{2,5,7},{3,4}} => [6,5,4,3,7,8,2,1] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2},{3,5,8},{4,6,7}} => {{1,4,6},{2,3,5},{7,8}} => [4,3,5,6,2,1,8,7] => ([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2,8},{3,6},{4,7},{5}} => {{1,7},{2,5},{3,6},{4},{8}} => [7,5,6,4,2,3,1,8] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,3,6,7},{4}} => {{1,4,8},{2,3,6,7},{5}} => [4,3,6,8,5,7,2,1] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4,7},{3,8},{5,6}} => {{1,6},{2,5,7,8},{3,4}} => [6,5,4,3,7,1,8,2] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1},{2,4,6},{3,5,8},{7}} => {{1,4,6},{2},{3,5,7},{8}} => [4,2,5,6,7,1,3,8] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
{{1,6,7},{2,4},{3,5,8}} => {{1,4,6},{2,3,8},{5,7}} => [4,3,8,6,7,1,5,2] => ([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4,8},{2,7},{3,5,6}} => {{1,5,8},{2,7},{3,4,6}} => [5,7,4,6,8,3,2,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4,7,8},{2,5,6},{3}} => {{1,2,5,8},{3,4,7},{6}} => [2,5,4,7,8,6,3,1] => ([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2,4,7},{3,6}} => {{1,4,8},{2,5,7},{3,6}} => [4,5,6,8,7,3,2,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,7},{2},{3},{4},{5,8},{6}} => {{1,4},{2,8},{3},{5},{6},{7}} => [4,8,3,1,5,6,7,2] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
{{1,3},{2,4,6},{5,7,8}} => {{1,2,4},{3,5,7},{6,8}} => [2,4,5,1,7,8,3,6] => ([(0,6),(1,2),(1,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
{{1,4},{2},{3,6,8},{5},{7}} => {{1,3,6},{2},{4},{5,8},{7}} => [3,2,6,4,8,1,7,5] => ([(0,1),(0,7),(1,7),(2,5),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
{{1,3},{2,6,8},{4},{5},{7}} => {{1,3,7},{2},{4},{5},{6,8}} => [3,2,7,4,5,8,1,6] => ([(0,1),(0,7),(1,7),(2,3),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1},{2},{3,6},{4,7},{5,8}} => {{1,4},{2,5},{3,6},{7},{8}} => [4,5,6,1,2,3,7,8] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
{{1,6},{2,3,4,5,8},{7}} => {{1,4,5,6,7},{2},{3,8}} => [4,2,8,5,6,7,1,3] => ([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
{{1,4,6,8},{2,7},{3,5}} => {{1,3,5,8},{2,7},{4,6}} => [3,7,5,6,8,4,2,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5,8},{2},{3,6},{4},{7}} => {{1,4,8},{2},{3,6},{5},{7}} => [4,2,6,8,5,3,7,1] => ([(0,4),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2},{3},{4},{5,7},{8}} => {{1},{2,4},{3,8},{5},{6},{7}} => [1,4,8,2,5,6,7,3] => ([(1,2),(1,7),(2,6),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,5},{2},{3},{4,6},{7},{8},{9}} => {{1},{2},{3},{4,6},{5,9},{7},{8}} => [1,2,3,6,9,4,7,8,5] => ([(3,4),(3,8),(4,7),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,6},{2},{3},{4},{5,7},{8},{9}} => {{1},{2},{3,5},{4,9},{6},{7},{8}} => [1,2,5,9,3,6,7,8,4] => ([(2,3),(2,8),(3,7),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,7},{2},{3},{4},{5},{6,8},{9}} => {{1},{2,4},{3,9},{5},{6},{7},{8}} => [1,4,9,2,5,6,7,8,3] => ([(1,2),(1,8),(2,7),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,8},{2},{3},{4},{5},{6},{7,9}} => {{1,3},{2,9},{4},{5},{6},{7},{8}} => [3,9,1,4,5,6,7,8,2] => ([(0,1),(0,8),(1,7),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,3,4,5,9},{6,8},{7}} => {{1,5,6,7,8,9},{2,4},{3}} => [5,4,3,2,6,7,8,9,1] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
{{1,2,8},{3,5,7},{4,6}} => {{1,7,8},{2,4,6},{3,5}} => [7,4,5,6,3,2,8,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,5},{2},{4,7},{6},{8}} => {{1},{2,5},{3},{4,6,8},{7}} => [1,5,3,6,2,8,7,4] => ([(1,2),(1,7),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
{{1},{2,5},{3,6,7},{4},{8}} => {{1},{2,3,6},{4,7},{5},{8}} => [1,3,6,7,5,2,4,8] => ([(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,6},{2},{3},{4,5,7},{8}} => {{1},{2,4,5},{3,8},{6},{7}} => [1,4,8,5,2,6,7,3] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3,6,7},{5},{8}} => {{1},{2,3,6},{4},{5,8},{7}} => [1,3,6,4,8,2,7,5] => ([(1,7),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
{{1,6,8},{2,4,5},{3,7}} => {{1,3,8},{2,6},{4,5,7}} => [3,6,8,5,7,2,4,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
{{1,4},{2,6,7},{3},{5},{8}} => {{1},{2,3,7},{4},{5,8},{6}} => [1,3,7,4,8,6,2,5] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
{{1,4},{2},{3,8},{5},{6},{7}} => {{1,6},{2},{3},{4},{5,8},{7}} => [6,2,3,4,8,1,7,5] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)
{{1,4},{2},{3,7},{5,8},{6}} => {{1,4},{2,6},{3},{5,8},{7}} => [4,6,3,1,8,2,7,5] => ([(0,3),(0,4),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,2,4},{3,7},{5,6,8}} => {{1,3,4},{2,6},{5,7,8}} => [3,6,4,1,7,2,8,5] => ([(0,5),(1,4),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(5,6),(6,7)],8)
{{1,3,7,8},{2,4,6},{5}} => {{1,2,6,8},{3,5,7},{4}} => [2,6,5,4,7,8,3,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
{{1,3,7},{2,5},{4,6,8}} => {{1,3,5},{2,6,8},{4,7}} => [3,6,5,7,1,8,4,2] => ([(0,5),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
Map
complement
Description
The complement of a set partition obtained by replacing $i$ with $n+1-i$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
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