Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00126: Permutations —cactus evacuation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Images
=>
Cc0007;cc-rep-0Cc0020;cc-rep-3
[[1]]=>[1]=>[1]=>([],1)
[[1,2]]=>[1,2]=>[1,2]=>([],2)
[[1],[2]]=>[2,1]=>[2,1]=>([(0,1)],2)
[[1,2,3]]=>[1,2,3]=>[1,2,3]=>([],3)
[[1,3],[2]]=>[2,1,3]=>[2,3,1]=>([(0,2),(1,2)],3)
[[1,2],[3]]=>[3,1,2]=>[1,3,2]=>([(1,2)],3)
[[1],[2],[3]]=>[3,2,1]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3)
[[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>([],4)
[[1,3,4],[2]]=>[2,1,3,4]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)
[[1,2,4],[3]]=>[3,1,2,4]=>[1,3,4,2]=>([(1,3),(2,3)],4)
[[1,2,3],[4]]=>[4,1,2,3]=>[1,2,4,3]=>([(2,3)],4)
[[1,3],[2,4]]=>[2,4,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)
[[1,2],[3,4]]=>[3,4,1,2]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)
[[1,4],[2],[3]]=>[3,2,1,4]=>[3,4,2,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[[1,3],[2],[4]]=>[4,2,1,3]=>[2,4,3,1]=>([(0,3),(1,2),(1,3),(2,3)],4)
[[1,2],[3],[4]]=>[4,3,1,2]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)
[[1],[2],[3],[4]]=>[4,3,2,1]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([],5)
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5)
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[1,3,4,5,2]=>([(1,4),(2,4),(3,4)],5)
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[1,2,4,5,3]=>([(2,4),(3,4)],5)
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[1,2,3,5,4]=>([(3,4)],5)
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[2,4,5,1,3]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[3,4,5,1,2]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[1,3,5,2,4]=>([(1,4),(2,3),(3,4)],5)
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[1,4,5,2,3]=>([(1,3),(1,4),(2,3),(2,4)],5)
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,4,5,2,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,5,3,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[1,4,5,3,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[2,3,5,4,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[1,3,5,4,2]=>([(1,4),(2,3),(2,4),(3,4)],5)
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[3,5,2,4,1]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[4,5,2,3,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[4,5,1,3,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[2,5,1,4,3]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[3,5,1,4,2]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[4,5,3,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[3,5,4,2,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[2,5,4,3,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[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)
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([],6)
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[1,3,4,5,6,2]=>([(1,5),(2,5),(3,5),(4,5)],6)
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[1,2,4,5,6,3]=>([(2,5),(3,5),(4,5)],6)
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[1,2,3,5,6,4]=>([(3,5),(4,5)],6)
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>([(4,5)],6)
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[2,4,5,6,1,3]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[3,4,5,6,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[2,3,5,6,1,4]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[1,3,5,6,2,4]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[1,4,5,6,2,3]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[2,3,4,6,1,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[1,3,4,6,2,5]=>([(1,5),(2,5),(3,4),(4,5)],6)
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[1,2,4,6,3,5]=>([(2,5),(3,4),(4,5)],6)
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[1,2,5,6,3,4]=>([(2,4),(2,5),(3,4),(3,5)],6)
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[3,4,5,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,5,6,3,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[1,4,5,6,3,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,3,5,6,4,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[1,3,5,6,4,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[1,2,5,6,4,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[2,3,4,6,5,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[1,3,4,6,5,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[1,2,4,6,5,3]=>([(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[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)
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[3,5,6,2,4,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[4,5,6,2,3,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[4,5,6,1,3,2]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[2,5,6,1,4,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[3,5,6,1,4,2]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[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)
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[2,4,6,3,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[1,4,6,3,5,2]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[2,5,6,3,4,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[1,5,6,3,4,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[1,5,6,2,4,3]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[2,4,6,1,5,3]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[3,4,6,1,5,2]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[2,3,6,1,5,4]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[1,3,6,2,5,4]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[1,4,6,2,5,3]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[4,5,6,3,2,1]=>([(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)
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[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)
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,5,6,4,3,1]=>([(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]]=>[5,4,3,1,2,6]=>[1,5,6,4,3,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[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)
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[2,4,6,5,3,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[1,4,6,5,3,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[2,3,6,5,4,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[1,3,6,5,4,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[4,6,2,5,1,3]=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[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)
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[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],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[4,6,3,5,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[5,6,3,4,2,1]=>([(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)
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[5,6,2,4,3,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[5,6,1,4,3,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[3,6,2,5,4,1]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[4,6,2,5,3,1]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[4,6,1,5,3,2]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[2,6,1,5,4,3]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[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)
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[5,6,4,3,2,1]=>([(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)
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[4,6,5,3,2,1]=>([(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)
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[3,6,5,4,2,1]=>([(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)
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[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)
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[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],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[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)
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([],7)
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[1,3,4,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[1,2,4,5,6,7,3]=>([(2,6),(3,6),(4,6),(5,6)],7)
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[1,2,3,5,6,7,4]=>([(3,6),(4,6),(5,6)],7)
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,7,5]=>([(4,6),(5,6)],7)
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>([(5,6)],7)
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[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)
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[3,4,5,6,7,1,2]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[2,3,5,6,7,1,4]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[1,3,5,6,7,2,4]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[1,4,5,6,7,2,3]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[2,3,4,6,7,1,5]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[1,3,4,6,7,2,5]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[1,2,4,6,7,3,5]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[1,2,5,6,7,3,4]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[2,3,4,5,7,1,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[1,3,4,5,7,2,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[1,2,4,5,7,3,6]=>([(2,6),(3,6),(4,5),(5,6)],7)
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[1,2,3,5,7,4,6]=>([(3,6),(4,5),(5,6)],7)
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[1,2,3,6,7,4,5]=>([(3,5),(3,6),(4,5),(4,6)],7)
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[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)
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[2,4,5,6,7,3,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[1,4,5,6,7,3,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[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)
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[1,3,5,6,7,4,2]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[1,2,5,6,7,4,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[2,3,4,6,7,5,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[1,3,4,6,7,5,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[1,2,4,6,7,5,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[1,2,3,6,7,5,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[2,3,4,5,7,6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[1,3,4,5,7,6,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[1,2,4,5,7,6,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[1,2,3,5,7,6,4]=>([(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>([(4,5),(4,6),(5,6)],7)
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[2,4,6,7,1,3,5]=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[3,4,6,7,1,2,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[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)
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[3,5,6,7,1,2,4]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[4,5,6,7,1,2,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[2,4,5,7,1,3,6]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[3,4,5,7,1,2,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[2,3,5,7,1,4,6]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[1,3,5,7,2,4,6]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[1,4,5,7,2,3,6]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[2,3,6,7,1,4,5]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[1,3,6,7,2,4,5]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[1,4,6,7,2,3,5]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[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)
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[3,5,6,7,2,4,1]=>([(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)
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[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)
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[4,5,6,7,1,3,2]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[2,5,6,7,1,4,3]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[3,5,6,7,1,4,2]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[3,4,6,7,2,5,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[2,4,6,7,3,5,1]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[1,4,6,7,3,5,2]=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[2,5,6,7,3,4,1]=>([(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)
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[1,5,6,7,3,4,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[1,5,6,7,2,4,3]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[2,4,6,7,1,5,3]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[3,4,6,7,1,5,2]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[2,3,6,7,1,5,4]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[1,3,6,7,2,5,4]=>([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[1,4,6,7,2,5,3]=>([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[3,4,5,7,2,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[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)
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[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)
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[2,3,5,7,4,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[1,3,5,7,4,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[1,2,5,7,4,6,3]=>([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[2,3,6,7,4,5,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[1,3,6,7,4,5,2]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[1,2,6,7,4,5,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[1,2,6,7,3,5,4]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[2,4,5,7,1,6,3]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[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)
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[2,3,5,7,1,6,4]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[1,3,5,7,2,6,4]=>([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[1,4,5,7,2,6,3]=>([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[2,3,4,7,1,6,5]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[1,3,4,7,2,6,5]=>([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[1,2,4,7,3,6,5]=>([(2,5),(3,4),(3,6),(4,6),(5,6)],7)
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[1,2,5,7,3,6,4]=>([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>([(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)
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>([(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)
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[2,5,6,7,4,3,1]=>([(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)
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[1,5,6,7,4,3,2]=>([(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)
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[3,4,6,7,5,2,1]=>([(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)
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[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)
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[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)
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[1,3,6,7,5,4,2]=>([(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]]=>[6,5,4,1,2,3,7]=>[1,2,6,7,5,4,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[3,4,5,7,6,2,1]=>([(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)
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[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)
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[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)
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[2,3,5,7,6,4,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[1,2,5,7,6,4,3]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[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)
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[1,3,4,7,6,5,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[3,5,7,2,4,6,1]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[4,5,7,2,3,6,1]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[4,5,7,1,3,6,2]=>([(0,5),(0,6),(1,2),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[2,5,7,1,4,6,3]=>([(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[3,5,7,1,4,6,2]=>([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[3,6,7,2,4,5,1]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[4,6,7,2,3,5,1]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[4,6,7,1,3,5,2]=>([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[5,6,7,2,3,4,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[5,6,7,1,3,4,2]=>([(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)
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[5,6,7,1,2,4,3]=>([(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)],7)
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[2,6,7,1,4,5,3]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[3,6,7,1,4,5,2]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[2,6,7,1,3,5,4]=>([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[3,6,7,1,2,5,4]=>([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[4,6,7,1,2,5,3]=>([(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)
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[2,4,7,1,3,6,5]=>([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[3,4,7,1,2,6,5]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[2,5,7,1,3,6,4]=>([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[3,5,7,1,2,6,4]=>([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[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)
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[3,6,7,2,5,1,4]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[4,6,7,2,5,1,3]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[4,6,7,3,5,1,2]=>([(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)
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[5,6,7,2,4,1,3]=>([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[5,6,7,3,4,1,2]=>([(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)
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[3,5,7,2,6,1,4]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[4,5,7,2,6,1,3]=>([(0,3),(0,4),(0,6),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[4,5,7,3,6,1,2]=>([(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)
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[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)
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[3,5,7,4,6,1,2]=>([(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)],7)
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[3,4,7,2,6,1,5]=>([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[2,4,7,3,6,1,5]=>([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[1,4,7,3,6,2,5]=>([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[2,5,7,3,6,1,4]=>([(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[1,5,7,3,6,2,4]=>([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[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)
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[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)
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[3,6,7,4,5,1,2]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[2,6,7,3,5,1,4]=>([(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[1,6,7,3,5,2,4]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[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],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[4,6,7,3,5,2,1]=>([(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)
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[5,6,7,3,4,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[5,6,7,2,4,3,1]=>([(0,1),(0,2),(0,3),(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],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[5,6,7,1,4,3,2]=>([(0,1),(0,2),(0,3),(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)
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[3,6,7,2,5,4,1]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[4,6,7,2,5,3,1]=>([(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),(4,6),(5,6)],7)
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[4,6,7,1,5,3,2]=>([(0,1),(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[2,6,7,1,5,4,3]=>([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[3,6,7,1,5,4,2]=>([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[4,5,7,3,6,2,1]=>([(0,4),(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)
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[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)
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[2,5,7,4,6,3,1]=>([(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)
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[1,5,7,4,6,3,2]=>([(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],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[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)
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[2,6,7,4,5,3,1]=>([(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)
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[1,6,7,4,5,3,2]=>([(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)
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[2,6,7,3,5,4,1]=>([(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)
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[1,6,7,3,5,4,2]=>([(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)
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[1,6,7,2,5,4,3]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[3,5,7,2,6,4,1]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[4,5,7,2,6,3,1]=>([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[4,5,7,1,6,3,2]=>([(0,2),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[2,5,7,1,6,4,3]=>([(0,3),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[3,5,7,1,6,4,2]=>([(0,3),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[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)
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[2,4,7,3,6,5,1]=>([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[1,4,7,3,6,5,2]=>([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[2,5,7,3,6,4,1]=>([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[1,5,7,3,6,4,2]=>([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[1,5,7,2,6,4,3]=>([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[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)
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[3,4,7,1,6,5,2]=>([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[2,3,7,1,6,5,4]=>([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[1,3,7,2,6,5,4]=>([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[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)
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[5,6,7,4,3,2,1]=>([(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)
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[4,6,7,5,3,2,1]=>([(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)
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[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)
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[2,6,7,5,4,3,1]=>([(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)
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[1,6,7,5,4,3,2]=>([(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)
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[4,5,7,6,3,2,1]=>([(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)
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[3,5,7,6,4,2,1]=>([(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)
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[2,5,7,6,4,3,1]=>([(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)
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[1,5,7,6,4,3,2]=>([(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)
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[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)
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[2,4,7,6,5,3,1]=>([(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)
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[1,4,7,6,5,3,2]=>([(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)
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[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)
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[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)
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[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)
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[4,7,3,6,2,5,1]=>([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[5,7,3,6,2,4,1]=>([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[5,7,4,6,2,3,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(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)
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[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)
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[6,7,3,5,2,4,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(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],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[6,7,4,5,2,3,1]=>([(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),(4,6),(5,6)],7)
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[6,7,4,5,1,3,2]=>([(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)
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[6,7,2,5,1,4,3]=>([(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)
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[6,7,3,5,1,4,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(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],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[3,7,2,6,1,5,4]=>([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[4,7,2,6,1,5,3]=>([(0,1),(0,4),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[4,7,3,6,1,5,2]=>([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[5,7,2,6,1,4,3]=>([(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)
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[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],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[5,7,4,6,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(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)
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[6,7,4,5,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[6,7,3,5,4,2,1]=>([(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),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[6,7,2,5,4,3,1]=>([(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),(4,6),(5,6)],7)
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[6,7,1,5,4,3,2]=>([(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)
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[4,7,3,6,5,2,1]=>([(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),(5,6)],7)
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[5,7,3,6,4,2,1]=>([(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)
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[5,7,2,6,4,3,1]=>([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[5,7,1,6,4,3,2]=>([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[3,7,2,6,5,4,1]=>([(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),(5,6)],7)
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[4,7,2,6,5,3,1]=>([(0,1),(0,5),(0,6),(1,4),(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],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[4,7,1,6,5,3,2]=>([(0,1),(0,6),(1,4),(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],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[2,7,1,6,5,4,3]=>([(0,1),(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],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[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)
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[6,7,5,4,3,2,1]=>([(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)
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[5,7,6,4,3,2,1]=>([(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)
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[4,7,6,5,3,2,1]=>([(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)
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[3,7,6,5,4,2,1]=>([(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)
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[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)
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[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],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[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)
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([],8)
[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[1,3,4,5,6,7,8,2]=>([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[1,2,4,5,6,7,8,3]=>([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,6,7,8,4]=>([(3,7),(4,7),(5,7),(6,7)],8)
[[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,7,8,5]=>([(4,7),(5,7),(6,7)],8)
[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,8,6]=>([(5,7),(6,7)],8)
[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>([(6,7)],8)
[[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[2,4,5,6,7,8,1,3]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[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)
[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[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)
[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[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)
[[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[1,4,5,6,7,8,2,3]=>([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,4,5,7,8],[2,6]]=>[2,6,1,3,4,5,7,8]=>[2,3,4,6,7,8,1,5]=>([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,5,7,8],[4,6]]=>[4,6,1,2,3,5,7,8]=>[1,2,4,6,7,8,3,5]=>([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[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)
[[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[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)
[[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[1,3,4,5,7,8,2,6]=>([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[1,2,4,5,7,8,3,6]=>([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[1,2,3,5,7,8,4,6]=>([(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[1,2,3,6,7,8,4,5]=>([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[2,3,4,5,6,8,1,7]=>([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[1,3,4,5,6,8,2,7]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[1,2,4,5,6,8,3,7]=>([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[1,2,3,5,6,8,4,7]=>([(3,7),(4,7),(5,6),(6,7)],8)
[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[1,2,3,4,6,8,5,7]=>([(4,7),(5,6),(6,7)],8)
[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,7,8,5,6]=>([(4,6),(4,7),(5,6),(5,7)],8)
[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[3,4,5,6,7,8,2,1]=>([(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)
[[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[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)
[[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[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)
[[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[2,3,5,6,7,8,4,1]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[1,3,5,6,7,8,4,2]=>([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[1,2,5,6,7,8,4,3]=>([(2,6),(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]]=>[6,2,1,3,4,5,7,8]=>[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)
[[1,2,4,5,7,8],[3],[6]]=>[6,3,1,2,4,5,7,8]=>[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)
[[1,2,3,5,7,8],[4],[6]]=>[6,4,1,2,3,5,7,8]=>[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)
[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,7,8,5,4]=>([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,5,6,8],[2],[7]]=>[7,2,1,3,4,5,6,8]=>[2,3,4,5,7,8,6,1]=>([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[1,3,4,5,7,8,6,2]=>([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,5,6,8],[4],[7]]=>[7,4,1,2,3,5,6,8]=>[1,2,4,5,7,8,6,3]=>([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[1,2,3,5,7,8,6,4]=>([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4,5,8],[6],[7]]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,8,6,5]=>([(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,5,6,7],[2],[8]]=>[8,2,1,3,4,5,6,7]=>[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)
[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[1,3,4,5,6,8,7,2]=>([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[1,2,4,5,6,8,7,3]=>([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[1,2,3,5,6,8,7,4]=>([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,6,8,7,5]=>([(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>([(5,6),(5,7),(6,7)],8)
[[1,3,5,7,8],[2,4,6]]=>[2,4,6,1,3,5,7,8]=>[2,4,6,7,8,1,3,5]=>([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,4,7,8],[3,5,6]]=>[3,5,6,1,2,4,7,8]=>[3,5,6,7,8,1,2,4]=>([(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)],8)
[[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[4,5,6,7,8,1,2,3]=>([(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)],8)
[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[1,3,5,7,8,2,4,6]=>([(1,7),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[1,3,4,5,8],[2,6,7]]=>[2,6,7,1,3,4,5,8]=>[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)
[[1,2,4,5,8],[3,6,7]]=>[3,6,7,1,2,4,5,8]=>[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)
[[1,2,3,5,8],[4,6,7]]=>[4,6,7,1,2,3,5,8]=>[1,4,6,7,8,2,3,5]=>([(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[1,5,6,7,8,2,3,4]=>([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[1,3,5,6,7],[2,4,8]]=>[2,4,8,1,3,5,6,7]=>[2,4,5,6,8,1,3,7]=>([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[3,4,5,6,8,1,2,7]=>([(0,5),(1,6),(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]]=>[2,5,8,1,3,4,6,7]=>[2,3,5,6,8,1,4,7]=>([(0,7),(1,7),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[1,4,5,6,8,2,3,7]=>([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,4,5,7],[2,6,8]]=>[2,6,8,1,3,4,5,7]=>[2,3,4,6,8,1,5,7]=>([(0,7),(1,7),(2,7),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
[[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[1,3,4,6,8,2,5,7]=>([(1,7),(2,7),(3,6),(4,5),(4,7),(5,6),(6,7)],8)
[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[1,2,4,6,8,3,5,7]=>([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[1,2,5,6,8,3,4,7]=>([(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[2,3,4,7,8,1,5,6]=>([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[1,3,4,7,8,2,5,6]=>([(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,3,5,6],[4,7,8]]=>[4,7,8,1,2,3,5,6]=>[1,2,4,7,8,3,5,6]=>([(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[1,2,5,7,8,3,4,6]=>([(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[1,2,6,7,8,3,4,5]=>([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[3,5,6,7,8,2,4,1]=>([(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),(5,7),(6,7)],8)
[[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[4,5,6,7,8,2,3,1]=>([(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),(5,7),(6,7)],8)
[[1,2,6,7,8],[3,5],[4]]=>[4,3,5,1,2,6,7,8]=>[4,5,6,7,8,1,3,2]=>([(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),(6,7)],8)
[[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>[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)
[[1,4,5,7,8],[2,6],[3]]=>[3,2,6,1,4,5,7,8]=>[3,4,6,7,8,2,5,1]=>([(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),(5,7),(6,7)],8)
[[1,3,5,7,8],[2,6],[4]]=>[4,2,6,1,3,5,7,8]=>[2,4,6,7,8,3,5,1]=>([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,4,7,8],[3,6],[5]]=>[5,3,6,1,2,4,7,8]=>[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)
[[1,3,5,7,8],[2,4],[6]]=>[6,2,4,1,3,5,7,8]=>[2,4,6,7,8,1,5,3]=>([(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)],8)
[[1,3,4,6,8],[2,7],[5]]=>[5,2,7,1,3,4,6,8]=>[2,3,5,7,8,4,6,1]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[1,2,5,7,8,4,6,3]=>([(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[1,2,6,7,8,4,5,3]=>([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[1,2,6,7,8,3,5,4]=>([(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[3,4,5,7,8,1,6,2]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)
[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[1,2,5,7,8,3,6,4]=>([(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[3,4,5,6,8,2,7,1]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5,6,7],[2,8],[4]]=>[4,2,8,1,3,5,6,7]=>[2,4,5,6,8,3,7,1]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,6,7],[2,8],[5]]=>[5,2,8,1,3,4,6,7]=>[2,3,5,6,8,4,7,1]=>([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[1,2,5,6,8,4,7,3]=>([(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[2,3,4,6,8,5,7,1]=>([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[1,2,4,6,8,5,7,3]=>([(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[1,2,3,6,8,5,7,4]=>([(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[2,3,4,7,8,5,6,1]=>([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,3,5,6],[4,8],[7]]=>[7,4,8,1,2,3,5,6]=>[1,2,4,7,8,5,6,3]=>([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[1,2,3,7,8,5,6,4]=>([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[1,2,3,7,8,4,6,5]=>([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,5,6,7],[2,4],[8]]=>[8,2,4,1,3,5,6,7]=>[2,4,5,6,8,1,7,3]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7)],8)
[[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[3,4,5,6,8,1,7,2]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
[[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[1,2,5,6,8,3,7,4]=>([(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
[[1,2,4,5,6],[3,7],[8]]=>[8,3,7,1,2,4,5,6]=>[1,3,4,5,8,2,7,6]=>([(1,7),(2,7),(3,7),(4,5),(4,6),(5,6),(6,7)],8)
[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[1,2,3,5,8,4,7,6]=>([(3,6),(4,5),(4,7),(5,7),(6,7)],8)
[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[1,2,3,6,8,4,7,5]=>([(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[4,5,6,7,8,3,2,1]=>([(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)
[[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[3,5,6,7,8,4,2,1]=>([(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)
[[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[2,5,6,7,8,4,3,1]=>([(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)
[[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[1,5,6,7,8,4,3,2]=>([(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)
[[1,4,5,7,8],[2],[3],[6]]=>[6,3,2,1,4,5,7,8]=>[3,4,6,7,8,5,2,1]=>([(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)
[[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>[2,4,6,7,8,5,3,1]=>([(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)
[[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[1,4,6,7,8,5,3,2]=>([(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)
[[1,2,3,7,8],[4],[5],[6]]=>[6,5,4,1,2,3,7,8]=>[1,2,6,7,8,5,4,3]=>([(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)
[[1,4,5,6,8],[2],[3],[7]]=>[7,3,2,1,4,5,6,8]=>[3,4,5,7,8,6,2,1]=>([(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)
[[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[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)
[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,8,6,5,4]=>([(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]]=>[8,3,2,1,4,5,6,7]=>[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)
[[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[2,4,5,6,8,7,3,1]=>([(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)
[[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[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)
[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[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)
[[1,2,3,6,7],[4],[5],[8]]=>[8,5,4,1,2,3,6,7]=>[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)
[[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[1,2,4,6,8,7,5,3]=>([(2,7),(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]]=>[8,6,5,1,2,3,4,7]=>[1,2,3,6,8,7,5,4]=>([(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[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)
[[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[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)
[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[1,2,3,5,8,7,6,4]=>([(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[2,4,6,8,1,3,5,7]=>([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[3,4,6,8,1,2,5,7]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[1,3,4,7],[2,5,6,8]]=>[2,5,6,8,1,3,4,7]=>[2,5,6,8,1,3,4,7]=>([(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[3,5,6,8,1,2,4,7]=>([(0,7),(1,5),(1,6),(2,3),(2,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[4,5,6,8,1,2,3,7]=>([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[1,3,5,6],[2,4,7,8]]=>[2,4,7,8,1,3,5,6]=>[2,4,7,8,1,3,5,6]=>([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,5,6],[3,4,7,8]]=>[3,4,7,8,1,2,5,6]=>[3,4,7,8,1,2,5,6]=>([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,4,6],[2,5,7,8]]=>[2,5,7,8,1,3,4,6]=>[2,5,7,8,1,3,4,6]=>([(0,7),(1,5),(1,6),(2,3),(2,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[3,5,7,8,1,2,4,6]=>([(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[4,5,7,8,1,2,3,6]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[2,6,7,8,1,3,4,5]=>([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[3,6,7,8,1,2,4,5]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[4,6,7,8,1,2,3,5]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[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)
[[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[3,5,7,8,2,4,6,1]=>([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,6,8],[2,4,7],[5]]=>[5,2,4,7,1,3,6,8]=>[2,5,7,8,1,4,6,3]=>([(0,6),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,6,8],[3,4,7],[5]]=>[5,3,4,7,1,2,6,8]=>[3,5,7,8,1,4,6,2]=>([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[4,6,7,8,2,3,5,1]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(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)
[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[5,6,7,8,2,3,4,1]=>([(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),(4,7),(5,7),(6,7)],8)
[[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[5,6,7,8,1,3,4,2]=>([(0,1),(0,2),(0,3),(0,4),(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)
[[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[5,6,7,8,1,2,4,3]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,8],[2,5,7],[6]]=>[6,2,5,7,1,3,4,8]=>[2,6,7,8,1,3,5,4]=>([(0,7),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[1,2,4,8],[3,5,7],[6]]=>[6,3,5,7,1,2,4,8]=>[3,6,7,8,1,2,5,4]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,5,8],[3,4,6],[7]]=>[7,3,4,6,1,2,5,8]=>[3,4,7,8,1,2,6,5]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,4,8],[3,5,6],[7]]=>[7,3,5,6,1,2,4,8]=>[3,5,7,8,1,2,6,4]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[3,5,6,8,2,4,7,1]=>([(0,6),(0,7),(1,4),(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)
[[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[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)
[[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>[4,5,6,8,1,3,7,2]=>([(0,5),(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)
[[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[2,5,6,8,1,4,7,3]=>([(0,6),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
[[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[3,4,6,8,2,5,7,1]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[2,4,6,8,3,5,7,1]=>([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,5,7],[3,6,8],[4]]=>[4,3,6,8,1,2,5,7]=>[1,4,6,8,3,5,7,2]=>([(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[2,4,6,8,1,5,7,3]=>([(0,6),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
[[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[2,3,6,8,1,5,7,4]=>([(0,7),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,7],[4,5,8],[6]]=>[6,4,5,8,1,2,3,7]=>[1,4,6,8,2,5,7,3]=>([(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)
[[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[3,4,7,8,2,5,6,1]=>([(0,6),(0,7),(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)
[[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[1,5,7,8,2,4,6,3]=>([(1,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>[1,6,7,8,3,4,5,2]=>([(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)
[[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[1,6,7,8,2,4,5,3]=>([(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)
[[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[1,6,7,8,2,3,5,4]=>([(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)],8)
[[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[1,5,7,8,2,3,6,4]=>([(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)
[[1,3,5,7],[2,4,6],[8]]=>[8,2,4,6,1,3,5,7]=>[2,4,6,8,1,3,7,5]=>([(0,7),(1,4),(1,7),(2,5),(2,6),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
[[1,3,4,7],[2,5,6],[8]]=>[8,2,5,6,1,3,4,7]=>[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)
[[1,2,4,7],[3,5,6],[8]]=>[8,3,5,6,1,2,4,7]=>[3,5,6,8,1,2,7,4]=>([(0,5),(0,6),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>[4,5,6,8,1,2,7,3]=>([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
[[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[2,4,5,8,1,3,7,6]=>([(0,7),(1,2),(1,6),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
[[1,3,4,6],[2,5,7],[8]]=>[8,2,5,7,1,3,4,6]=>[2,3,5,8,1,4,7,6]=>([(0,7),(1,7),(2,5),(2,7),(3,4),(3,6),(4,6),(5,6),(6,7)],8)
[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[1,3,5,8,2,4,7,6]=>([(1,6),(2,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
[[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[2,3,6,8,1,4,7,5]=>([(0,6),(1,6),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)
[[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>[1,4,6,8,2,3,7,5]=>([(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[1,5,6,8,2,3,7,4]=>([(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
[[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[4,6,7,8,3,5,1,2]=>([(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)
[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[5,6,7,8,3,4,1,2]=>([(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)
[[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[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)
[[1,3,6,8],[2,4],[5,7]]=>[5,7,2,4,1,3,6,8]=>[2,5,7,8,4,6,1,3]=>([(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)
[[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[3,4,7,8,2,6,1,5]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,5,8],[3,6],[4,7]]=>[4,7,3,6,1,2,5,8]=>[1,4,7,8,3,6,2,5]=>([(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,8],[2,6],[5,7]]=>[5,7,2,6,1,3,4,8]=>[2,5,7,8,3,6,1,4]=>([(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)
[[1,2,4,8],[3,6],[5,7]]=>[5,7,3,6,1,2,4,8]=>[1,5,7,8,3,6,2,4]=>([(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)
[[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[3,5,6,8,4,7,1,2]=>([(0,6),(0,7),(1,5),(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],[2,6],[4,8]]=>[4,8,2,6,1,3,5,7]=>[2,4,6,8,3,7,1,5]=>([(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[1,5,6,8,3,7,2,4]=>([(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
[[1,2,3,7],[4,6],[5,8]]=>[5,8,4,6,1,2,3,7]=>[1,5,6,8,4,7,2,3]=>([(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)
[[1,3,5,7],[2,4],[6,8]]=>[6,8,2,4,1,3,5,7]=>[2,4,6,8,5,7,1,3]=>([(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)
[[1,2,5,7],[3,4],[6,8]]=>[6,8,3,4,1,2,5,7]=>[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)
[[1,2,4,7],[3,5],[6,8]]=>[6,8,3,5,1,2,4,7]=>[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)
[[1,2,3,7],[4,5],[6,8]]=>[6,8,4,5,1,2,3,7]=>[1,4,6,8,5,7,2,3]=>([(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)
[[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[3,4,5,8,2,7,1,6]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[2,4,5,8,3,7,1,6]=>([(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[1,3,5,8,4,7,2,6]=>([(1,7),(2,4),(2,7),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[1,2,5,8,4,7,3,6]=>([(2,5),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[2,3,6,8,4,7,1,5]=>([(0,7),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[2,4,7,8,5,6,1,3]=>([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[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)
[[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[2,3,7,8,5,6,1,4]=>([(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],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[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)
[[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[1,2,7,8,4,6,3,5]=>([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[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)
[[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[4,6,7,8,3,5,2,1]=>([(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),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[5,6,7,8,3,4,2,1]=>([(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),(6,7)],8)
[[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[5,6,7,8,1,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(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)
[[1,3,7,8],[2,5],[4],[6]]=>[6,4,2,5,1,3,7,8]=>[4,6,7,8,2,5,3,1]=>([(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),(4,6),(4,7),(5,7),(6,7)],8)
[[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[2,6,7,8,1,5,4,3]=>([(0,4),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(5,6),(5,7),(6,7)],8)
[[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>[4,5,7,8,3,6,2,1]=>([(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),(5,6),(5,7),(6,7)],8)
[[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[3,5,7,8,4,6,2,1]=>([(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)
[[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[3,6,7,8,4,5,2,1]=>([(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),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[1,6,7,8,4,5,3,2]=>([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[1,6,7,8,3,5,4,2]=>([(1,2),(1,3),(1,4),(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)
[[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[3,5,7,8,2,6,4,1]=>([(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),(5,7),(6,7)],8)
[[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[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)
[[1,3,5,8],[2,6],[4],[7]]=>[7,4,2,6,1,3,5,8]=>[2,4,7,8,3,6,5,1]=>([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[1,5,7,8,3,6,4,2]=>([(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),(5,7),(6,7)],8)
[[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>[1,3,7,8,2,6,5,4]=>([(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)
[[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[4,5,6,8,3,7,2,1]=>([(0,5),(0,6),(0,7),(1,5),(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)
[[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[3,5,6,8,4,7,2,1]=>([(0,6),(0,7),(1,5),(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],[3,8],[4],[5]]=>[5,4,3,8,1,2,6,7]=>[1,5,6,8,4,7,3,2]=>([(1,5),(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)
[[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[3,4,6,8,5,7,2,1]=>([(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)
[[1,3,5,7],[2,8],[4],[6]]=>[6,4,2,8,1,3,5,7]=>[2,4,6,8,5,7,3,1]=>([(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)
[[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[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)
[[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[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)
[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[1,4,7,8,5,6,3,2]=>([(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)
[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[1,3,7,8,5,6,4,2]=>([(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)
[[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[1,2,7,8,5,6,4,3]=>([(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)
[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[1,2,7,8,3,6,5,4]=>([(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[3,4,6,8,2,7,5,1]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[2,4,6,8,3,7,5,1]=>([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[2,4,6,8,1,7,5,3]=>([(0,6),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)
[[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[1,4,6,8,2,7,5,3]=>([(1,4),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
[[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[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)
[[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[1,2,5,8,4,7,6,3]=>([(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[1,3,6,8,4,7,5,2]=>([(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[2,4,5,8,1,7,6,3]=>([(0,6),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7)],8)
[[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[2,3,5,8,1,7,6,4]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(5,7)],8)
[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[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)
[[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[2,3,4,8,1,7,6,5]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[1,3,4,8,2,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[1,2,4,8,3,7,6,5]=>([(2,3),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[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)
[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[5,6,7,8,4,3,2,1]=>([(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),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,7,8],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7,8]=>[2,6,7,8,5,4,3,1]=>([(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)
[[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[1,6,7,8,5,4,3,2]=>([(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)
[[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[3,5,7,8,6,4,2,1]=>([(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)
[[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[2,4,7,8,6,5,3,1]=>([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[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)
[[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[1,2,7,8,6,5,4,3]=>([(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)
[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[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)
[[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[3,5,6,8,7,4,2,1]=>([(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)
[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[2,4,6,8,7,5,3,1]=>([(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)
[[1,2,5,7],[3],[4],[6],[8]]=>[8,6,4,3,1,2,5,7]=>[1,4,6,8,7,5,3,2]=>([(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)
[[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[3,4,5,8,7,6,2,1]=>([(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)
[[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[2,3,5,8,7,6,4,1]=>([(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)
[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[1,3,5,8,7,6,4,2]=>([(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)
[[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[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)
[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[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)
[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[1,2,4,8,7,6,5,3]=>([(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>([(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,4,7],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7]=>[3,6,8,2,5,7,1,4]=>([(0,5),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
[[1,2,7],[3,5,8],[4,6]]=>[4,6,3,5,8,1,2,7]=>[4,6,8,3,5,7,1,2]=>([(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),(4,5),(4,6),(4,7),(5,6),(5,7)],8)
[[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[5,6,8,2,4,7,1,3]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
[[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[4,7,8,3,5,6,1,2]=>([(0,5),(0,6),(0,7),(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),(4,7),(5,6),(5,7)],8)
[[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[5,7,8,2,4,6,1,3]=>([(0,3),(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,4,5],[2,6,8],[3,7]]=>[3,7,2,6,8,1,4,5]=>[3,7,8,2,4,6,1,5]=>([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[4,7,8,1,3,6,2,5]=>([(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)
[[1,3,4],[2,6,8],[5,7]]=>[5,7,2,6,8,1,3,4]=>[5,7,8,2,3,6,1,4]=>([(0,1),(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[5,7,8,1,4,6,2,3]=>([(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)
[[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[6,7,8,1,3,5,2,4]=>([(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)],8)
[[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[6,7,8,1,4,5,2,3]=>([(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),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[3,5,8,2,4,7,1,6]=>([(0,4),(0,6),(1,5),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[4,5,8,2,3,7,1,6]=>([(0,3),(0,6),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[4,5,8,1,3,7,2,6]=>([(0,4),(0,7),(1,2),(1,3),(1,7),(2,5),(2,6),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[3,6,8,2,4,7,1,5]=>([(0,5),(0,7),(1,2),(1,6),(1,7),(2,4),(2,6),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4],[3,6,7],[5,8]]=>[5,8,3,6,7,1,2,4]=>[5,6,8,1,3,7,2,4]=>([(0,4),(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)
[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[2,6,8,1,5,7,3,4]=>([(0,2),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,4],[3,5,7],[6,8]]=>[6,8,3,5,7,1,2,4]=>[3,6,8,1,5,7,2,4]=>([(0,2),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)
[[1,2,3],[4,5,7],[6,8]]=>[6,8,4,5,7,1,2,3]=>[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)
[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[2,7,8,1,4,6,3,5]=>([(0,3),(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)],8)
[[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[2,7,8,1,5,6,3,4]=>([(0,1),(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],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[3,7,8,1,5,6,2,4]=>([(0,1),(0,7),(1,5),(1,6),(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],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[4,7,8,1,5,6,2,3]=>([(0,1),(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[4,6,8,3,5,7,2,1]=>([(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),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>[3,6,8,2,5,7,4,1]=>([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[4,6,8,1,5,7,3,2]=>([(0,2),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[2,6,8,1,5,7,4,3]=>([(0,2),(1,5),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[4,7,8,3,5,6,2,1]=>([(0,5),(0,6),(0,7),(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),(4,7),(5,6),(5,7),(6,7)],8)
[[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[5,7,8,3,4,6,2,1]=>([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(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)
[[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[5,7,8,2,4,6,3,1]=>([(0,1),(0,5),(0,6),(0,7),(1,3),(1,4),(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)
[[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>[5,7,8,1,4,6,3,2]=>([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(1,7),(2,3),(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],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[6,7,8,3,4,5,2,1]=>([(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)
[[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>[6,7,8,2,4,5,3,1]=>([(0,3),(0,4),(0,5),(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)
[[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[6,7,8,1,4,5,3,2]=>([(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)
[[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[6,7,8,2,3,5,4,1]=>([(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),(4,7),(5,7),(6,7)],8)
[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[6,7,8,1,2,5,4,3]=>([(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)
[[1,3,4],[2,6,8],[5],[7]]=>[7,5,2,6,8,1,3,4]=>[5,7,8,2,3,6,4,1]=>([(0,1),(0,2),(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4],[3,5,8],[6],[7]]=>[7,6,3,5,8,1,2,4]=>[3,7,8,1,2,6,5,4]=>([(0,1),(0,2),(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)
[[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[4,7,8,1,2,6,5,3]=>([(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)
[[1,4,6],[2,5,7],[3],[8]]=>[8,3,2,5,7,1,4,6]=>[3,5,8,2,4,7,6,1]=>([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[4,5,8,2,3,7,6,1]=>([(0,1),(0,6),(0,7),(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)
[[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[2,5,8,1,4,7,6,3]=>([(0,5),(1,4),(1,5),(1,6),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)
[[1,4,5],[2,6,7],[3],[8]]=>[8,3,2,6,7,1,4,5]=>[3,6,8,2,4,7,5,1]=>([(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5],[2,6,7],[4],[8]]=>[8,4,2,6,7,1,3,5]=>[4,6,8,2,3,7,5,1]=>([(0,3),(0,4),(0,7),(1,5),(1,6),(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)
[[1,2,3],[4,6,7],[5],[8]]=>[8,5,4,6,7,1,2,3]=>[5,6,8,1,2,7,4,3]=>([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5],[2,4,7],[6],[8]]=>[8,6,2,4,7,1,3,5]=>[2,6,8,1,4,7,5,3]=>([(0,3),(1,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[3,6,8,1,2,7,5,4]=>([(0,2),(0,3),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
[[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>[4,6,8,1,2,7,5,3]=>([(0,2),(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[2,4,8,1,3,7,6,5]=>([(0,6),(1,2),(1,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)
[[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[3,4,8,1,2,7,6,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)
[[1,2,4],[3,5,6],[7],[8]]=>[8,7,3,5,6,1,2,4]=>[3,5,8,1,2,7,6,4]=>([(0,4),(0,5),(1,4),(1,5),(1,6),(2,3),(2,6),(2,7),(3,6),(3,7),(4,7),(5,7),(6,7)],8)
[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[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)
[[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[4,7,8,3,6,2,5,1]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(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)
[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[4,6,8,3,7,2,5,1]=>([(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[3,6,8,5,7,1,4,2]=>([(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)],8)
[[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[4,5,8,3,7,2,6,1]=>([(0,4),(0,6),(0,7),(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)
[[1,3,6],[2,7],[4,8],[5]]=>[5,4,8,2,7,1,3,6]=>[2,5,8,4,7,3,6,1]=>([(0,7),(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)
[[1,2,6],[3,7],[4,8],[5]]=>[5,4,8,3,7,1,2,6]=>[1,5,8,4,7,3,6,2]=>([(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)
[[1,4,5],[2,7],[3,8],[6]]=>[6,3,8,2,7,1,4,5]=>[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)
[[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[3,7,8,5,6,2,4,1]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(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)
[[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[4,7,8,5,6,1,3,2]=>([(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),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)
[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[2,7,8,5,6,1,4,3]=>([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(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)
[[1,2,6],[3,4],[5,8],[7]]=>[7,5,8,3,4,1,2,6]=>[3,7,8,5,6,1,4,2]=>([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(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)
[[1,4,5],[2,6],[3,8],[7]]=>[7,3,8,2,6,1,4,5]=>[3,7,8,4,6,2,5,1]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(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)
[[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[2,7,8,5,6,3,4,1]=>([(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),(5,7),(6,7)],8)
[[1,2,4],[3,6],[5,8],[7]]=>[7,5,8,3,6,1,2,4]=>[1,7,8,5,6,3,4,2]=>([(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)
[[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[3,6,8,2,7,1,5,4]=>([(0,5),(0,7),(1,2),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[5,6,8,3,7,1,4,2]=>([(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),(4,7),(6,7)],8)
[[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[3,5,8,2,7,1,6,4]=>([(0,5),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,6),(3,4),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
[[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[2,5,8,4,7,1,6,3]=>([(0,7),(1,3),(1,5),(1,6),(2,4),(2,6),(2,7),(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]]=>[8,3,7,2,6,1,4,5]=>[3,4,8,2,7,1,6,5]=>([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[2,4,8,3,7,1,6,5]=>([(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[1,4,8,3,7,2,6,5]=>([(1,4),(1,6),(2,3),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[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)
[[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[2,6,8,3,7,1,5,4]=>([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(4,7),(5,7),(6,7)],8)
[[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[1,6,8,3,7,2,5,4]=>([(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],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[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)
[[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[5,7,8,4,6,3,2,1]=>([(0,4),(0,5),(0,6),(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),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[6,7,8,2,5,4,3,1]=>([(0,1),(0,2),(0,3),(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)
[[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[6,7,8,1,5,4,3,2]=>([(0,1),(0,2),(0,3),(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)
[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[5,6,8,4,7,3,2,1]=>([(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)
[[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[3,6,8,5,7,4,2,1]=>([(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),(5,6),(5,7),(6,7)],8)
[[1,3,7],[2,8],[4],[5],[6]]=>[6,5,4,2,8,1,3,7]=>[2,6,8,5,7,4,3,1]=>([(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)
[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[1,6,8,5,7,4,3,2]=>([(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)
[[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[3,7,8,5,6,4,2,1]=>([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[1,7,8,3,6,5,4,2]=>([(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),(5,7),(6,7)],8)
[[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[4,6,8,2,7,5,3,1]=>([(0,3),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[2,6,8,1,7,5,4,3]=>([(0,1),(1,3),(1,7),(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)
[[1,2,7],[3,4],[5],[6],[8]]=>[8,6,5,3,4,1,2,7]=>[3,6,8,1,7,5,4,2]=>([(0,1),(0,7),(1,3),(1,6),(2,4),(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)
[[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[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)
[[1,2,5],[3,7],[4],[6],[8]]=>[8,6,4,3,7,1,2,5]=>[1,6,8,4,7,5,3,2]=>([(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)
[[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[1,6,8,2,7,5,4,3]=>([(1,3),(1,7),(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)
[[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[3,5,8,2,7,6,4,1]=>([(0,4),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[3,5,8,1,7,6,4,2]=>([(0,2),(0,7),(1,2),(1,5),(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],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[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)
[[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[2,4,8,3,7,6,5,1]=>([(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],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[1,4,8,3,7,6,5,2]=>([(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)
[[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[2,5,8,3,7,6,4,1]=>([(0,7),(1,2),(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)
[[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[1,5,8,3,7,6,4,2]=>([(1,2),(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)
[[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[1,5,8,2,7,6,4,3]=>([(1,2),(1,7),(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)
[[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[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)
[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[1,3,8,2,7,6,5,4]=>([(1,2),(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],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[6,7,8,5,4,3,2,1]=>([(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),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[5,7,8,6,4,3,2,1]=>([(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],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[4,7,8,6,5,3,2,1]=>([(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)
[[1,4,8],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4,8]=>[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)
[[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[2,7,8,6,5,4,3,1]=>([(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)
[[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[1,7,8,6,5,4,3,2]=>([(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)
[[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[5,6,8,7,4,3,2,1]=>([(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),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[4,6,8,7,5,3,2,1]=>([(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)
[[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[3,6,8,7,5,4,2,1]=>([(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),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[2,6,8,7,5,4,3,1]=>([(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],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[1,6,8,7,5,4,3,2]=>([(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)
[[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[4,5,8,7,6,3,2,1]=>([(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)
[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[3,5,8,7,6,4,2,1]=>([(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)
[[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[1,5,8,7,6,4,3,2]=>([(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)
[[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[3,4,8,7,6,5,2,1]=>([(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)
[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[2,4,8,7,6,5,3,1]=>([(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)
[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[1,4,8,7,6,5,3,2]=>([(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)
[[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[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)
[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[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)
[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[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)
[[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[4,8,3,7,2,6,1,5]=>([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(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],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[5,8,3,7,2,6,1,4]=>([(0,1),(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(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],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[5,8,4,7,2,6,1,3]=>([(0,2),(0,3),(0,5),(0,7),(1,4),(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],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[5,8,4,7,3,6,1,2]=>([(0,3),(0,5),(0,6),(0,7),(1,2),(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],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[6,8,3,7,2,5,1,4]=>([(0,2),(0,3),(0,5),(0,7),(1,4),(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)
[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[6,8,4,7,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(1,2),(1,4),(1,5),(1,6),(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],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[6,8,4,7,3,5,1,2]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(1,2),(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)
[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[6,8,5,7,2,4,1,3]=>([(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)
[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[6,8,5,7,3,4,1,2]=>([(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)],8)
[[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[7,8,3,6,2,5,1,4]=>([(0,3),(0,5),(0,6),(0,7),(1,2),(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)
[[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[7,8,4,6,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(1,2),(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)
[[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[7,8,4,6,3,5,1,2]=>([(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)],8)
[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[7,8,5,6,2,4,1,3]=>([(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)],8)
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[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],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[5,8,4,7,3,6,2,1]=>([(0,3),(0,5),(0,6),(0,7),(1,2),(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)
[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[6,8,4,7,3,5,2,1]=>([(0,1),(0,3),(0,5),(0,6),(0,7),(1,2),(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)
[[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[6,8,5,7,3,4,2,1]=>([(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)
[[1,2],[3,7],[4,8],[5],[6]]=>[6,5,4,8,3,7,1,2]=>[6,8,5,7,1,4,3,2]=>([(0,1),(0,2),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[7,8,5,6,3,4,2,1]=>([(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),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[7,8,5,6,2,4,3,1]=>([(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),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)
[[1,4],[2,5],[3,8],[6],[7]]=>[7,6,3,8,2,5,1,4]=>[7,8,3,6,2,5,4,1]=>([(0,3),(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),(5,7),(6,7)],8)
[[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[7,8,2,6,1,5,4,3]=>([(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)
[[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[7,8,3,6,1,5,4,2]=>([(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),(4,7),(5,6),(5,7)],8)
[[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[5,8,3,7,2,6,4,1]=>([(0,1),(0,4),(0,6),(0,7),(1,3),(1,4),(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],[2,6],[4,7],[5],[8]]=>[8,5,4,7,2,6,1,3]=>[5,8,4,7,2,6,3,1]=>([(0,2),(0,3),(0,6),(0,7),(1,4),(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),(5,7),(6,7)],8)
[[1,2],[3,6],[4,7],[5],[8]]=>[8,5,4,7,3,6,1,2]=>[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)
[[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[6,8,3,7,2,5,4,1]=>([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[6,8,4,7,2,5,3,1]=>([(0,1),(0,3),(0,4),(0,6),(0,7),(1,2),(1,4),(1,5),(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],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[6,8,4,7,1,5,3,2]=>([(0,2),(0,3),(0,4),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[3,8,2,7,1,6,5,4]=>([(0,1),(0,5),(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)
[[1,3],[2,5],[4,6],[7],[8]]=>[8,7,4,6,2,5,1,3]=>[4,8,2,7,1,6,5,3]=>([(0,1),(0,4),(0,6),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)
[[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[4,8,3,7,1,6,5,2]=>([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)
[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[5,8,2,7,1,6,4,3]=>([(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)
[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[5,8,3,7,1,6,4,2]=>([(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)
[[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[6,8,5,7,4,3,2,1]=>([(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),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[7,8,5,6,4,3,2,1]=>([(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)
[[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[7,8,1,6,5,4,3,2]=>([(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)
[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[5,8,4,7,6,3,2,1]=>([(0,3),(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)
[[1,3],[2,7],[4],[5],[6],[8]]=>[8,6,5,4,2,7,1,3]=>[6,8,2,7,5,4,3,1]=>([(0,2),(0,6),(0,7),(1,3),(1,4),(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),(5,7),(6,7)],8)
[[1,2],[3,7],[4],[5],[6],[8]]=>[8,6,5,4,3,7,1,2]=>[6,8,1,7,5,4,3,2]=>([(0,2),(0,7),(1,3),(1,4),(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),(5,6),(5,7),(6,7)],8)
[[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[4,8,3,7,6,5,2,1]=>([(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),(6,7)],8)
[[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[5,8,3,7,6,4,2,1]=>([(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)
[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[5,8,2,7,6,4,3,1]=>([(0,1),(0,6),(0,7),(1,4),(1,5),(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],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[3,8,2,7,6,5,4,1]=>([(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),(6,7)],8)
[[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[4,8,2,7,6,5,3,1]=>([(0,1),(0,6),(0,7),(1,5),(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],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[2,8,1,7,6,5,4,3]=>([(0,1),(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]]=>[8,7,6,5,3,4,1,2]=>[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],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[7,8,6,5,4,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(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],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[6,8,7,5,4,3,2,1]=>([(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)
[[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[5,8,7,6,4,3,2,1]=>([(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),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[4,8,7,6,5,3,2,1]=>([(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)
[[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[3,8,7,6,5,4,2,1]=>([(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)
[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[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)
[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[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],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[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)
[[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[2,4,6,8,10,1,3,5,7,9]=>([(0,9),(1,8),(2,7),(2,8),(3,6),(3,9),(4,5),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3,5,7,8],[2,4,6,9,10]]=>[2,4,6,9,10,1,3,5,7,8]=>[2,4,6,9,10,1,3,5,7,8]=>([(0,9),(1,7),(1,8),(2,7),(2,8),(3,6),(3,9),(4,5),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3,5,6,9],[2,4,7,8,10]]=>[2,4,7,8,10,1,3,5,6,9]=>[2,4,7,8,10,1,3,5,6,9]=>([(0,9),(1,8),(2,7),(2,9),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
[[1,3,5,6,8],[2,4,7,9,10]]=>[2,4,7,9,10,1,3,5,6,8]=>[2,4,7,9,10,1,3,5,6,8]=>([(0,9),(1,7),(1,8),(2,6),(2,9),(3,5),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3,5,6,7],[2,4,8,9,10]]=>[2,4,8,9,10,1,3,5,6,7]=>[2,4,8,9,10,1,3,5,6,7]=>([(0,9),(1,5),(1,9),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
[[1,3,4,7,9],[2,5,6,8,10]]=>[2,5,6,8,10,1,3,4,7,9]=>[2,5,6,8,10,1,3,4,7,9]=>([(0,9),(1,8),(2,7),(2,9),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
[[1,3,4,7,8],[2,5,6,9,10]]=>[2,5,6,9,10,1,3,4,7,8]=>[2,5,6,9,10,1,3,4,7,8]=>([(0,9),(1,7),(1,8),(2,7),(2,8),(3,5),(3,6),(3,9),(4,5),(4,6),(4,9),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3,4,6,9],[2,5,7,8,10]]=>[2,5,7,8,10,1,3,4,6,9]=>[2,5,7,8,10,1,3,4,6,9]=>([(0,9),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,9),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
[[1,3,4,6,8],[2,5,7,9,10]]=>[2,5,7,9,10,1,3,4,6,8]=>[2,5,7,9,10,1,3,4,6,8]=>([(0,9),(1,7),(1,8),(2,5),(2,6),(2,9),(3,4),(3,7),(3,8),(4,5),(4,6),(4,9),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3,4,6,7],[2,5,8,9,10]]=>[2,5,8,9,10,1,3,4,6,7]=>[2,5,8,9,10,1,3,4,6,7]=>([(0,9),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,9),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
[[1,3,4,5,9],[2,6,7,8,10]]=>[2,6,7,8,10,1,3,4,5,9]=>[2,6,7,8,10,1,3,4,5,9]=>([(0,9),(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),(5,9),(6,9),(7,9),(8,9)],10)
[[1,3,4,5,8],[2,6,7,9,10]]=>[2,6,7,9,10,1,3,4,5,8]=>[2,6,7,9,10,1,3,4,5,8]=>([(0,9),(1,7),(1,8),(2,4),(2,5),(2,6),(2,9),(3,4),(3,5),(3,6),(3,9),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3,4,5,7],[2,6,8,9,10]]=>[2,6,8,9,10,1,3,4,5,7]=>[2,6,8,9,10,1,3,4,5,7]=>([(0,9),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,9),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
[[1,3,4,5,6],[2,7,8,9,10]]=>[2,7,8,9,10,1,3,4,5,6]=>[2,7,8,9,10,1,3,4,5,6]=>([(0,9),(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),(5,9),(6,9),(7,9),(8,9)],10)
[[1,2,5,7,9],[3,4,6,8,10]]=>[3,4,6,8,10,1,2,5,7,9]=>[3,4,6,8,10,1,2,5,7,9]=>([(0,9),(1,7),(1,8),(2,7),(2,8),(3,6),(3,9),(4,5),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
[[1,2,5,7,8],[3,4,6,9,10]]=>[3,4,6,9,10,1,2,5,7,8]=>[3,4,6,9,10,1,2,5,7,8]=>([(0,6),(0,7),(1,6),(1,7),(2,8),(2,9),(3,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,5,6,9],[3,4,7,8,10]]=>[3,4,7,8,10,1,2,5,6,9]=>[3,4,7,8,10,1,2,5,6,9]=>([(0,9),(1,7),(1,8),(2,7),(2,8),(3,5),(3,6),(3,9),(4,5),(4,6),(4,9),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[[1,2,5,6,8],[3,4,7,9,10]]=>[3,4,7,9,10,1,2,5,6,8]=>[3,4,7,9,10,1,2,5,6,8]=>([(0,6),(0,7),(1,8),(1,9),(2,8),(2,9),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,5,6,7],[3,4,8,9,10]]=>[3,4,8,9,10,1,2,5,6,7]=>[3,4,8,9,10,1,2,5,6,7]=>([(0,8),(0,9),(1,8),(1,9),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,4,7,9],[3,5,6,8,10]]=>[3,5,6,8,10,1,2,4,7,9]=>[3,5,6,8,10,1,2,4,7,9]=>([(0,9),(1,7),(1,8),(2,6),(2,9),(3,5),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
[[1,2,4,7,8],[3,5,6,9,10]]=>[3,5,6,9,10,1,2,4,7,8]=>[3,5,6,9,10,1,2,4,7,8]=>([(0,6),(0,7),(1,8),(1,9),(2,8),(2,9),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,4,6,9],[3,5,7,8,10]]=>[3,5,7,8,10,1,2,4,6,9]=>[3,5,7,8,10,1,2,4,6,9]=>([(0,9),(1,7),(1,8),(2,5),(2,6),(2,9),(3,4),(3,7),(3,8),(4,5),(4,6),(4,9),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[[1,2,4,6,8],[3,5,7,9,10]]=>[3,5,7,9,10,1,2,4,6,8]=>[3,5,7,9,10,1,2,4,6,8]=>([(0,8),(0,9),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,8),(3,9),(4,5),(4,6),(4,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,4,6,7],[3,5,8,9,10]]=>[3,5,8,9,10,1,2,4,6,7]=>[3,5,8,9,10,1,2,4,6,7]=>([(0,8),(0,9),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,8),(3,9),(4,5),(4,6),(4,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,4,5,9],[3,6,7,8,10]]=>[3,6,7,8,10,1,2,4,5,9]=>[3,6,7,8,10,1,2,4,5,9]=>([(0,9),(1,7),(1,8),(2,4),(2,5),(2,6),(2,9),(3,4),(3,5),(3,6),(3,9),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[[1,2,4,5,8],[3,6,7,9,10]]=>[3,6,7,9,10,1,2,4,5,8]=>[3,6,7,9,10,1,2,4,5,8]=>([(0,8),(0,9),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,4,5,7],[3,6,8,9,10]]=>[3,6,8,9,10,1,2,4,5,7]=>[3,6,8,9,10,1,2,4,5,7]=>([(0,8),(0,9),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,4,5,6],[3,7,8,9,10]]=>[3,7,8,9,10,1,2,4,5,6]=>[3,7,8,9,10,1,2,4,5,6]=>([(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,3,7,9],[4,5,6,8,10]]=>[4,5,6,8,10,1,2,3,7,9]=>[4,5,6,8,10,1,2,3,7,9]=>([(0,9),(1,5),(1,9),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
[[1,2,3,7,8],[4,5,6,9,10]]=>[4,5,6,9,10,1,2,3,7,8]=>[4,5,6,9,10,1,2,3,7,8]=>([(0,8),(0,9),(1,8),(1,9),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,3,6,9],[4,5,7,8,10]]=>[4,5,7,8,10,1,2,3,6,9]=>[4,5,7,8,10,1,2,3,6,9]=>([(0,9),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,9),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
[[1,2,3,6,8],[4,5,7,9,10]]=>[4,5,7,9,10,1,2,3,6,8]=>[4,5,7,9,10,1,2,3,6,8]=>([(0,8),(0,9),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,8),(3,9),(4,5),(4,6),(4,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,3,6,7],[4,5,8,9,10]]=>[4,5,8,9,10,1,2,3,6,7]=>[4,5,8,9,10,1,2,3,6,7]=>([(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)
[[1,2,3,5,9],[4,6,7,8,10]]=>[4,6,7,8,10,1,2,3,5,9]=>[4,6,7,8,10,1,2,3,5,9]=>([(0,9),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,9),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
[[1,2,3,5,8],[4,6,7,9,10]]=>[4,6,7,9,10,1,2,3,5,8]=>[4,6,7,9,10,1,2,3,5,8]=>([(0,8),(0,9),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,3,5,7],[4,6,8,9,10]]=>[4,6,8,9,10,1,2,3,5,7]=>[4,6,8,9,10,1,2,3,5,7]=>([(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)
[[1,2,3,5,6],[4,7,8,9,10]]=>[4,7,8,9,10,1,2,3,5,6]=>[4,7,8,9,10,1,2,3,5,6]=>([(0,7),(0,8),(0,9),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)
[[1,2,3,4,9],[5,6,7,8,10]]=>[5,6,7,8,10,1,2,3,4,9]=>[5,6,7,8,10,1,2,3,4,9]=>([(0,9),(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),(5,9),(6,9),(7,9),(8,9)],10)
[[1,2,3,4,8],[5,6,7,9,10]]=>[5,6,7,9,10,1,2,3,4,8]=>[5,6,7,9,10,1,2,3,4,8]=>([(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,3,4,7],[5,6,8,9,10]]=>[5,6,8,9,10,1,2,3,4,7]=>[5,6,8,9,10,1,2,3,4,7]=>([(0,7),(0,8),(0,9),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9)],10)
[[1,2,3,4,6],[5,7,8,9,10]]=>[5,7,8,9,10,1,2,3,4,6]=>[5,7,8,9,10,1,2,3,4,6]=>([(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)
[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[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)
[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>([(0,11),(1,10),(2,9),(2,10),(3,8),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[2,4,6,8,11,12,1,3,5,7,9,10]=>[2,4,6,8,11,12,1,3,5,7,9,10]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,8),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[2,4,6,9,10,12,1,3,5,7,8,11]=>[2,4,6,9,10,12,1,3,5,7,8,11]=>([(0,11),(1,10),(2,9),(2,11),(3,7),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,9),(5,11),(6,7),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[2,4,6,9,11,12,1,3,5,7,8,10]=>[2,4,6,9,11,12,1,3,5,7,8,10]=>([(0,11),(1,8),(1,11),(2,9),(2,10),(3,7),(3,9),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[2,4,6,10,11,12,1,3,5,7,8,9]=>[2,4,6,10,11,12,1,3,5,7,8,9]=>([(0,11),(1,7),(1,11),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[2,4,7,8,10,12,1,3,5,6,9,11]=>[2,4,7,8,10,12,1,3,5,6,9,11]=>([(0,11),(1,10),(2,9),(2,10),(3,8),(3,11),(4,6),(4,7),(4,9),(4,10),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[2,4,7,8,11,12,1,3,5,6,9,10]=>[2,4,7,8,11,12,1,3,5,6,9,10]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,8),(3,11),(4,6),(4,7),(4,9),(4,10),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[2,4,7,9,10,12,1,3,5,6,8,11]=>[2,4,7,9,10,12,1,3,5,6,8,11]=>([(0,11),(1,10),(2,9),(2,11),(3,7),(3,8),(3,10),(4,5),(4,6),(4,9),(4,11),(5,7),(5,8),(5,10),(6,7),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[2,4,7,9,11,12,1,3,5,6,8,10]=>[2,4,7,9,11,12,1,3,5,6,8,10]=>([(0,11),(1,8),(1,11),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,6),(4,8),(4,11),(5,7),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[2,4,7,10,11,12,1,3,5,6,8,9]=>[2,4,7,10,11,12,1,3,5,6,8,9]=>([(0,11),(1,7),(1,11),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,6),(4,8),(4,9),(4,10),(5,6),(5,8),(5,9),(5,10),(6,7),(6,11),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[2,4,8,9,10,12,1,3,5,6,7,11]=>[2,4,8,9,10,12,1,3,5,6,7,11]=>([(0,11),(1,10),(2,9),(2,11),(3,6),(3,7),(3,8),(3,10),(4,6),(4,7),(4,8),(4,10),(5,6),(5,7),(5,8),(5,10),(6,9),(6,11),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[2,4,8,9,11,12,1,3,5,6,7,10]=>[2,4,8,9,11,12,1,3,5,6,7,10]=>([(0,11),(1,8),(1,11),(2,9),(2,10),(3,6),(3,7),(3,9),(3,10),(4,6),(4,7),(4,9),(4,10),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[2,4,8,10,11,12,1,3,5,6,7,9]=>[2,4,8,10,11,12,1,3,5,6,7,9]=>([(0,11),(1,7),(1,11),(2,8),(2,9),(2,10),(3,6),(3,8),(3,9),(3,10),(4,6),(4,8),(4,9),(4,10),(5,6),(5,8),(5,9),(5,10),(6,7),(6,11),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[2,4,9,10,11,12,1,3,5,6,7,8]=>[2,4,9,10,11,12,1,3,5,6,7,8]=>([(0,11),(1,6),(1,11),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[2,5,6,8,10,12,1,3,4,7,9,11]=>[2,5,6,8,10,12,1,3,4,7,9,11]=>([(0,11),(1,10),(2,9),(2,11),(3,7),(3,8),(3,10),(4,7),(4,8),(4,10),(5,6),(5,9),(5,11),(6,7),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[2,5,6,8,11,12,1,3,4,7,9,10]=>[2,5,6,8,11,12,1,3,4,7,9,10]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,7),(3,8),(3,11),(4,7),(4,8),(4,11),(5,6),(5,9),(5,10),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[2,5,6,9,10,12,1,3,4,7,8,11]=>[2,5,6,9,10,12,1,3,4,7,8,11]=>([(0,11),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[2,5,6,9,11,12,1,3,4,7,8,10]=>[2,5,6,9,11,12,1,3,4,7,8,10]=>([(0,11),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[2,5,6,10,11,12,1,3,4,7,8,9]=>[2,5,6,10,11,12,1,3,4,7,8,9]=>([(0,11),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[2,5,7,8,10,12,1,3,4,6,9,11]=>[2,5,7,8,10,12,1,3,4,6,9,11]=>([(0,11),(1,10),(2,9),(2,11),(3,7),(3,8),(3,10),(4,5),(4,6),(4,9),(4,11),(5,7),(5,8),(5,10),(6,7),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[2,5,7,8,11,12,1,3,4,6,9,10]=>[2,5,7,8,11,12,1,3,4,6,9,10]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,7),(3,8),(3,11),(4,5),(4,6),(4,9),(4,10),(5,7),(5,8),(5,11),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[2,5,7,9,10,12,1,3,4,6,8,11]=>[2,5,7,9,10,12,1,3,4,6,8,11]=>([(0,11),(1,10),(2,8),(2,9),(2,10),(3,6),(3,7),(3,11),(4,5),(4,8),(4,9),(4,10),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[2,5,7,9,11,12,1,3,4,6,8,10]=>[2,5,7,9,11,12,1,3,4,6,8,10]=>([(0,11),(1,9),(1,10),(2,7),(2,8),(2,11),(3,6),(3,9),(3,10),(4,5),(4,7),(4,8),(4,11),(5,6),(5,9),(5,10),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[2,5,7,10,11,12,1,3,4,6,8,9]=>[2,5,7,10,11,12,1,3,4,6,8,9]=>([(0,11),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,6),(3,7),(3,11),(4,5),(4,8),(4,9),(4,10),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[2,5,8,9,10,12,1,3,4,6,7,11]=>[2,5,8,9,10,12,1,3,4,6,7,11]=>([(0,11),(1,10),(2,8),(2,9),(2,11),(3,5),(3,6),(3,7),(3,10),(4,5),(4,6),(4,7),(4,10),(5,8),(5,9),(5,11),(6,8),(6,9),(6,11),(7,8),(7,9),(7,11),(8,10),(9,10),(10,11)],12)
[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[2,5,8,9,11,12,1,3,4,6,7,10]=>[2,5,8,9,11,12,1,3,4,6,7,10]=>([(0,11),(1,9),(1,10),(2,7),(2,8),(2,11),(3,5),(3,6),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,7),(5,8),(5,11),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[2,5,8,10,11,12,1,3,4,6,7,9]=>[2,5,8,10,11,12,1,3,4,6,7,9]=>([(0,11),(1,8),(1,9),(1,10),(2,6),(2,7),(2,11),(3,5),(3,8),(3,9),(3,10),(4,5),(4,8),(4,9),(4,10),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[2,5,9,10,11,12,1,3,4,6,7,8]=>[2,5,9,10,11,12,1,3,4,6,7,8]=>([(0,11),(1,5),(1,6),(1,11),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[2,6,7,8,10,12,1,3,4,5,9,11]=>[2,6,7,8,10,12,1,3,4,5,9,11]=>([(0,11),(1,10),(2,9),(2,11),(3,6),(3,7),(3,8),(3,10),(4,6),(4,7),(4,8),(4,10),(5,6),(5,7),(5,8),(5,10),(6,9),(6,11),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[2,6,7,8,11,12,1,3,4,5,9,10]=>[2,6,7,8,11,12,1,3,4,5,9,10]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,6),(3,7),(3,8),(3,11),(4,6),(4,7),(4,8),(4,11),(5,6),(5,7),(5,8),(5,11),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[2,6,7,9,10,12,1,3,4,5,8,11]=>[2,6,7,9,10,12,1,3,4,5,8,11]=>([(0,11),(1,10),(2,8),(2,9),(2,11),(3,5),(3,6),(3,7),(3,10),(4,5),(4,6),(4,7),(4,10),(5,8),(5,9),(5,11),(6,8),(6,9),(6,11),(7,8),(7,9),(7,11),(8,10),(9,10),(10,11)],12)
[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[2,6,7,9,11,12,1,3,4,5,8,10]=>[2,6,7,9,11,12,1,3,4,5,8,10]=>([(0,11),(1,9),(1,10),(2,8),(2,9),(2,10),(3,5),(3,6),(3,7),(3,11),(4,5),(4,6),(4,7),(4,11),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[2,6,7,10,11,12,1,3,4,5,8,9]=>[2,6,7,10,11,12,1,3,4,5,8,9]=>([(0,11),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,5),(3,6),(3,7),(3,11),(4,5),(4,6),(4,7),(4,11),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[2,6,8,9,10,12,1,3,4,5,7,11]=>[2,6,8,9,10,12,1,3,4,5,7,11]=>([(0,11),(1,10),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,6),(3,11),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[2,6,8,9,11,12,1,3,4,5,7,10]=>[2,6,8,9,11,12,1,3,4,5,7,10]=>([(0,11),(1,9),(1,10),(2,6),(2,7),(2,8),(2,11),(3,4),(3,5),(3,9),(3,10),(4,6),(4,7),(4,8),(4,11),(5,6),(5,7),(5,8),(5,11),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[2,6,8,10,11,12,1,3,4,5,7,9]=>[2,6,8,10,11,12,1,3,4,5,7,9]=>([(0,11),(1,8),(1,9),(1,10),(2,5),(2,6),(2,7),(2,11),(3,4),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,11),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[2,6,9,10,11,12,1,3,4,5,7,8]=>[2,6,9,10,11,12,1,3,4,5,7,8]=>([(0,11),(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,6),(3,11),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[2,7,8,9,10,12,1,3,4,5,6,11]=>[2,7,8,9,10,12,1,3,4,5,6,11]=>([(0,11),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[2,7,8,9,11,12,1,3,4,5,6,10]=>[2,7,8,9,11,12,1,3,4,5,6,10]=>([(0,11),(1,9),(1,10),(2,5),(2,6),(2,7),(2,8),(2,11),(3,5),(3,6),(3,7),(3,8),(3,11),(4,5),(4,6),(4,7),(4,8),(4,11),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[2,7,8,10,11,12,1,3,4,5,6,9]=>[2,7,8,10,11,12,1,3,4,5,6,9]=>([(0,11),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,11),(3,4),(3,5),(3,6),(3,7),(3,11),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[2,7,9,10,11,12,1,3,4,5,6,8]=>[2,7,9,10,11,12,1,3,4,5,6,8]=>([(0,11),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(2,5),(2,6),(2,11),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>([(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[3,4,6,8,10,12,1,2,5,7,9,11]=>[3,4,6,8,10,12,1,2,5,7,9,11]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,8),(3,11),(4,7),(4,9),(4,10),(5,6),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[3,4,6,8,11,12,1,2,5,7,9,10]=>[3,4,6,8,11,12,1,2,5,7,9,10]=>([(0,8),(0,9),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,7),(4,10),(4,11),(5,6),(5,8),(5,9),(6,7),(6,10),(6,11),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[3,4,6,9,10,12,1,2,5,7,8,11]=>[3,4,6,9,10,12,1,2,5,7,8,11]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,7),(3,8),(3,11),(4,7),(4,8),(4,11),(5,6),(5,9),(5,10),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[3,4,6,9,11,12,1,2,5,7,8,10]=>[3,4,6,9,11,12,1,2,5,7,8,10]=>([(0,8),(0,9),(1,10),(1,11),(2,10),(2,11),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[3,4,6,10,11,12,1,2,5,7,8,9]=>[3,4,6,10,11,12,1,2,5,7,8,9]=>([(0,10),(0,11),(1,10),(1,11),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[3,4,7,8,10,12,1,2,5,6,9,11]=>[3,4,7,8,10,12,1,2,5,6,9,11]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,8),(3,11),(4,6),(4,7),(4,9),(4,10),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[3,4,7,8,11,12,1,2,5,6,9,10]=>[3,4,7,8,11,12,1,2,5,6,9,10]=>([(0,10),(0,11),(1,8),(1,9),(2,8),(2,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[3,4,7,9,10,12,1,2,5,6,8,11]=>[3,4,7,9,10,12,1,2,5,6,8,11]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,7),(3,8),(3,11),(4,5),(4,6),(4,9),(4,10),(5,7),(5,8),(5,11),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[3,4,7,9,11,12,1,2,5,6,8,10]=>[3,4,7,9,11,12,1,2,5,6,8,10]=>([(0,8),(0,9),(1,10),(1,11),(2,10),(2,11),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[3,4,7,10,11,12,1,2,5,6,8,9]=>[3,4,7,10,11,12,1,2,5,6,8,9]=>([(0,10),(0,11),(1,10),(1,11),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[3,4,8,9,10,12,1,2,5,6,7,11]=>[3,4,8,9,10,12,1,2,5,6,7,11]=>([(0,11),(1,9),(1,10),(2,9),(2,10),(3,6),(3,7),(3,8),(3,11),(4,6),(4,7),(4,8),(4,11),(5,6),(5,7),(5,8),(5,11),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[3,4,8,9,11,12,1,2,5,6,7,10]=>[3,4,8,9,11,12,1,2,5,6,7,10]=>([(0,8),(0,9),(1,10),(1,11),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[3,4,8,10,11,12,1,2,5,6,7,9]=>[3,4,8,10,11,12,1,2,5,6,7,9]=>([(0,10),(0,11),(1,10),(1,11),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[3,4,9,10,11,12,1,2,5,6,7,8]=>[3,4,9,10,11,12,1,2,5,6,7,8]=>([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[3,5,6,8,10,12,1,2,4,7,9,11]=>[3,5,6,8,10,12,1,2,4,7,9,11]=>([(0,11),(1,8),(1,11),(2,9),(2,10),(3,7),(3,9),(3,10),(4,7),(4,9),(4,10),(5,6),(5,8),(5,11),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[3,5,6,8,11,12,1,2,4,7,9,10]=>[3,5,6,8,11,12,1,2,4,7,9,10]=>([(0,8),(0,9),(1,10),(1,11),(2,10),(2,11),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[3,5,6,9,10,12,1,2,4,7,8,11]=>[3,5,6,9,10,12,1,2,4,7,8,11]=>([(0,11),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[3,5,6,9,11,12,1,2,4,7,8,10]=>[3,5,6,9,11,12,1,2,4,7,8,10]=>([(0,10),(0,11),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,6),(4,10),(4,11),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[3,5,6,10,11,12,1,2,4,7,8,9]=>[3,5,6,10,11,12,1,2,4,7,8,9]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,6),(4,10),(4,11),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[3,5,7,8,10,12,1,2,4,6,9,11]=>[3,5,7,8,10,12,1,2,4,6,9,11]=>([(0,11),(1,8),(1,11),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,6),(4,8),(4,11),(5,7),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[3,5,7,8,11,12,1,2,4,6,9,10]=>[3,5,7,8,11,12,1,2,4,6,9,10]=>([(0,8),(0,9),(1,10),(1,11),(2,10),(2,11),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[3,5,7,9,10,12,1,2,4,6,8,11]=>[3,5,7,9,10,12,1,2,4,6,8,11]=>([(0,11),(1,9),(1,10),(2,7),(2,8),(2,11),(3,6),(3,9),(3,10),(4,5),(4,7),(4,8),(4,11),(5,6),(5,9),(5,10),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[3,5,7,9,11,12,1,2,4,6,8,10]=>[3,5,7,9,11,12,1,2,4,6,8,10]=>([(0,10),(0,11),(1,8),(1,9),(2,7),(2,8),(2,9),(3,6),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[3,5,7,10,11,12,1,2,4,6,8,9]=>[3,5,7,10,11,12,1,2,4,6,8,9]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,6),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[3,5,8,9,10,12,1,2,4,6,7,11]=>[3,5,8,9,10,12,1,2,4,6,7,11]=>([(0,11),(1,9),(1,10),(2,8),(2,9),(2,10),(3,5),(3,6),(3,7),(3,11),(4,5),(4,6),(4,7),(4,11),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[3,5,8,9,11,12,1,2,4,6,7,10]=>[3,5,8,9,11,12,1,2,4,6,7,10]=>([(0,8),(0,9),(1,10),(1,11),(2,7),(2,10),(2,11),(3,5),(3,6),(3,8),(3,9),(4,5),(4,6),(4,8),(4,9),(5,7),(5,10),(5,11),(6,7),(6,10),(6,11),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[3,5,8,10,11,12,1,2,4,6,7,9]=>[3,5,8,10,11,12,1,2,4,6,7,9]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,6),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[3,5,9,10,11,12,1,2,4,6,7,8]=>[3,5,9,10,11,12,1,2,4,6,7,8]=>([(0,10),(0,11),(1,5),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[3,6,7,8,10,12,1,2,4,5,9,11]=>[3,6,7,8,10,12,1,2,4,5,9,11]=>([(0,11),(1,8),(1,11),(2,9),(2,10),(3,6),(3,7),(3,9),(3,10),(4,6),(4,7),(4,9),(4,10),(5,6),(5,7),(5,9),(5,10),(6,8),(6,11),(7,8),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[3,6,7,8,11,12,1,2,4,5,9,10]=>[3,6,7,8,11,12,1,2,4,5,9,10]=>([(0,8),(0,9),(1,10),(1,11),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[3,6,7,9,10,12,1,2,4,5,8,11]=>[3,6,7,9,10,12,1,2,4,5,8,11]=>([(0,11),(1,9),(1,10),(2,7),(2,8),(2,11),(3,5),(3,6),(3,9),(3,10),(4,5),(4,6),(4,9),(4,10),(5,7),(5,8),(5,11),(6,7),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[3,6,7,9,11,12,1,2,4,5,8,10]=>[3,6,7,9,11,12,1,2,4,5,8,10]=>([(0,8),(0,9),(1,10),(1,11),(2,7),(2,10),(2,11),(3,5),(3,6),(3,8),(3,9),(4,5),(4,6),(4,8),(4,9),(5,7),(5,10),(5,11),(6,7),(6,10),(6,11),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[3,6,7,10,11,12,1,2,4,5,8,9]=>[3,6,7,10,11,12,1,2,4,5,8,9]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,5),(3,6),(3,10),(3,11),(4,5),(4,6),(4,10),(4,11),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[3,6,8,9,10,12,1,2,4,5,7,11]=>[3,6,8,9,10,12,1,2,4,5,7,11]=>([(0,11),(1,9),(1,10),(2,6),(2,7),(2,8),(2,11),(3,4),(3,5),(3,9),(3,10),(4,6),(4,7),(4,8),(4,11),(5,6),(5,7),(5,8),(5,11),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[3,6,8,9,11,12,1,2,4,5,7,10]=>[3,6,8,9,11,12,1,2,4,5,7,10]=>([(0,10),(0,11),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[3,6,8,10,11,12,1,2,4,5,7,9]=>[3,6,8,10,11,12,1,2,4,5,7,9]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[3,6,9,10,11,12,1,2,4,5,7,8]=>[3,6,9,10,11,12,1,2,4,5,7,8]=>([(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[3,7,8,9,10,12,1,2,4,5,6,11]=>[3,7,8,9,10,12,1,2,4,5,6,11]=>([(0,11),(1,9),(1,10),(2,5),(2,6),(2,7),(2,8),(2,11),(3,5),(3,6),(3,7),(3,8),(3,11),(4,5),(4,6),(4,7),(4,8),(4,11),(5,9),(5,10),(6,9),(6,10),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[3,7,8,9,11,12,1,2,4,5,6,10]=>[3,7,8,9,11,12,1,2,4,5,6,10]=>([(0,10),(0,11),(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),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[3,7,8,10,11,12,1,2,4,5,6,9]=>[3,7,8,10,11,12,1,2,4,5,6,9]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,10),(2,11),(3,4),(3,5),(3,6),(3,10),(3,11),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[3,7,9,10,11,12,1,2,4,5,6,8]=>[3,7,9,10,11,12,1,2,4,5,6,8]=>([(0,10),(0,11),(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),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[3,8,9,10,11,12,1,2,4,5,6,7]=>[3,8,9,10,11,12,1,2,4,5,6,7]=>([(0,10),(0,11),(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),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[4,5,6,8,10,12,1,2,3,7,9,11]=>[4,5,6,8,10,12,1,2,3,7,9,11]=>([(0,11),(1,7),(1,11),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,8),(4,9),(4,10),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[4,5,6,8,11,12,1,2,3,7,9,10]=>[4,5,6,8,11,12,1,2,3,7,9,10]=>([(0,10),(0,11),(1,10),(1,11),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[4,5,6,9,10,12,1,2,3,7,8,11]=>[4,5,6,9,10,12,1,2,3,7,8,11]=>([(0,11),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,6),(4,7),(4,11),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[4,5,6,9,11,12,1,2,3,7,8,10]=>[4,5,6,9,11,12,1,2,3,7,8,10]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,6),(4,10),(4,11),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[4,5,6,10,11,12,1,2,3,7,8,9]=>[4,5,6,10,11,12,1,2,3,7,8,9]=>([(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(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)],12)
[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[4,5,7,8,10,12,1,2,3,6,9,11]=>[4,5,7,8,10,12,1,2,3,6,9,11]=>([(0,11),(1,7),(1,11),(2,8),(2,9),(2,10),(3,8),(3,9),(3,10),(4,6),(4,8),(4,9),(4,10),(5,6),(5,8),(5,9),(5,10),(6,7),(6,11),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[4,5,7,8,11,12,1,2,3,6,9,10]=>[4,5,7,8,11,12,1,2,3,6,9,10]=>([(0,10),(0,11),(1,10),(1,11),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[4,5,7,9,10,12,1,2,3,6,8,11]=>[4,5,7,9,10,12,1,2,3,6,8,11]=>([(0,11),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,6),(3,7),(3,11),(4,5),(4,8),(4,9),(4,10),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[4,5,7,9,11,12,1,2,3,6,8,10]=>[4,5,7,9,11,12,1,2,3,6,8,10]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,6),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[4,5,7,10,11,12,1,2,3,6,8,9]=>[4,5,7,10,11,12,1,2,3,6,8,9]=>([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,5),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[4,5,8,9,10,12,1,2,3,6,7,11]=>[4,5,8,9,10,12,1,2,3,6,7,11]=>([(0,11),(1,8),(1,9),(1,10),(2,8),(2,9),(2,10),(3,5),(3,6),(3,7),(3,11),(4,5),(4,6),(4,7),(4,11),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[4,5,8,9,11,12,1,2,3,6,7,10]=>[4,5,8,9,11,12,1,2,3,6,7,10]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,5),(3,6),(3,10),(3,11),(4,5),(4,6),(4,10),(4,11),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[4,5,8,10,11,12,1,2,3,6,7,9]=>[4,5,8,10,11,12,1,2,3,6,7,9]=>([(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[4,5,9,10,11,12,1,2,3,6,7,8]=>[4,5,9,10,11,12,1,2,3,6,7,8]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[4,6,7,8,10,12,1,2,3,5,9,11]=>[4,6,7,8,10,12,1,2,3,5,9,11]=>([(0,11),(1,7),(1,11),(2,8),(2,9),(2,10),(3,6),(3,8),(3,9),(3,10),(4,6),(4,8),(4,9),(4,10),(5,6),(5,8),(5,9),(5,10),(6,7),(6,11),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[4,6,7,8,11,12,1,2,3,5,9,10]=>[4,6,7,8,11,12,1,2,3,5,9,10]=>([(0,10),(0,11),(1,10),(1,11),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[4,6,7,9,10,12,1,2,3,5,8,11]=>[4,6,7,9,10,12,1,2,3,5,8,11]=>([(0,11),(1,8),(1,9),(1,10),(2,6),(2,7),(2,11),(3,5),(3,8),(3,9),(3,10),(4,5),(4,8),(4,9),(4,10),(5,6),(5,7),(5,11),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[4,6,7,9,11,12,1,2,3,5,8,10]=>[4,6,7,9,11,12,1,2,3,5,8,10]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,6),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(4,5),(4,7),(4,8),(4,9),(5,6),(5,10),(5,11),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[4,6,7,10,11,12,1,2,3,5,8,9]=>[4,6,7,10,11,12,1,2,3,5,8,9]=>([(0,6),(0,7),(0,8),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[4,6,8,9,10,12,1,2,3,5,7,11]=>[4,6,8,9,10,12,1,2,3,5,7,11]=>([(0,11),(1,8),(1,9),(1,10),(2,5),(2,6),(2,7),(2,11),(3,4),(3,8),(3,9),(3,10),(4,5),(4,6),(4,7),(4,11),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[4,6,8,9,11,12,1,2,3,5,7,10]=>[4,6,8,9,11,12,1,2,3,5,7,10]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[4,6,8,10,11,12,1,2,3,5,7,9]=>[4,6,8,10,11,12,1,2,3,5,7,9]=>([(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[4,6,9,10,11,12,1,2,3,5,7,8]=>[4,6,9,10,11,12,1,2,3,5,7,8]=>([(0,9),(0,10),(0,11),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[4,7,8,9,10,12,1,2,3,5,6,11]=>[4,7,8,9,10,12,1,2,3,5,6,11]=>([(0,11),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,11),(3,4),(3,5),(3,6),(3,7),(3,11),(4,8),(4,9),(4,10),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,11),(9,11),(10,11)],12)
[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[4,7,8,9,11,12,1,2,3,5,6,10]=>[4,7,8,9,11,12,1,2,3,5,6,10]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,10),(2,11),(3,4),(3,5),(3,6),(3,10),(3,11),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[4,7,8,10,11,12,1,2,3,5,6,9]=>[4,7,8,10,11,12,1,2,3,5,6,9]=>([(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(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)],12)
[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[4,7,9,10,11,12,1,2,3,5,6,8]=>[4,7,9,10,11,12,1,2,3,5,6,8]=>([(0,9),(0,10),(0,11),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(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)],12)
[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[4,8,9,10,11,12,1,2,3,5,6,7]=>[4,8,9,10,11,12,1,2,3,5,6,7]=>([(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(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)],12)
[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[5,6,7,8,10,12,1,2,3,4,9,11]=>[5,6,7,8,10,12,1,2,3,4,9,11]=>([(0,11),(1,6),(1,11),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[5,6,7,8,11,12,1,2,3,4,9,10]=>[5,6,7,8,11,12,1,2,3,4,9,10]=>([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[5,6,7,9,10,12,1,2,3,4,8,11]=>[5,6,7,9,10,12,1,2,3,4,8,11]=>([(0,11),(1,5),(1,6),(1,11),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[5,6,7,9,11,12,1,2,3,4,8,10]=>[5,6,7,9,11,12,1,2,3,4,8,10]=>([(0,10),(0,11),(1,5),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[5,6,7,10,11,12,1,2,3,4,8,9]=>[5,6,7,10,11,12,1,2,3,4,8,9]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[5,6,8,9,10,12,1,2,3,4,7,11]=>[5,6,8,9,10,12,1,2,3,4,7,11]=>([(0,11),(1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,6),(3,11),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[5,6,8,9,11,12,1,2,3,4,7,10]=>[5,6,8,9,11,12,1,2,3,4,7,10]=>([(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[5,6,8,10,11,12,1,2,3,4,7,9]=>[5,6,8,10,11,12,1,2,3,4,7,9]=>([(0,9),(0,10),(0,11),(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,4),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11)],12)
[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[5,6,9,10,11,12,1,2,3,4,7,8]=>[5,6,9,10,11,12,1,2,3,4,7,8]=>([(0,8),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)
[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[5,7,8,9,10,12,1,2,3,4,6,11]=>[5,7,8,9,10,12,1,2,3,4,6,11]=>([(0,11),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(2,5),(2,6),(2,11),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,11),(9,11),(10,11)],12)
[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[5,7,8,9,11,12,1,2,3,4,6,10]=>[5,7,8,9,11,12,1,2,3,4,6,10]=>([(0,10),(0,11),(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),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[5,7,8,10,11,12,1,2,3,4,6,9]=>[5,7,8,10,11,12,1,2,3,4,6,9]=>([(0,9),(0,10),(0,11),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(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)],12)
[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[5,7,9,10,11,12,1,2,3,4,6,8]=>[5,7,9,10,11,12,1,2,3,4,6,8]=>([(0,8),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)
[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[5,8,9,10,11,12,1,2,3,4,6,7]=>[5,8,9,10,11,12,1,2,3,4,6,7]=>([(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)
[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[6,7,8,9,10,12,1,2,3,4,5,11]=>[6,7,8,9,10,12,1,2,3,4,5,11]=>([(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[6,7,8,9,11,12,1,2,3,4,5,10]=>[6,7,8,9,11,12,1,2,3,4,5,10]=>([(0,10),(0,11),(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),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[6,7,8,10,11,12,1,2,3,4,5,9]=>[6,7,8,10,11,12,1,2,3,4,5,9]=>([(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(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)],12)
[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[6,7,9,10,11,12,1,2,3,4,5,8]=>[6,7,9,10,11,12,1,2,3,4,5,8]=>([(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)
[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[6,8,9,10,11,12,1,2,3,4,5,7]=>[6,8,9,10,11,12,1,2,3,4,5,7]=>([(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(2,8),(2,9),(2,10),(2,11),(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)],12)
[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[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]=>[1,2,3,4,5,6,7,8,9]=>([],9)
[[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>([(7,8)],9)
[[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,8,9,6,7]=>([(5,7),(5,8),(6,7),(6,8)],9)
[[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>([(6,7),(6,8),(7,8)],9)
[[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,7,9,5,8,6]=>([(4,7),(4,8),(5,6),(5,8),(6,7),(7,8)],9)
[[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>([(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[1,6,7,8,9,2,3,4,5]=>([(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)],9)
[[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>([(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>([(3,4),(3,5),(3,6),(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],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[7,8,9,4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>([(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[7,9,5,8,3,6,1,4,2]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,2,3,4,5,6,7,8,9,10]]=>[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]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>([(8,9)],10)
[[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,9,10,7,8]=>([(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>([(7,8),(7,9),(8,9)],10)
[[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>([(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>([(5,6),(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]]=>[10,9,8,6,7,1,2,3,4,5]=>[1,2,3,6,10,4,9,8,7,5]=>([(3,4),(3,9),(4,8),(5,6),(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]]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>([(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)
[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,1,2,3,4]=>[1,2,7,10,5,9,3,8,6,4]=>([(2,3),(2,4),(2,8),(2,9),(3,4),(3,7),(3,9),(4,6),(4,8),(5,6),(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]]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>([(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)
[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,4,5,1,2,3]=>[1,8,10,6,9,4,7,2,5,3]=>([(1,2),(1,4),(1,5),(1,6),(1,7),(1,9),(2,3),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>([(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],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[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],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(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)
[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>([],12)
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(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]]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(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)
[[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[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)
[[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[3,4,5,6,7,8,9,1,2]=>([(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)],9)
[[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,2,1]=>([(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)
[[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[4,5,6,7,8,9,1,2,3]=>([(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)],9)
[[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[4,5,6,7,8,9,2,3,1]=>([(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),(6,8),(7,8)],9)
[[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[5,6,7,8,9,1,2,3,4]=>([(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)],9)
[[1,3,4,5],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5]=>[6,7,8,9,2,3,4,5,1]=>([(0,4),(0,5),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[7,8,9,6,5,4,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[8,9,6,7,4,5,2,3,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,8),(7,8)],9)
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[8,9,6,7,5,4,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[8,9,7,6,5,4,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[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)
[[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[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)
[[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>([(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)
[[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[4,5,6,7,8,9,10,1,2,3]=>([(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)],10)
[[1,3,6,7,8,9,10],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9,10]=>[4,5,6,7,8,9,10,2,3,1]=>([(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),(7,9),(8,9)],10)
[[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[5,6,7,8,9,10,1,2,3,4]=>([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)
[[1,2,7,8,9,10],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9,10]=>[5,6,7,8,9,10,3,4,1,2]=>([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>([(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),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,2,5,6],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6]=>[7,8,9,10,3,4,5,6,1,2]=>([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2,9,10],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10]=>[7,8,9,10,5,6,3,4,1,2]=>([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,3,4],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4]=>[8,9,10,5,6,7,2,3,4,1]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(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),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,9),(7,9),(8,9)],10)
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[9,10,8,7,6,5,4,3,2,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(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)
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8]=>[7,9,6,8,5,4,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,4,7],[2,5,8],[3,6,9]]=>[3,6,9,2,5,8,1,4,7]=>[3,6,9,2,5,8,1,4,7]=>([(0,6),(0,8),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,8),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[[1,4,6,7,8,9],[2,5],[3]]=>[3,2,5,1,4,6,7,8,9]=>[3,5,6,7,8,9,2,4,1]=>([(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),(6,8),(7,8)],9)
[[1,3,5,7,8,9],[2,4,6]]=>[2,4,6,1,3,5,7,8,9]=>[2,4,6,7,8,9,1,3,5]=>([(0,8),(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)],9)
[[1,3,5,6,7,8,9],[2,4]]=>[2,4,1,3,5,6,7,8,9]=>[2,4,5,6,7,8,9,1,3]=>([(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)],9)
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[5,10,4,9,3,8,2,7,1,6]=>[5,10,4,9,3,8,2,7,1,6]=>([(0,3),(0,5),(0,7),(0,9),(1,2),(1,4),(1,6),(1,8),(2,4),(2,6),(2,8),(2,9),(3,5),(3,7),(3,8),(3,9),(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)
[[1,3,5,6,7,8,9,10],[2,4]]=>[2,4,1,3,5,6,7,8,9,10]=>[2,4,5,6,7,8,9,10,1,3]=>([(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)
[[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,9,6,8]=>([(5,8),(6,7),(7,8)],9)
[[1,2,3,4,5,6,7,9],[8,10]]=>[8,10,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,10,7,9]=>([(6,9),(7,8),(8,9)],10)
[[1,2],[3,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,3,4,1,2]=>[8,10,7,9,5,6,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3,4],[5,7],[6,8],[9,10]]=>[9,10,6,8,5,7,3,4,1,2]=>[9,10,6,8,5,7,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3,4],[5,7],[6,9],[8,10]]=>[8,10,6,9,5,7,3,4,1,2]=>[8,10,6,9,5,7,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(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),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3,4],[5,8],[6,9],[7,10]]=>[7,10,6,9,5,8,3,4,1,2]=>[7,10,6,9,5,8,3,4,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(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),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,3,5,1,2]=>[9,10,7,8,4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3,5],[4,6],[7,9],[8,10]]=>[8,10,7,9,4,6,3,5,1,2]=>[8,10,7,9,4,6,3,5,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(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)],10)
[[1,2],[3,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,3,5,1,2]=>[9,10,6,8,4,7,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(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),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,3,5,1,2]=>[8,10,6,9,4,7,3,5,1,2]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,2],[3,5],[4,8],[6,9],[7,10]]=>[7,10,6,9,4,8,3,5,1,2]=>[7,10,6,9,4,8,3,5,1,2]=>([(0,2),(0,3),(0,5),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(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),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
[[1,2],[3,6],[4,7],[5,8],[9,10]]=>[9,10,5,8,4,7,3,6,1,2]=>[9,10,5,8,4,7,3,6,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(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),(6,8),(6,9),(7,8),(7,9)],10)
[[1,2],[3,6],[4,7],[5,9],[8,10]]=>[8,10,5,9,4,7,3,6,1,2]=>[8,10,5,9,4,7,3,6,1,2]=>([(0,2),(0,3),(0,5),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(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),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
[[1,2],[3,6],[4,8],[5,9],[7,10]]=>[7,10,5,9,4,8,3,6,1,2]=>[7,10,5,9,4,8,3,6,1,2]=>([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,4),(1,6),(1,7),(1,8),(2,4),(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),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,3,7,1,2]=>[6,10,5,9,4,8,3,7,1,2]=>([(0,3),(0,5),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,8),(1,9),(2,4),(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)],10)
[[1,3],[2,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,2,4,1,3]=>[9,10,7,8,5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)
[[1,3],[2,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,2,4,1,3]=>[8,10,7,9,5,6,2,4,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(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)],10)
[[1,3],[2,4],[5,7],[6,8],[9,10]]=>[9,10,6,8,5,7,2,4,1,3]=>[9,10,6,8,5,7,2,4,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(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)],10)
[[1,3],[2,4],[5,7],[6,9],[8,10]]=>[8,10,6,9,5,7,2,4,1,3]=>[8,10,6,9,5,7,2,4,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(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],[5,8],[6,9],[7,10]]=>[7,10,6,9,5,8,2,4,1,3]=>[7,10,6,9,5,8,2,4,1,3]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,3],[2,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,2,5,1,3]=>[9,10,7,8,4,6,2,5,1,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(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),(6,8),(6,9),(7,8),(7,9)],10)
[[1,3],[2,5],[4,6],[7,9],[8,10]]=>[8,10,7,9,4,6,2,5,1,3]=>[8,10,7,9,4,6,2,5,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(3,9),(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],[2,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,2,5,1,3]=>[9,10,6,8,4,7,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,3],[2,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,2,5,1,3]=>[8,10,6,9,4,7,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,8),(4,9),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,3],[2,5],[4,8],[6,9],[7,10]]=>[7,10,6,9,4,8,2,5,1,3]=>[7,10,6,9,4,8,2,5,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,7),(6,8),(7,8),(7,9),(8,9)],10)
[[1,3],[2,6],[4,7],[5,8],[9,10]]=>[9,10,5,8,4,7,2,6,1,3]=>[9,10,5,8,4,7,2,6,1,3]=>([(0,2),(0,3),(0,5),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(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),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
[[1,3],[2,6],[4,7],[5,9],[8,10]]=>[8,10,5,9,4,7,2,6,1,3]=>[8,10,5,9,4,7,2,6,1,3]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(3,4),(3,5),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3],[2,6],[4,8],[5,9],[7,10]]=>[7,10,5,9,4,8,2,6,1,3]=>[7,10,5,9,4,8,2,6,1,3]=>([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(1,3),(1,4),(1,5),(1,6),(1,8),(1,9),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(4,6),(4,7),(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],[2,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,2,7,1,3]=>[6,10,5,9,4,8,2,7,1,3]=>([(0,2),(0,4),(0,6),(0,7),(0,9),(1,3),(1,5),(1,7),(1,8),(1,9),(2,4),(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),(6,8),(6,9),(7,8),(8,9)],10)
[[1,4],[2,5],[3,6],[7,8],[9,10]]=>[9,10,7,8,3,6,2,5,1,4]=>[9,10,7,8,3,6,2,5,1,4]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(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),(6,8),(6,9),(7,8),(7,9)],10)
[[1,4],[2,5],[3,6],[7,9],[8,10]]=>[8,10,7,9,3,6,2,5,1,4]=>[8,10,7,9,3,6,2,5,1,4]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,9),(5,6),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,4],[2,5],[3,7],[6,8],[9,10]]=>[9,10,6,8,3,7,2,5,1,4]=>[9,10,6,8,3,7,2,5,1,4]=>([(0,2),(0,3),(0,5),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(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),(6,7),(6,8),(6,9),(7,9),(8,9)],10)
[[1,4],[2,5],[3,7],[6,9],[8,10]]=>[8,10,6,9,3,7,2,5,1,4]=>[8,10,6,9,3,7,2,5,1,4]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,8),(5,9),(6,7),(6,8),(7,8),(7,9),(8,9)],10)
[[1,4],[2,5],[3,8],[6,9],[7,10]]=>[7,10,6,9,3,8,2,5,1,4]=>[7,10,6,9,3,8,2,5,1,4]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(0,9),(1,2),(1,4),(1,5),(1,6),(1,8),(2,4),(2,6),(2,7),(2,8),(2,9),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,4],[2,6],[3,7],[5,8],[9,10]]=>[9,10,5,8,3,7,2,6,1,4]=>[9,10,5,8,3,7,2,6,1,4]=>([(0,1),(0,3),(0,5),(0,6),(0,7),(0,9),(1,2),(1,4),(1,6),(1,7),(1,8),(2,4),(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),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,4],[2,6],[3,7],[5,9],[8,10]]=>[8,10,5,9,3,7,2,6,1,4]=>[8,10,5,9,3,7,2,6,1,4]=>([(0,2),(0,3),(0,4),(0,7),(0,8),(0,9),(1,3),(1,4),(1,5),(1,6),(1,8),(1,9),(2,4),(2,5),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,8),(4,6),(4,7),(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],[2,6],[3,8],[5,9],[7,10]]=>[7,10,5,9,3,8,2,6,1,4]=>[7,10,5,9,3,8,2,6,1,4]=>([(0,1),(0,2),(0,3),(0,5),(0,7),(0,9),(1,2),(1,3),(1,4),(1,6),(1,8),(2,4),(2,6),(2,8),(2,9),(3,5),(3,7),(3,8),(3,9),(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],[2,7],[3,8],[5,9],[6,10]]=>[6,10,5,9,3,8,2,7,1,4]=>[6,10,5,9,3,8,2,7,1,4]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(1,4),(1,5),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,5],[2,6],[3,7],[4,8],[9,10]]=>[9,10,4,8,3,7,2,6,1,5]=>[9,10,4,8,3,7,2,6,1,5]=>([(0,3),(0,5),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,8),(1,9),(2,4),(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)],10)
[[1,5],[2,6],[3,7],[4,9],[8,10]]=>[8,10,4,9,3,7,2,6,1,5]=>[8,10,4,9,3,7,2,6,1,5]=>([(0,2),(0,4),(0,6),(0,7),(0,9),(1,3),(1,5),(1,7),(1,8),(1,9),(2,4),(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),(6,8),(6,9),(7,8),(8,9)],10)
[[1,5],[2,6],[3,8],[4,9],[7,10]]=>[7,10,4,9,3,8,2,6,1,5]=>[7,10,4,9,3,8,2,6,1,5]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(1,4),(1,5),(1,7),(1,8),(1,9),(2,3),(2,5),(2,6),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)
[[1,5],[2,7],[3,8],[4,9],[6,10]]=>[6,10,4,9,3,8,2,7,1,5]=>[6,10,4,9,3,8,2,7,1,5]=>([(0,1),(0,3),(0,5),(0,7),(0,9),(1,2),(1,4),(1,6),(1,8),(2,4),(2,6),(2,8),(2,9),(3,5),(3,7),(3,8),(3,9),(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],[3,4],[5,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,5,6,3,4,1,2]=>[10,12,9,11,7,8,5,6,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,5,6,3,4,1,2]=>[11,12,8,10,7,9,5,6,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,5,6,3,4,1,2]=>[10,12,8,11,7,9,5,6,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,5,6,3,4,1,2]=>[9,12,8,11,7,10,5,6,3,4,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,5,7,3,4,1,2]=>[11,12,9,10,6,8,5,7,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,5,7,3,4,1,2]=>[10,12,9,11,6,8,5,7,3,4,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,5,7,3,4,1,2]=>[11,12,8,10,6,9,5,7,3,4,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,5,7,3,4,1,2]=>[10,12,8,11,6,9,5,7,3,4,1,2]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,5,7,3,4,1,2]=>[9,12,8,11,6,10,5,7,3,4,1,2]=>([(0,2),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,5,8,3,4,1,2]=>[11,12,7,10,6,9,5,8,3,4,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,5,8,3,4,1,2]=>[10,12,7,11,6,9,5,8,3,4,1,2]=>([(0,2),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,5,8,3,4,1,2]=>[9,12,7,11,6,10,5,8,3,4,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,5,9,3,4,1,2]=>[8,12,7,11,6,10,5,9,3,4,1,2]=>([(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,4,6,3,5,1,2]=>[11,12,9,10,7,8,4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,4,6,3,5,1,2]=>[10,12,9,11,7,8,4,6,3,5,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,4,6,3,5,1,2]=>[11,12,8,10,7,9,4,6,3,5,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,4,6,3,5,1,2]=>[10,12,8,11,7,9,4,6,3,5,1,2]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(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],[3,5],[4,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,4,6,3,5,1,2]=>[9,12,8,11,7,10,4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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)],12)
[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,4,7,3,5,1,2]=>[11,12,9,10,6,8,4,7,3,5,1,2]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,4,7,3,5,1,2]=>[10,12,9,11,6,8,4,7,3,5,1,2]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(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],[3,5],[4,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,4,7,3,5,1,2]=>[11,12,8,10,6,9,4,7,3,5,1,2]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,4,7,3,5,1,2]=>[10,12,8,11,6,9,4,7,3,5,1,2]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(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),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,4,7,3,5,1,2]=>[9,12,8,11,6,10,4,7,3,5,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,4,8,3,5,1,2]=>[11,12,7,10,6,9,4,8,3,5,1,2]=>([(0,2),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,4,8,3,5,1,2]=>[10,12,7,11,6,9,4,8,3,5,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,4,8,3,5,1,2]=>[9,12,7,11,6,10,4,8,3,5,1,2]=>([(0,1),(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(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),(5,9),(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),(9,11),(10,11)],12)
[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,4,9,3,5,1,2]=>[8,12,7,11,6,10,4,9,3,5,1,2]=>([(0,2),(0,4),(0,6),(0,7),(0,9),(0,10),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,4,7,3,6,1,2]=>[11,12,9,10,5,8,4,7,3,6,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,4,7,3,6,1,2]=>[10,12,9,11,5,8,4,7,3,6,1,2]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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)],12)
[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,4,7,3,6,1,2]=>[11,12,8,10,5,9,4,7,3,6,1,2]=>([(0,2),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,4,7,3,6,1,2]=>[10,12,8,11,5,9,4,7,3,6,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,4,7,3,6,1,2]=>[9,12,8,11,5,10,4,7,3,6,1,2]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(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),(4,8),(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),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,4,8,3,6,1,2]=>[11,12,7,10,5,9,4,8,3,6,1,2]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,4,8,3,6,1,2]=>[10,12,7,11,5,9,4,8,3,6,1,2]=>([(0,1),(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(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),(5,9),(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),(9,11),(10,11)],12)
[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,4,8,3,6,1,2]=>[9,12,7,11,5,10,4,8,3,6,1,2]=>([(0,1),(0,2),(0,3),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,8),(1,9),(1,10),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,4,9,3,6,1,2]=>[8,12,7,11,5,10,4,9,3,6,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(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),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,4,8,3,7,1,2]=>[11,12,6,10,5,9,4,8,3,7,1,2]=>([(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,4,8,3,7,1,2]=>[10,12,6,11,5,9,4,8,3,7,1,2]=>([(0,2),(0,4),(0,6),(0,7),(0,9),(0,10),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,4,8,3,7,1,2]=>[9,12,6,11,5,10,4,8,3,7,1,2]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(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),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,4,9,3,7,1,2]=>[8,12,6,11,5,10,4,9,3,7,1,2]=>([(0,1),(0,3),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,6),(1,8),(1,9),(1,10),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,4,9,3,8,1,2]=>[7,12,6,11,5,10,4,9,3,8,1,2]=>([(0,3),(0,5),(0,7),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,8),(1,10),(1,11),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(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)],12)
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,2,4,1,3]=>[11,12,9,10,7,8,5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,5,6,2,4,1,3]=>[10,12,9,11,7,8,5,6,2,4,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,5,6,2,4,1,3]=>[11,12,8,10,7,9,5,6,2,4,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,5,6,2,4,1,3]=>[10,12,8,11,7,9,5,6,2,4,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(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],[5,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,5,6,2,4,1,3]=>[9,12,8,11,7,10,5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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)],12)
[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,5,7,2,4,1,3]=>[11,12,9,10,6,8,5,7,2,4,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,5,7,2,4,1,3]=>[10,12,9,11,6,8,5,7,2,4,1,3]=>([(0,2),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(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],[5,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,5,7,2,4,1,3]=>[11,12,8,10,6,9,5,7,2,4,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(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],[5,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,5,7,2,4,1,3]=>[10,12,8,11,6,9,5,7,2,4,1,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,10),(3,11),(4,6),(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],[5,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,5,7,2,4,1,3]=>[9,12,8,11,6,10,5,7,2,4,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,10),(5,11),(6,7),(6,8),(6,9),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,5,8,2,4,1,3]=>[11,12,7,10,6,9,5,8,2,4,1,3]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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)],12)
[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,5,8,2,4,1,3]=>[10,12,7,11,6,9,5,8,2,4,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,10),(5,11),(6,7),(6,8),(6,9),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,5,8,2,4,1,3]=>[9,12,7,11,6,10,5,8,2,4,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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],[5,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,5,9,2,4,1,3]=>[8,12,7,11,6,10,5,9,2,4,1,3]=>([(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(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),(6,8),(6,9),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,4,6,2,5,1,3]=>[11,12,9,10,7,8,4,6,2,5,1,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,4,6,2,5,1,3]=>[10,12,9,11,7,8,4,6,2,5,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(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],[2,5],[4,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,4,6,2,5,1,3]=>[11,12,8,10,7,9,4,6,2,5,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(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],[2,5],[4,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,4,6,2,5,1,3]=>[10,12,8,11,7,9,4,6,2,5,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,3),(2,4),(2,5),(2,7),(2,8),(2,9),(2,11),(3,4),(3,5),(3,6),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(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],[2,5],[4,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,4,6,2,5,1,3]=>[9,12,8,11,7,10,4,6,2,5,1,3]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,10),(1,11),(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),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(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],[2,5],[4,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,4,7,2,5,1,3]=>[11,12,9,10,6,8,4,7,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,4,7,2,5,1,3]=>[10,12,9,11,6,8,4,7,2,5,1,3]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,10),(3,11),(4,6),(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],[2,5],[4,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,4,7,2,5,1,3]=>[11,12,8,10,6,9,4,7,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(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),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,4,7,2,5,1,3]=>[10,12,8,11,6,9,4,7,2,5,1,3]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(2,3),(2,4),(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),(4,8),(4,9),(4,10),(4,11),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,10),(6,11),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,4,7,2,5,1,3]=>[9,12,8,11,6,10,4,7,2,5,1,3]=>([(0,2),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,3),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,4,8,2,5,1,3]=>[11,12,7,10,6,9,4,8,2,5,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,4,8,2,5,1,3]=>[10,12,7,11,6,9,4,8,2,5,1,3]=>([(0,3),(0,4),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(6,7),(6,9),(6,10),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,4,8,2,5,1,3]=>[9,12,7,11,6,10,4,8,2,5,1,3]=>([(0,3),(0,4),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(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),(2,11),(3,4),(3,6),(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),(6,9),(6,10),(7,8),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,4,9,2,5,1,3]=>[8,12,7,11,6,10,4,9,2,5,1,3]=>([(0,2),(0,4),(0,6),(0,7),(0,8),(0,9),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,4,7,2,6,1,3]=>[11,12,9,10,5,8,4,7,2,6,1,3]=>([(0,2),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,4,7,2,6,1,3]=>[10,12,9,11,5,8,4,7,2,6,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,10),(5,11),(6,7),(6,8),(6,9),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,4,7,2,6,1,3]=>[11,12,8,10,5,9,4,7,2,6,1,3]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,4,7,2,6,1,3]=>[10,12,8,11,5,9,4,7,2,6,1,3]=>([(0,3),(0,4),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(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),(6,7),(6,9),(6,10),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,4,7,2,6,1,3]=>[9,12,8,11,5,10,4,7,2,6,1,3]=>([(0,3),(0,4),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(2,11),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,10),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,4,8,2,6,1,3]=>[11,12,7,10,5,9,4,8,2,6,1,3]=>([(0,1),(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(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),(5,9),(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),(9,11),(10,11)],12)
[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,4,8,2,6,1,3]=>[10,12,7,11,5,9,4,8,2,6,1,3]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,7),(2,8),(2,10),(2,11),(3,5),(3,6),(3,7),(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),(6,10),(7,9),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,4,8,2,6,1,3]=>[9,12,7,11,5,10,4,8,2,6,1,3]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,7),(2,8),(2,10),(3,4),(3,6),(3,7),(3,8),(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),(6,8),(6,9),(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],[2,6],[4,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,4,9,2,6,1,3]=>[8,12,7,11,5,10,4,9,2,6,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,8),(0,9),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(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),(5,7),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(10,11)],12)
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,4,8,2,7,1,3]=>[11,12,6,10,5,9,4,8,2,7,1,3]=>([(0,2),(0,4),(0,6),(0,7),(0,9),(0,10),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,4,8,2,7,1,3]=>[10,12,6,11,5,9,4,8,2,7,1,3]=>([(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(6,10),(6,11),(7,9),(7,10),(7,11),(8,9),(8,10),(9,11),(10,11)],12)
[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,4,8,2,7,1,3]=>[9,12,6,11,5,10,4,8,2,7,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(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),(5,7),(5,8),(5,9),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,4,9,2,7,1,3]=>[8,12,6,11,5,10,4,9,2,7,1,3]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,6),(3,7),(3,8),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(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],[2,8],[4,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,4,9,2,8,1,3]=>[7,12,6,11,5,10,4,9,2,8,1,3]=>([(0,2),(0,4),(0,6),(0,8),(0,9),(0,11),(1,3),(1,5),(1,7),(1,9),(1,10),(1,11),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(10,11)],12)
[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,3,6,2,5,1,4]=>[11,12,9,10,7,8,3,6,2,5,1,4]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,3,6,2,5,1,4]=>[10,12,9,11,7,8,3,6,2,5,1,4]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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)],12)
[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,3,6,2,5,1,4]=>[11,12,8,10,7,9,3,6,2,5,1,4]=>([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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)],12)
[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,3,6,2,5,1,4]=>[10,12,8,11,7,9,3,6,2,5,1,4]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,10),(1,11),(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),(4,7),(4,8),(4,9),(4,11),(5,6),(5,8),(5,9),(5,10),(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)
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,3,6,2,5,1,4]=>[9,12,8,11,7,10,3,6,2,5,1,4]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,7),(2,8),(2,9),(2,11),(3,4),(3,5),(3,6),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(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)
[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,3,7,2,5,1,4]=>[11,12,9,10,6,8,3,7,2,5,1,4]=>([(0,2),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,3),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,3,7,2,5,1,4]=>[10,12,9,11,6,8,3,7,2,5,1,4]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,10),(5,11),(6,7),(6,8),(6,9),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,3,7,2,5,1,4]=>[11,12,8,10,6,9,3,7,2,5,1,4]=>([(0,2),(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(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),(5,7),(5,8),(5,9),(5,10),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,3,7,2,5,1,4]=>[10,12,8,11,6,9,3,7,2,5,1,4]=>([(0,2),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,11),(1,3),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(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),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,3,7,2,5,1,4]=>[9,12,8,11,6,10,3,7,2,5,1,4]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,7),(1,8),(1,10),(2,3),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(4,7),(4,8),(4,10),(4,11),(5,6),(5,7),(5,9),(5,10),(5,11),(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)
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,3,8,2,5,1,4]=>[11,12,7,10,6,9,3,8,2,5,1,4]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(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),(4,8),(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),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,3,8,2,5,1,4]=>[10,12,7,11,6,9,3,8,2,5,1,4]=>([(0,3),(0,4),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(2,9),(2,11),(3,4),(3,5),(3,6),(3,7),(3,10),(3,11),(4,5),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,10),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,3,8,2,5,1,4]=>[9,12,7,11,6,10,3,8,2,5,1,4]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(0,11),(1,2),(1,3),(1,4),(1,7),(1,8),(1,9),(1,10),(2,3),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,6),(3,7),(3,8),(3,10),(3,11),(4,5),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(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)
[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,3,9,2,5,1,4]=>[8,12,7,11,6,10,3,9,2,5,1,4]=>([(0,2),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,10),(4,11),(5,6),(5,7),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,3,7,2,6,1,4]=>[11,12,9,10,5,8,3,7,2,6,1,4]=>([(0,3),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,3,7,2,6,1,4]=>[10,12,9,11,5,8,3,7,2,6,1,4]=>([(0,1),(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(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)
[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,3,7,2,6,1,4]=>[11,12,8,10,5,9,3,7,2,6,1,4]=>([(0,1),(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(1,10),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(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),(5,9),(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),(9,11),(10,11)],12)
[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,3,7,2,6,1,4]=>[10,12,8,11,5,9,3,7,2,6,1,4]=>([(0,3),(0,4),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(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),(2,11),(3,4),(3,6),(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),(6,9),(6,10),(7,8),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,3,7,2,6,1,4]=>[9,12,8,11,5,10,3,7,2,6,1,4]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,7),(0,9),(0,11),(1,2),(1,3),(1,4),(1,7),(1,8),(1,9),(1,10),(2,3),(2,5),(2,6),(2,7),(2,8),(2,10),(2,11),(3,6),(3,7),(3,8),(3,10),(3,11),(4,5),(4,6),(4,7),(4,9),(4,10),(4,11),(5,6),(5,8),(5,9),(5,10),(5,11),(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)
[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,3,8,2,6,1,4]=>[11,12,7,10,5,9,3,8,2,6,1,4]=>([(0,1),(0,2),(0,3),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,8),(1,9),(1,10),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,3,8,2,6,1,4]=>[10,12,7,11,5,9,3,8,2,6,1,4]=>([(0,1),(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,2),(1,5),(1,6),(1,7),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,7),(2,8),(2,10),(3,4),(3,6),(3,7),(3,8),(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),(6,8),(6,9),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,3,8,2,6,1,4]=>[9,12,7,11,5,10,3,8,2,6,1,4]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,7),(0,9),(0,11),(1,2),(1,3),(1,4),(1,5),(1,6),(1,8),(1,10),(2,3),(2,4),(2,6),(2,8),(2,10),(2,11),(3,5),(3,7),(3,9),(3,10),(3,11),(4,6),(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)
[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,3,9,2,6,1,4]=>[8,12,7,11,5,10,3,9,2,6,1,4]=>([(0,2),(0,3),(0,4),(0,6),(0,7),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(4,6),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,10),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,3,8,2,7,1,4]=>[11,12,6,10,5,9,3,8,2,7,1,4]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(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),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,3,8,2,7,1,4]=>[10,12,6,11,5,9,3,8,2,7,1,4]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(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),(5,7),(5,8),(5,9),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(10,11)],12)
[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,3,8,2,7,1,4]=>[9,12,6,11,5,10,3,8,2,7,1,4]=>([(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,3),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(6,7),(6,8),(6,10),(7,9),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,3,9,2,7,1,4]=>[8,12,6,11,5,10,3,9,2,7,1,4]=>([(0,1),(0,2),(0,4),(0,5),(0,9),(0,10),(0,11),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,7),(2,8),(2,10),(3,4),(3,6),(3,7),(3,8),(3,10),(3,11),(4,5),(4,7),(4,9),(4,11),(5,6),(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)
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,3,9,2,8,1,4]=>[7,12,6,11,5,10,3,9,2,8,1,4]=>([(0,2),(0,4),(0,5),(0,7),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,7),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(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),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>[11,12,9,10,4,8,3,7,2,6,1,5]=>[11,12,9,10,4,8,3,7,2,6,1,5]=>([(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(8,10),(8,11),(9,10),(9,11)],12)
[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>[10,12,9,11,4,8,3,7,2,6,1,5]=>[10,12,9,11,4,8,3,7,2,6,1,5]=>([(0,3),(0,5),(0,6),(0,7),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(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),(6,8),(6,9),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>[11,12,8,10,4,9,3,7,2,6,1,5]=>[11,12,8,10,4,9,3,7,2,6,1,5]=>([(0,2),(0,4),(0,6),(0,7),(0,9),(0,10),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>[10,12,8,11,4,9,3,7,2,6,1,5]=>[10,12,8,11,4,9,3,7,2,6,1,5]=>([(0,2),(0,4),(0,6),(0,7),(0,8),(0,9),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(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),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(9,10),(9,11),(10,11)],12)
[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>[9,12,8,11,4,10,3,7,2,6,1,5]=>[9,12,8,11,4,10,3,7,2,6,1,5]=>([(0,2),(0,4),(0,5),(0,6),(0,8),(0,9),(0,11),(1,3),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,10),(4,11),(5,6),(5,7),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>[11,12,7,10,4,9,3,8,2,6,1,5]=>[11,12,7,10,4,9,3,8,2,6,1,5]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(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),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(9,11),(10,11)],12)
[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>[10,12,7,11,4,9,3,8,2,6,1,5]=>[10,12,7,11,4,9,3,8,2,6,1,5]=>([(0,2),(0,3),(0,5),(0,6),(0,8),(0,9),(0,11),(1,4),(1,5),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,9),(2,10),(2,11),(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),(5,7),(5,9),(5,10),(5,11),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(10,11)],12)
[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>[9,12,7,11,4,10,3,8,2,6,1,5]=>[9,12,7,11,4,10,3,8,2,6,1,5]=>([(0,2),(0,3),(0,4),(0,6),(0,7),(0,9),(0,11),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,5),(3,8),(3,9),(3,10),(3,11),(4,6),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,7),(6,8),(6,10),(7,8),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>[8,12,7,11,4,10,3,9,2,6,1,5]=>[8,12,7,11,4,10,3,9,2,6,1,5]=>([(0,3),(0,5),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,5),(2,6),(2,8),(2,10),(3,4),(3,5),(3,7),(3,9),(3,11),(4,5),(4,6),(4,8),(4,10),(4,11),(5,7),(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],[2,7],[3,8],[4,9],[6,10],[11,12]]=>[11,12,6,10,4,9,3,8,2,7,1,5]=>[11,12,6,10,4,9,3,8,2,7,1,5]=>([(0,1),(0,3),(0,5),(0,7),(0,8),(0,9),(0,11),(1,2),(1,4),(1,6),(1,8),(1,9),(1,10),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>[10,12,6,11,4,9,3,8,2,7,1,5]=>[10,12,6,11,4,9,3,8,2,7,1,5]=>([(0,2),(0,3),(0,5),(0,6),(0,9),(0,10),(0,11),(1,3),(1,4),(1,6),(1,7),(1,8),(1,10),(1,11),(2,5),(2,6),(2,7),(2,9),(2,10),(2,11),(3,4),(3,6),(3,7),(3,8),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(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],[2,7],[3,8],[4,10],[6,11],[9,12]]=>[9,12,6,11,4,10,3,8,2,7,1,5]=>[9,12,6,11,4,10,3,8,2,7,1,5]=>([(0,1),(0,2),(0,4),(0,5),(0,9),(0,10),(0,11),(1,4),(1,5),(1,8),(1,9),(1,10),(1,11),(2,3),(2,4),(2,6),(2,7),(2,8),(2,10),(3,4),(3,6),(3,7),(3,8),(3,10),(3,11),(4,5),(4,7),(4,9),(4,11),(5,6),(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],[2,7],[3,9],[4,10],[6,11],[8,12]]=>[8,12,6,11,4,10,3,9,2,7,1,5]=>[8,12,6,11,4,10,3,9,2,7,1,5]=>([(0,1),(0,2),(0,3),(0,5),(0,7),(0,9),(0,11),(1,2),(1,3),(1,4),(1,6),(1,8),(1,10),(2,4),(2,6),(2,8),(2,10),(2,11),(3,5),(3,7),(3,9),(3,10),(3,11),(4,6),(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)
[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>[7,12,6,11,4,10,3,9,2,8,1,5]=>[7,12,6,11,4,10,3,9,2,8,1,5]=>([(0,2),(0,3),(0,5),(0,6),(0,8),(0,11),(1,4),(1,5),(1,7),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,10),(2,11),(3,6),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(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)
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>[11,12,5,10,4,9,3,8,2,7,1,6]=>[11,12,5,10,4,9,3,8,2,7,1,6]=>([(0,3),(0,5),(0,7),(0,9),(0,10),(0,11),(1,2),(1,4),(1,6),(1,8),(1,10),(1,11),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(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)],12)
[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>[10,12,5,11,4,9,3,8,2,7,1,6]=>[10,12,5,11,4,9,3,8,2,7,1,6]=>([(0,2),(0,4),(0,6),(0,8),(0,9),(0,11),(1,3),(1,5),(1,7),(1,9),(1,10),(1,11),(2,4),(2,6),(2,8),(2,9),(2,10),(2,11),(3,5),(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),(6,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(8,10),(8,11),(9,10),(10,11)],12)
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>[9,12,5,11,4,10,3,8,2,7,1,6]=>[9,12,5,11,4,10,3,8,2,7,1,6]=>([(0,2),(0,4),(0,5),(0,7),(0,9),(0,11),(1,3),(1,6),(1,7),(1,8),(1,10),(1,11),(2,4),(2,5),(2,7),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,5),(4,6),(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),(7,10),(8,9),(8,10),(8,11),(9,10),(9,11),(10,11)],12)
[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>[8,12,5,11,4,10,3,9,2,7,1,6]=>[8,12,5,11,4,10,3,9,2,7,1,6]=>([(0,2),(0,3),(0,5),(0,6),(0,8),(0,11),(1,4),(1,5),(1,7),(1,9),(1,10),(1,11),(2,3),(2,5),(2,6),(2,8),(2,10),(2,11),(3,6),(3,8),(3,9),(3,10),(3,11),(4,5),(4,7),(4,8),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(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)
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>[7,12,5,11,4,10,3,9,2,8,1,6]=>[7,12,5,11,4,10,3,9,2,8,1,6]=>([(0,1),(0,3),(0,5),(0,7),(0,9),(0,11),(1,2),(1,4),(1,6),(1,8),(1,10),(2,4),(2,6),(2,8),(2,10),(2,11),(3,5),(3,7),(3,9),(3,10),(3,11),(4,6),(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)
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>([(0,3),(0,5),(0,7),(0,9),(0,11),(1,2),(1,4),(1,6),(1,8),(1,10),(2,4),(2,6),(2,8),(2,10),(2,11),(3,5),(3,7),(3,9),(3,10),(3,11),(4,6),(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)
[[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,9,7]=>([(6,8),(7,8)],9)
[[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,10,8]=>([(7,9),(8,9)],10)
[[1,2,3,4,5,10],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5,10]=>[1,6,7,8,9,10,2,3,4,5]=>([(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)
[]=>[]=>[]=>([],0)
[[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,2]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[7,9,8,6,5,4,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[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)
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[8,10,9,7,6,5,4,3,2,1]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(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)
[[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[2,3,4,5,6,7,9,1,8]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[2,3,4,5,6,7,9,8,1]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(6,8),(7,8)],9)
[[1,3,4,5,6,7],[2,8,9]]=>[2,8,9,1,3,4,5,6,7]=>[2,3,4,5,8,9,1,6,7]=>([(0,8),(1,8),(2,8),(3,8),(4,6),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[2,3,9,8,7,6,5,4,1]=>([(0,8),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[2,9,8,7,6,5,4,3,1]=>([(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,10,1,9]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,10,9,1]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(7,9),(8,9)],10)
[[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[2,3,4,5,6,9,10,1,7,8]=>([(0,9),(1,9),(2,9),(3,9),(4,9),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,2,1,3]=>[2,10,9,8,7,6,5,4,3,1]=>([(0,9),(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)
[[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[1,2,4,5,6,7,8,9,10,3]=>([(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[1,2,3,5,6,7,8,9,10,4]=>([(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[1,2,3,4,5,6,8,9,10,7]=>([(6,9),(7,9),(8,9)],10)
[[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[1,2,3,4,5,7,8,9,10,6]=>([(5,9),(6,9),(7,9),(8,9)],10)
[[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[1,2,3,4,6,7,8,9,10,5]=>([(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[[1,2,4,5,6,7,8,9,10,11,12],[3]]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>([(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
[[1,2,5,6,7,8],[3,4],[9]]=>[9,3,4,1,2,5,6,7,8]=>[3,4,5,6,7,9,1,8,2]=>([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8)],9)
[[1,2,5,6,7,8,9],[3,4],[10]]=>[10,3,4,1,2,5,6,7,8,9]=>[3,4,5,6,7,8,10,1,9,2]=>([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9)],10)
[[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[1,4,5,6,7,8,9,3,2]=>([(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)
[[1,2,4,5,6,7,8,9],[3],[10]]=>[10,3,1,2,4,5,6,7,8,9]=>[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)
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[3,10,9,8,7,6,5,4,2,1]=>([(0,8),(0,9),(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)
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[4,10,9,8,7,6,5,3,2,1]=>([(0,7),(0,8),(0,9),(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)
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[10,9,7,6,5,4,3,2,1,8]=>[7,10,9,8,6,5,4,3,2,1]=>([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(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)
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[10,9,8,6,5,4,3,2,1,7]=>[6,10,9,8,7,5,4,3,2,1]=>([(0,5),(0,6),(0,7),(0,8),(0,9),(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)
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,4,3,2,1,6]=>[5,10,9,8,7,6,4,3,2,1]=>([(0,6),(0,7),(0,8),(0,9),(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)
[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,1,2,4]=>[1,3,9,8,7,6,5,4,2]=>([(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(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)
[[1,2,3,5],[4],[6],[7],[8],[9]]=>[9,8,7,6,4,1,2,3,5]=>[1,2,4,9,8,7,6,5,3]=>([(2,8),(3,4),(3,5),(3,6),(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],[3,4],[5,6],[7,9],[8]]=>[8,7,9,5,6,3,4,1,2]=>[8,9,5,7,3,6,1,4,2]=>([(0,1),(0,3),(0,4),(0,5),(0,6),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(2,3),(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),(7,8)],9)
[[1,2,3,4,6],[5],[7],[8],[9]]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,9,8,7,6,4]=>([(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[[1,2,3,4,5,7],[6],[8],[9]]=>[9,8,6,1,2,3,4,5,7]=>[1,2,3,4,6,9,8,7,5]=>([(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)
[[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,9,8,6]=>([(5,8),(6,7),(6,8),(7,8)],9)
[[1,2,4,5,6,7,8],[3,9]]=>[3,9,1,2,4,5,6,7,8]=>[1,3,4,5,6,7,9,2,8]=>([(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[[1,2,4,5,6,7,8,9],[3,10]]=>[3,10,1,2,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,10,2,9]=>([(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[[1,2],[3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,9,1,2]=>[8,9,1,7,6,5,4,3,2]=>([(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8)],9)
[[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[2,3,4,5,6,8,9,1,7]=>([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(5,8),(6,7),(6,8)],9)
[[1,2,3,4,6],[5,7,8,9]]=>[5,7,8,9,1,2,3,4,6]=>[1,5,7,8,9,2,3,4,6]=>([(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(3,8),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8)],9)
[[1,2,3,4,5,7,8],[6,9]]=>[6,9,1,2,3,4,5,7,8]=>[1,2,3,4,6,7,9,5,8]=>([(4,8),(5,8),(6,7),(7,8)],9)
[[1,4,5,6,7,8],[2,9],[3]]=>[3,2,9,1,4,5,6,7,8]=>[3,4,5,6,7,9,2,8,1]=>([(0,7),(0,8),(1,7),(1,8),(2,7),(2,8),(3,7),(3,8),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
cactus evacuation
Description
The cactus evacuation of a permutation.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
This is the involution obtained by applying evacuation to the recording tableau, while preserving the insertion tableau.
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.
searching the database
Sorry, this map was not found in the database.