Identifier
Mp00113: Perfect matchings —reverse⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
=>
Cc0012;cc-rep-0Cc0012;cc-rep-1Cc0014;cc-rep-3
[(1,2)]=>[(1,2)]=>[2,1]=>([],2) [(1,2),(3,4)]=>[(1,2),(3,4)]=>[2,1,4,3]=>([(0,2),(0,3),(1,2),(1,3)],4) [(1,3),(2,4)]=>[(1,3),(2,4)]=>[3,4,1,2]=>([(0,3),(1,2)],4) [(1,4),(2,3)]=>[(1,4),(2,3)]=>[3,4,2,1]=>([(2,3)],4) [(1,2),(3,4),(5,6)]=>[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) [(1,3),(2,4),(5,6)]=>[(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) [(1,4),(2,3),(5,6)]=>[(1,2),(3,6),(4,5)]=>[2,1,5,6,4,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) [(1,5),(2,3),(4,6)]=>[(1,3),(2,6),(4,5)]=>[3,5,1,6,4,2]=>([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) [(1,6),(2,3),(4,5)]=>[(1,6),(2,3),(4,5)]=>[3,5,2,6,4,1]=>([(1,4),(1,5),(2,3),(2,4),(3,5)],6) [(1,6),(2,4),(3,5)]=>[(1,6),(2,4),(3,5)]=>[4,5,6,2,3,1]=>([(1,3),(2,4),(4,5)],6) [(1,5),(2,4),(3,6)]=>[(1,4),(2,6),(3,5)]=>[4,5,6,1,3,2]=>([(0,5),(1,3),(1,4),(5,2)],6) [(1,4),(2,5),(3,6)]=>[(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>([(0,5),(1,4),(4,2),(5,3)],6) [(1,3),(2,5),(4,6)]=>[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) [(1,2),(3,5),(4,6)]=>[(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) [(1,2),(3,6),(4,5)]=>[(1,4),(2,3),(5,6)]=>[3,4,2,1,6,5]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) [(1,3),(2,6),(4,5)]=>[(1,5),(2,3),(4,6)]=>[3,5,2,6,1,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) [(1,4),(2,6),(3,5)]=>[(1,5),(2,4),(3,6)]=>[4,5,6,2,1,3]=>([(0,5),(1,5),(2,3),(3,4)],6) [(1,5),(2,6),(3,4)]=>[(1,5),(2,6),(3,4)]=>[4,5,6,3,1,2]=>([(1,3),(2,4),(4,5)],6) [(1,6),(2,5),(3,4)]=>[(1,6),(2,5),(3,4)]=>[4,5,6,3,2,1]=>([(3,4),(4,5)],6) [(1,2),(3,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8) [(1,3),(2,4),(5,6),(7,8)]=>[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8) [(1,4),(2,3),(5,6),(7,8)]=>[(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,7,8,6,5]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8) [(1,5),(2,3),(4,6),(7,8)]=>[(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,7,3,8,6,4]=>([(0,6),(0,7),(1,6),(1,7),(3,5),(6,3),(6,4),(7,2),(7,4),(7,5)],8) [(1,6),(2,3),(4,5),(7,8)]=>[(1,2),(3,8),(4,5),(6,7)]=>[2,1,5,7,4,8,6,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(6,2),(6,3),(7,3),(7,4)],8) [(1,7),(2,3),(4,5),(6,8)]=>[(1,3),(2,8),(4,5),(6,7)]=>[3,5,1,7,4,8,6,2]=>([(0,3),(0,7),(1,2),(1,6),(1,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8) [(1,8),(2,3),(4,5),(6,7)]=>[(1,8),(2,3),(4,5),(6,7)]=>[3,5,2,7,4,8,6,1]=>([(1,3),(1,7),(2,6),(2,7),(3,5),(3,6),(6,4),(7,4),(7,5)],8) [(1,8),(2,4),(3,5),(6,7)]=>[(1,8),(2,3),(4,6),(5,7)]=>[3,6,2,7,8,4,5,1]=>([(1,6),(1,7),(2,3),(2,6),(3,7),(6,5),(7,4)],8) [(1,7),(2,4),(3,5),(6,8)]=>[(1,3),(2,8),(4,6),(5,7)]=>[3,6,1,7,8,4,5,2]=>([(0,5),(0,7),(1,4),(1,6),(1,7),(5,6),(6,3),(7,2)],8) [(1,6),(2,4),(3,5),(7,8)]=>[(1,2),(3,8),(4,6),(5,7)]=>[2,1,6,7,8,4,5,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,3),(6,4),(7,2)],8) [(1,5),(2,4),(3,6),(7,8)]=>[(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,7,8,3,5,4]=>([(0,6),(0,7),(1,6),(1,7),(5,4),(6,5),(7,2),(7,3)],8) [(1,4),(2,5),(3,6),(7,8)]=>[(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8) [(1,3),(2,5),(4,6),(7,8)]=>[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8) [(1,2),(3,5),(4,6),(7,8)]=>[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(6,3),(7,2)],8) [(1,2),(3,6),(4,5),(7,8)]=>[(1,2),(3,6),(4,5),(7,8)]=>[2,1,5,6,4,3,8,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8) [(1,3),(2,6),(4,5),(7,8)]=>[(1,2),(3,7),(4,5),(6,8)]=>[2,1,5,7,4,8,3,6]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(4,7),(5,2),(5,7),(6,3),(6,7)],8) [(1,4),(2,6),(3,5),(7,8)]=>[(1,2),(3,7),(4,6),(5,8)]=>[2,1,6,7,8,4,3,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(5,2),(6,4),(7,4)],8) [(1,5),(2,6),(3,4),(7,8)]=>[(1,2),(3,7),(4,8),(5,6)]=>[2,1,6,7,8,5,3,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,3),(6,4),(7,2)],8) [(1,6),(2,5),(3,4),(7,8)]=>[(1,2),(3,8),(4,7),(5,6)]=>[2,1,6,7,8,5,4,3]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(7,2)],8) [(1,7),(2,5),(3,4),(6,8)]=>[(1,3),(2,8),(4,7),(5,6)]=>[3,6,1,7,8,5,4,2]=>([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(1,7),(4,7),(7,2)],8) [(1,8),(2,5),(3,4),(6,7)]=>[(1,8),(2,3),(4,7),(5,6)]=>[3,6,2,7,8,5,4,1]=>([(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,7),(7,4)],8) [(1,8),(2,6),(3,4),(5,7)]=>[(1,8),(2,4),(3,7),(5,6)]=>[4,6,7,2,8,5,3,1]=>([(1,4),(1,6),(2,3),(2,6),(2,7),(4,5),(5,7)],8) [(1,7),(2,6),(3,4),(5,8)]=>[(1,4),(2,8),(3,7),(5,6)]=>[4,6,7,1,8,5,3,2]=>([(0,5),(0,7),(1,2),(1,3),(1,6),(1,7),(4,6),(5,4)],8) [(1,6),(2,7),(3,4),(5,8)]=>[(1,4),(2,7),(3,8),(5,6)]=>[4,6,7,1,8,5,2,3]=>([(0,4),(0,7),(1,5),(1,6),(1,7),(3,6),(4,3),(5,2)],8) [(1,5),(2,7),(3,4),(6,8)]=>[(1,3),(2,7),(4,8),(5,6)]=>[3,6,1,7,8,5,2,4]=>([(0,4),(0,6),(0,7),(1,3),(1,5),(1,6),(3,7),(4,5),(7,2)],8) [(1,4),(2,7),(3,5),(6,8)]=>[(1,3),(2,7),(4,6),(5,8)]=>[3,6,1,7,8,4,2,5]=>([(0,3),(0,6),(1,4),(1,6),(1,7),(3,7),(4,5),(6,5),(7,2)],8) [(1,3),(2,7),(4,5),(6,8)]=>[(1,3),(2,7),(4,5),(6,8)]=>[3,5,1,7,4,8,2,6]=>([(0,3),(0,6),(1,2),(1,5),(1,6),(2,7),(3,5),(3,7),(5,4),(6,4),(6,7)],8) [(1,2),(3,7),(4,5),(6,8)]=>[(1,3),(2,6),(4,5),(7,8)]=>[3,5,1,6,4,2,8,7]=>([(0,2),(0,4),(1,3),(1,4),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8) [(1,2),(3,8),(4,5),(6,7)]=>[(1,6),(2,3),(4,5),(7,8)]=>[3,5,2,6,4,1,8,7]=>([(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) [(1,3),(2,8),(4,5),(6,7)]=>[(1,7),(2,3),(4,5),(6,8)]=>[3,5,2,7,4,8,1,6]=>([(0,7),(1,4),(1,6),(2,3),(2,4),(3,6),(3,7),(4,5),(4,7),(6,5)],8) [(1,4),(2,8),(3,5),(6,7)]=>[(1,7),(2,3),(4,6),(5,8)]=>[3,6,2,7,8,4,1,5]=>([(0,6),(1,5),(1,7),(2,3),(2,5),(3,7),(5,6),(7,4)],8) [(1,5),(2,8),(3,4),(6,7)]=>[(1,7),(2,3),(4,8),(5,6)]=>[3,6,2,7,8,5,1,4]=>([(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,6),(6,4)],8) [(1,6),(2,8),(3,4),(5,7)]=>[(1,7),(2,4),(3,8),(5,6)]=>[4,6,7,2,8,5,1,3]=>([(0,5),(1,5),(1,6),(1,7),(2,3),(2,6),(3,4),(4,7)],8) [(1,7),(2,8),(3,4),(5,6)]=>[(1,7),(2,8),(3,4),(5,6)]=>[4,6,7,3,8,5,1,2]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8) [(1,8),(2,7),(3,4),(5,6)]=>[(1,8),(2,7),(3,4),(5,6)]=>[4,6,7,3,8,5,2,1]=>([(2,6),(2,7),(3,4),(3,6),(4,5),(5,7)],8) [(1,8),(2,7),(3,5),(4,6)]=>[(1,8),(2,7),(3,5),(4,6)]=>[5,6,7,8,3,4,2,1]=>([(2,4),(3,5),(5,6),(6,7)],8) [(1,7),(2,8),(3,5),(4,6)]=>[(1,7),(2,8),(3,5),(4,6)]=>[5,6,7,8,3,4,1,2]=>([(0,5),(1,4),(2,7),(6,3),(7,6)],8) [(1,6),(2,8),(3,5),(4,7)]=>[(1,7),(2,5),(3,8),(4,6)]=>[5,6,7,8,2,4,1,3]=>([(0,7),(1,6),(2,4),(2,7),(5,3),(6,5)],8) [(1,5),(2,8),(3,6),(4,7)]=>[(1,7),(2,5),(3,6),(4,8)]=>[5,6,7,8,2,3,1,4]=>([(0,7),(1,6),(2,4),(4,7),(5,3),(6,5)],8) [(1,4),(2,8),(3,6),(5,7)]=>[(1,7),(2,4),(3,6),(5,8)]=>[4,6,7,2,8,3,1,5]=>([(0,7),(1,3),(1,7),(2,4),(2,6),(3,5),(4,7),(5,6)],8) [(1,3),(2,8),(4,6),(5,7)]=>[(1,7),(2,4),(3,5),(6,8)]=>[4,5,7,2,3,8,1,6]=>([(0,7),(1,3),(2,4),(3,5),(3,7),(4,6),(4,7),(5,6)],8) [(1,2),(3,8),(4,6),(5,7)]=>[(1,6),(2,4),(3,5),(7,8)]=>[4,5,6,2,3,1,8,7]=>([(0,6),(0,7),(1,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) [(1,2),(3,7),(4,6),(5,8)]=>[(1,4),(2,6),(3,5),(7,8)]=>[4,5,6,1,3,2,8,7]=>([(0,5),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8) [(1,3),(2,7),(4,6),(5,8)]=>[(1,4),(2,7),(3,5),(6,8)]=>[4,5,7,1,3,8,2,6]=>([(0,5),(1,2),(1,4),(2,7),(3,6),(4,6),(4,7),(5,3),(5,7)],8) [(1,4),(2,7),(3,6),(5,8)]=>[(1,4),(2,7),(3,6),(5,8)]=>[4,6,7,1,8,3,2,5]=>([(0,5),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(4,6),(5,4)],8) [(1,5),(2,7),(3,6),(4,8)]=>[(1,5),(2,7),(3,6),(4,8)]=>[5,6,7,8,1,3,2,4]=>([(0,6),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5)],8) [(1,6),(2,7),(3,5),(4,8)]=>[(1,5),(2,7),(3,8),(4,6)]=>[5,6,7,8,1,4,2,3]=>([(0,7),(1,4),(1,6),(5,3),(6,2),(7,5)],8) [(1,7),(2,6),(3,5),(4,8)]=>[(1,5),(2,8),(3,7),(4,6)]=>[5,6,7,8,1,4,3,2]=>([(0,7),(1,3),(1,4),(1,5),(6,2),(7,6)],8) [(1,8),(2,6),(3,5),(4,7)]=>[(1,8),(2,5),(3,7),(4,6)]=>[5,6,7,8,2,4,3,1]=>([(1,7),(2,4),(2,5),(6,3),(7,6)],8) [(1,8),(2,5),(3,6),(4,7)]=>[(1,8),(2,5),(3,6),(4,7)]=>[5,6,7,8,2,3,4,1]=>([(1,6),(2,7),(5,4),(6,5),(7,3)],8) [(1,7),(2,5),(3,6),(4,8)]=>[(1,5),(2,8),(3,6),(4,7)]=>[5,6,7,8,1,3,4,2]=>([(0,7),(1,4),(1,6),(5,3),(6,2),(7,5)],8) [(1,6),(2,5),(3,7),(4,8)]=>[(1,5),(2,6),(3,8),(4,7)]=>[5,6,7,8,1,2,4,3]=>([(0,6),(1,7),(5,4),(6,5),(7,2),(7,3)],8) [(1,5),(2,6),(3,7),(4,8)]=>[(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) [(1,4),(2,6),(3,7),(5,8)]=>[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8) [(1,3),(2,6),(4,7),(5,8)]=>[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8) [(1,2),(3,6),(4,7),(5,8)]=>[(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8) [(1,2),(3,5),(4,7),(6,8)]=>[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8) [(1,3),(2,5),(4,7),(6,8)]=>[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8) [(1,4),(2,5),(3,7),(6,8)]=>[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8) [(1,5),(2,4),(3,7),(6,8)]=>[(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,7,8,2,5,4]=>([(0,4),(0,7),(1,3),(1,5),(1,6),(3,7),(4,5),(4,6),(7,2)],8) [(1,6),(2,4),(3,7),(5,8)]=>[(1,4),(2,6),(3,8),(5,7)]=>[4,6,7,1,8,2,5,3]=>([(0,5),(0,7),(1,4),(1,6),(3,7),(4,3),(5,2),(5,6)],8) [(1,7),(2,4),(3,6),(5,8)]=>[(1,4),(2,8),(3,6),(5,7)]=>[4,6,7,1,8,3,5,2]=>([(0,5),(0,7),(1,2),(1,3),(1,6),(3,7),(4,6),(5,4)],8) [(1,8),(2,4),(3,6),(5,7)]=>[(1,8),(2,4),(3,6),(5,7)]=>[4,6,7,2,8,3,5,1]=>([(1,4),(1,7),(2,3),(2,6),(3,7),(4,5),(5,6)],8) [(1,8),(2,3),(4,6),(5,7)]=>[(1,8),(2,4),(3,5),(6,7)]=>[4,5,7,2,3,8,6,1]=>([(1,3),(2,4),(3,5),(3,7),(4,6),(4,7),(5,6)],8) [(1,7),(2,3),(4,6),(5,8)]=>[(1,4),(2,8),(3,5),(6,7)]=>[4,5,7,1,3,8,6,2]=>([(0,5),(1,2),(1,4),(3,6),(4,6),(4,7),(5,3),(5,7)],8) [(1,6),(2,3),(4,7),(5,8)]=>[(1,4),(2,5),(3,8),(6,7)]=>[4,5,7,1,2,8,6,3]=>([(0,5),(1,4),(3,6),(4,3),(4,7),(5,2),(5,6),(5,7)],8) [(1,5),(2,3),(4,7),(6,8)]=>[(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,7,2,8,6,4]=>([(0,3),(0,7),(1,2),(1,6),(2,5),(2,7),(3,4),(3,5),(3,6),(7,4)],8) [(1,4),(2,3),(5,7),(6,8)]=>[(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,7,8,6,5]=>([(0,4),(1,3),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,2)],8) [(1,3),(2,4),(5,7),(6,8)]=>[(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8) [(1,2),(3,4),(5,7),(6,8)]=>[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>([(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) [(1,2),(3,4),(5,8),(6,7)]=>[(1,4),(2,3),(5,6),(7,8)]=>[3,4,2,1,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8) [(1,3),(2,4),(5,8),(6,7)]=>[(1,4),(2,3),(5,7),(6,8)]=>[3,4,2,1,7,8,5,6]=>([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(6,5),(7,4)],8) [(1,4),(2,3),(5,8),(6,7)]=>[(1,4),(2,3),(5,8),(6,7)]=>[3,4,2,1,7,8,6,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8) [(1,5),(2,3),(4,8),(6,7)]=>[(1,5),(2,3),(4,8),(6,7)]=>[3,5,2,7,1,8,6,4]=>([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4)],8) [(1,6),(2,3),(4,8),(5,7)]=>[(1,5),(2,4),(3,8),(6,7)]=>[4,5,7,2,1,8,6,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4),(3,7),(4,6)],8) [(1,7),(2,3),(4,8),(5,6)]=>[(1,5),(2,8),(3,4),(6,7)]=>[4,5,7,3,1,8,6,2]=>([(0,6),(0,7),(1,4),(2,3),(2,6),(2,7),(4,5),(4,7),(5,6)],8) [(1,8),(2,3),(4,7),(5,6)]=>[(1,8),(2,5),(3,4),(6,7)]=>[4,5,7,3,2,8,6,1]=>([(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(4,7),(5,6)],8) [(1,8),(2,4),(3,7),(5,6)]=>[(1,8),(2,6),(3,4),(5,7)]=>[4,6,7,3,8,2,5,1]=>([(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(5,6)],8) [(1,7),(2,4),(3,8),(5,6)]=>[(1,6),(2,8),(3,4),(5,7)]=>[4,6,7,3,8,1,5,2]=>([(0,6),(0,7),(1,3),(1,7),(2,4),(2,7),(4,5),(5,6)],8) [(1,6),(2,4),(3,8),(5,7)]=>[(1,6),(2,4),(3,8),(5,7)]=>[4,6,7,2,8,1,5,3]=>([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(4,6)],8) [(1,5),(2,4),(3,8),(6,7)]=>[(1,6),(2,3),(4,8),(5,7)]=>[3,6,2,7,8,1,5,4]=>([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(5,4)],8) [(1,4),(2,5),(3,8),(6,7)]=>[(1,6),(2,3),(4,7),(5,8)]=>[3,6,2,7,8,1,4,5]=>([(0,7),(1,6),(1,7),(2,4),(2,7),(4,6),(6,5),(7,3)],8) [(1,3),(2,5),(4,8),(6,7)]=>[(1,5),(2,3),(4,7),(6,8)]=>[3,5,2,7,1,8,4,6]=>([(0,4),(0,7),(1,5),(1,7),(2,3),(2,7),(3,5),(3,6),(5,4),(7,6)],8) [(1,2),(3,5),(4,8),(6,7)]=>[(1,5),(2,3),(4,6),(7,8)]=>[3,5,2,6,1,4,8,7]=>([(0,7),(1,6),(1,7),(2,3),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8) [(1,2),(3,6),(4,8),(5,7)]=>[(1,5),(2,4),(3,6),(7,8)]=>[4,5,6,2,1,3,8,7]=>([(0,5),(1,5),(2,3),(3,4),(4,6),(4,7),(5,6),(5,7)],8) [(1,3),(2,6),(4,8),(5,7)]=>[(1,5),(2,4),(3,7),(6,8)]=>[4,5,7,2,1,8,3,6]=>([(0,5),(0,7),(1,5),(1,7),(2,3),(3,4),(3,6),(4,7),(5,6)],8) [(1,4),(2,6),(3,8),(5,7)]=>[(1,6),(2,4),(3,7),(5,8)]=>[4,6,7,2,8,1,3,5]=>([(0,5),(1,5),(1,6),(2,3),(2,7),(3,4),(4,6),(5,7)],8) [(1,5),(2,6),(3,8),(4,7)]=>[(1,6),(2,5),(3,7),(4,8)]=>[5,6,7,8,2,1,3,4]=>([(0,7),(1,7),(2,6),(5,3),(6,5),(7,4)],8) [(1,6),(2,5),(3,8),(4,7)]=>[(1,6),(2,5),(3,8),(4,7)]=>[5,6,7,8,2,1,4,3]=>([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4)],8) [(1,7),(2,5),(3,8),(4,6)]=>[(1,6),(2,8),(3,5),(4,7)]=>[5,6,7,8,3,1,4,2]=>([(0,7),(1,6),(2,4),(2,7),(5,3),(6,5)],8) [(1,8),(2,5),(3,7),(4,6)]=>[(1,8),(2,6),(3,5),(4,7)]=>[5,6,7,8,3,2,4,1]=>([(1,4),(2,7),(3,7),(4,6),(6,5)],8) [(1,8),(2,6),(3,7),(4,5)]=>[(1,8),(2,6),(3,7),(4,5)]=>[5,6,7,8,4,2,3,1]=>([(2,4),(3,5),(5,6),(6,7)],8) [(1,7),(2,6),(3,8),(4,5)]=>[(1,6),(2,8),(3,7),(4,5)]=>[5,6,7,8,4,1,3,2]=>([(1,7),(2,4),(2,5),(6,3),(7,6)],8) [(1,6),(2,7),(3,8),(4,5)]=>[(1,6),(2,7),(3,8),(4,5)]=>[5,6,7,8,4,1,2,3]=>([(1,6),(2,7),(5,4),(6,5),(7,3)],8) [(1,5),(2,7),(3,8),(4,6)]=>[(1,6),(2,7),(3,5),(4,8)]=>[5,6,7,8,3,1,2,4]=>([(0,7),(1,6),(2,4),(4,7),(5,3),(6,5)],8) [(1,4),(2,7),(3,8),(5,6)]=>[(1,6),(2,7),(3,4),(5,8)]=>[4,6,7,3,8,1,2,5]=>([(0,6),(0,7),(1,4),(2,3),(2,7),(3,5),(4,7),(5,6)],8) [(1,3),(2,7),(4,8),(5,6)]=>[(1,5),(2,7),(3,4),(6,8)]=>[4,5,7,3,1,8,2,6]=>([(0,6),(0,7),(1,4),(2,3),(2,6),(3,7),(4,5),(4,7),(5,6)],8) [(1,2),(3,7),(4,8),(5,6)]=>[(1,5),(2,6),(3,4),(7,8)]=>[4,5,6,3,1,2,8,7]=>([(0,6),(0,7),(1,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8) [(1,2),(3,8),(4,7),(5,6)]=>[(1,6),(2,5),(3,4),(7,8)]=>[4,5,6,3,2,1,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8) [(1,3),(2,8),(4,7),(5,6)]=>[(1,7),(2,5),(3,4),(6,8)]=>[4,5,7,3,2,8,1,6]=>([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(4,7),(5,6)],8) [(1,4),(2,8),(3,7),(5,6)]=>[(1,7),(2,6),(3,4),(5,8)]=>[4,6,7,3,8,2,1,5]=>([(0,7),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(5,6)],8) [(1,5),(2,8),(3,7),(4,6)]=>[(1,7),(2,6),(3,5),(4,8)]=>[5,6,7,8,3,2,1,4]=>([(0,4),(1,7),(2,7),(3,7),(4,6),(6,5)],8) [(1,6),(2,8),(3,7),(4,5)]=>[(1,7),(2,6),(3,8),(4,5)]=>[5,6,7,8,4,2,1,3]=>([(1,4),(2,7),(3,7),(4,6),(6,5)],8) [(1,7),(2,8),(3,6),(4,5)]=>[(1,7),(2,8),(3,6),(4,5)]=>[5,6,7,8,4,3,1,2]=>([(2,4),(3,5),(5,6),(6,7)],8) [(1,8),(2,7),(3,6),(4,5)]=>[(1,8),(2,7),(3,6),(4,5)]=>[5,6,7,8,4,3,2,1]=>([(4,5),(5,7),(7,6)],8) [(1,2),(3,4),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>([(0,8),(0,9),(1,8),(1,9),(4,6),(4,7),(5,6),(5,7),(6,2),(6,3),(7,2),(7,3),(8,4),(8,5),(9,4),(9,5)],10) [(1,4),(2,3),(5,6),(7,8),(9,10)]=>[(1,2),(3,4),(5,6),(7,10),(8,9)]=>[2,1,4,3,6,5,9,10,8,7]=>([(0,6),(0,7),(1,6),(1,7),(5,2),(6,8),(6,9),(7,8),(7,9),(8,3),(8,4),(8,5),(9,3),(9,4),(9,5)],10) [(1,6),(2,3),(4,5),(7,8),(9,10)]=>[(1,2),(3,4),(5,10),(6,7),(8,9)]=>[2,1,4,3,7,9,6,10,8,5]=>([(0,8),(0,9),(1,8),(1,9),(2,5),(6,2),(6,4),(7,4),(7,5),(8,3),(8,6),(8,7),(9,3),(9,6),(9,7)],10) [(1,8),(2,3),(4,5),(6,7),(9,10)]=>[(1,2),(3,10),(4,5),(6,7),(8,9)]=>[2,1,5,7,4,9,6,10,8,3]=>([(0,5),(0,7),(0,9),(1,5),(1,7),(1,9),(2,4),(2,6),(6,3),(7,2),(7,8),(8,3),(8,4),(9,6),(9,8)],10) [(1,10),(2,3),(4,5),(6,7),(8,9)]=>[(1,10),(2,3),(4,5),(6,7),(8,9)]=>[3,5,2,7,4,9,6,10,8,1]=>([(1,3),(1,7),(2,7),(2,9),(3,8),(3,9),(6,5),(7,6),(7,8),(8,4),(8,5),(9,4),(9,6)],10) [(1,2),(3,6),(4,5),(7,8),(9,10)]=>[(1,2),(3,4),(5,8),(6,7),(9,10)]=>[2,1,4,3,7,8,6,5,10,9]=>([(0,6),(0,7),(1,6),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,2),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],10) [(1,6),(2,5),(3,4),(7,8),(9,10)]=>[(1,2),(3,4),(5,10),(6,9),(7,8)]=>[2,1,4,3,8,9,10,7,6,5]=>([(0,8),(0,9),(1,8),(1,9),(2,3),(7,2),(8,4),(8,5),(8,6),(8,7),(9,4),(9,5),(9,6),(9,7)],10) [(1,8),(2,5),(3,4),(6,7),(9,10)]=>[(1,2),(3,10),(4,5),(6,9),(7,8)]=>[2,1,5,8,4,9,10,7,6,3]=>([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(3,6),(6,2),(8,3),(8,4),(8,5),(9,4),(9,5),(9,6)],10) [(1,10),(2,5),(3,4),(6,7),(8,9)]=>[(1,10),(2,3),(4,5),(6,9),(7,8)]=>[3,5,2,8,4,9,10,7,6,1]=>([(1,4),(1,9),(2,8),(2,9),(4,5),(4,6),(4,8),(7,3),(8,7),(9,5),(9,6),(9,7)],10) [(1,2),(3,8),(4,5),(6,7),(9,10)]=>[(1,2),(3,8),(4,5),(6,7),(9,10)]=>[2,1,5,7,4,8,6,3,10,9]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,2),(6,3),(7,3),(7,4)],10) [(1,8),(2,7),(3,4),(5,6),(9,10)]=>[(1,2),(3,10),(4,9),(5,6),(7,8)]=>[2,1,6,8,9,5,10,7,4,3]=>([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,3),(3,5),(8,2),(8,4),(9,4),(9,5)],10) [(1,10),(2,7),(3,4),(5,6),(8,9)]=>[(1,10),(2,3),(4,9),(5,6),(7,8)]=>[3,6,2,8,9,5,10,7,4,1]=>([(1,4),(1,6),(1,9),(2,6),(2,7),(2,9),(3,8),(4,5),(4,7),(7,3),(9,5),(9,8)],10) [(1,2),(3,10),(4,5),(6,7),(8,9)]=>[(1,8),(2,3),(4,5),(6,7),(9,10)]=>[3,5,2,7,4,8,6,1,10,9]=>([(0,8),(0,9),(1,3),(1,7),(2,6),(2,7),(3,5),(3,6),(4,8),(4,9),(5,8),(5,9),(6,4),(7,4),(7,5)],10) [(1,10),(2,9),(3,4),(5,6),(7,8)]=>[(1,10),(2,9),(3,4),(5,6),(7,8)]=>[4,6,8,3,9,5,10,7,2,1]=>([(2,6),(2,7),(3,4),(3,6),(4,5),(4,9),(5,7),(6,8),(6,9),(7,8)],10) [(1,2),(3,4),(5,8),(6,7),(9,10)]=>[(1,2),(3,6),(4,5),(7,8),(9,10)]=>[2,1,5,6,4,3,8,7,10,9]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,8),(2,9),(5,8),(5,9),(6,8),(6,9),(7,2),(8,3),(8,4),(9,3),(9,4)],10) [(1,4),(2,3),(5,8),(6,7),(9,10)]=>[(1,2),(3,6),(4,5),(7,10),(8,9)]=>[2,1,5,6,4,3,9,10,8,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,7),(3,8),(3,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,3),(9,2)],10) [(1,8),(2,3),(4,7),(5,6),(9,10)]=>[(1,2),(3,10),(4,7),(5,6),(8,9)]=>[2,1,6,7,9,5,4,10,8,3]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,9),(3,8),(5,8),(5,9),(6,8),(6,9),(7,2)],10) [(1,10),(2,3),(4,7),(5,6),(8,9)]=>[(1,10),(2,3),(4,7),(5,6),(8,9)]=>[3,6,2,7,9,5,4,10,8,1]=>([(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,7),(4,9),(5,8),(5,9),(6,8),(6,9),(7,4),(7,8)],10) [(1,2),(3,8),(4,7),(5,6),(9,10)]=>[(1,2),(3,8),(4,7),(5,6),(9,10)]=>[2,1,6,7,8,5,4,3,10,9]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,2)],10) [(1,8),(2,7),(3,6),(4,5),(9,10)]=>[(1,2),(3,10),(4,9),(5,8),(6,7)]=>[2,1,7,8,9,10,6,5,4,3]=>([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(4,3),(9,2)],10) [(1,10),(2,7),(3,6),(4,5),(8,9)]=>[(1,10),(2,3),(4,9),(5,8),(6,7)]=>[3,7,2,8,9,10,6,5,4,1]=>([(1,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(2,9),(3,4),(5,9),(9,3)],10) [(1,2),(3,10),(4,7),(5,6),(8,9)]=>[(1,8),(2,3),(4,7),(5,6),(9,10)]=>[3,6,2,7,8,5,4,1,10,9]=>([(0,8),(0,9),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,4)],10) [(1,10),(2,9),(3,6),(4,5),(7,8)]=>[(1,10),(2,9),(3,4),(5,8),(6,7)]=>[4,7,8,3,9,10,6,5,2,1]=>([(2,7),(2,8),(2,9),(3,5),(3,7),(3,8),(5,6),(6,9),(9,4)],10) [(1,2),(3,4),(5,10),(6,7),(8,9)]=>[(1,6),(2,3),(4,5),(7,8),(9,10)]=>[3,5,2,6,4,1,8,7,10,9]=>([(0,8),(0,9),(1,3),(1,4),(2,4),(2,7),(3,7),(4,8),(4,9),(7,8),(7,9),(8,5),(8,6),(9,5),(9,6)],10) [(1,4),(2,3),(5,10),(6,7),(8,9)]=>[(1,6),(2,3),(4,5),(7,10),(8,9)]=>[3,5,2,6,4,1,9,10,8,7]=>([(0,7),(0,8),(0,9),(1,5),(1,6),(2,4),(2,5),(4,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(9,3)],10) [(1,10),(2,3),(4,9),(5,6),(7,8)]=>[(1,10),(2,7),(3,4),(5,6),(8,9)]=>[4,6,7,3,9,5,2,10,8,1]=>([(1,8),(1,9),(2,6),(2,7),(3,4),(3,7),(4,5),(5,6),(5,8),(6,9),(7,8),(7,9)],10) [(1,2),(3,10),(4,9),(5,6),(7,8)]=>[(1,8),(2,7),(3,4),(5,6),(9,10)]=>[4,6,7,3,8,5,2,1,10,9]=>([(0,8),(0,9),(1,8),(1,9),(2,6),(2,7),(3,4),(3,6),(4,5),(5,7),(6,8),(6,9),(7,8),(7,9)],10) [(1,10),(2,9),(3,8),(4,5),(6,7)]=>[(1,10),(2,9),(3,8),(4,5),(6,7)]=>[5,7,8,9,4,10,6,3,2,1]=>([(3,8),(3,9),(4,5),(4,8),(5,7),(6,9),(7,6)],10) [(1,2),(3,4),(5,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,6),(7,8),(9,10)]=>[3,4,2,1,6,5,8,7,10,9]=>([(0,8),(0,9),(1,8),(1,9),(2,3),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10) [(1,4),(2,3),(5,6),(7,10),(8,9)]=>[(1,4),(2,3),(5,6),(7,10),(8,9)]=>[3,4,2,1,6,5,9,10,8,7]=>([(0,8),(0,9),(1,8),(1,9),(2,4),(4,8),(4,9),(7,3),(8,5),(8,6),(8,7),(9,5),(9,6),(9,7)],10) [(1,6),(2,3),(4,5),(7,10),(8,9)]=>[(1,4),(2,3),(5,10),(6,7),(8,9)]=>[3,4,2,1,7,9,6,10,8,5]=>([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,4),(3,6),(4,7),(4,8),(4,9),(8,5),(8,6),(9,3),(9,5)],10) [(1,10),(2,3),(4,5),(6,9),(7,8)]=>[(1,10),(2,5),(3,4),(6,7),(8,9)]=>[4,5,7,3,2,9,6,10,8,1]=>([(1,8),(1,9),(2,8),(2,9),(3,4),(4,5),(4,9),(5,6),(5,8),(8,7),(9,6),(9,7)],10) [(1,2),(3,6),(4,5),(7,10),(8,9)]=>[(1,4),(2,3),(5,8),(6,7),(9,10)]=>[3,4,2,1,7,8,6,5,10,9]=>([(0,4),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,5),(3,6),(4,7),(4,8),(4,9),(7,3),(8,5),(8,6),(9,5),(9,6)],10) [(1,6),(2,5),(3,4),(7,10),(8,9)]=>[(1,4),(2,3),(5,10),(6,9),(7,8)]=>[3,4,2,1,8,9,10,7,6,5]=>([(0,5),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(5,6),(5,7),(5,8),(5,9),(9,3)],10) [(1,10),(2,5),(3,4),(6,9),(7,8)]=>[(1,10),(2,5),(3,4),(6,9),(7,8)]=>[4,5,8,3,2,9,10,7,6,1]=>([(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,5),(5,6),(5,8),(5,9),(6,7),(7,4)],10) [(1,2),(3,10),(4,5),(6,9),(7,8)]=>[(1,8),(2,5),(3,4),(6,7),(9,10)]=>[4,5,7,3,2,8,6,1,10,9]=>([(0,6),(0,9),(1,6),(1,9),(2,7),(2,8),(3,4),(4,5),(4,9),(5,6),(6,7),(6,8),(9,7),(9,8)],10) [(1,10),(2,9),(3,4),(5,8),(6,7)]=>[(1,10),(2,9),(3,6),(4,5),(7,8)]=>[5,6,8,9,4,3,10,7,2,1]=>([(2,5),(3,8),(3,9),(4,8),(4,9),(5,7),(5,8),(6,9),(7,6)],10) [(1,2),(3,4),(5,10),(6,9),(7,8)]=>[(1,6),(2,5),(3,4),(7,8),(9,10)]=>[4,5,6,3,2,1,8,7,10,9]=>([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,4),(4,5),(5,8),(5,9),(8,6),(8,7),(9,6),(9,7)],10) [(1,4),(2,3),(5,10),(6,9),(7,8)]=>[(1,6),(2,5),(3,4),(7,10),(8,9)]=>[4,5,6,3,2,1,9,10,8,7]=>([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,5),(5,6),(6,7),(6,8),(6,9),(9,4)],10) [(1,10),(2,3),(4,9),(5,8),(6,7)]=>[(1,10),(2,7),(3,6),(4,5),(8,9)]=>[5,6,7,9,4,3,2,10,8,1]=>([(1,5),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,7),(6,8),(7,6),(7,9)],10) [(1,2),(3,10),(4,9),(5,8),(6,7)]=>[(1,8),(2,7),(3,6),(4,5),(9,10)]=>[5,6,7,8,4,3,2,1,10,9]=>([(0,5),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,7),(6,8),(6,9),(7,6)],10) [(1,10),(2,9),(3,8),(4,7),(5,6)]=>[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[6,7,8,9,10,5,4,3,2,1]=>([(5,6),(6,9),(8,7),(9,8)],10) [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>([(6,7),(7,11),(9,10),(10,8),(11,9)],12) [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[2,1,7,8,9,10,6,5,4,3,12,11]=>([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(3,10),(3,11),(4,3),(5,2),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[3,7,2,8,9,11,6,5,4,12,10,1]=>([(1,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(2,9),(3,4),(3,11),(4,10),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,3)],12) [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[3,7,2,8,9,10,6,5,4,1,12,11]=>([(0,10),(0,11),(1,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(2,9),(3,4),(4,10),(4,11),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,3)],12) [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[2,1,7,8,9,11,6,5,4,12,10,3]=>([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(3,10),(4,3),(4,11),(6,2),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12) [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[4,7,8,3,10,11,6,5,12,9,2,1]=>([(2,7),(2,8),(2,9),(3,5),(3,7),(3,8),(4,11),(5,6),(6,9),(6,10),(7,10),(7,11),(8,10),(8,11),(9,4)],12) [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>([(0,8),(0,9),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(7,2),(8,3),(8,4),(8,7),(9,3),(9,4),(9,7),(10,5),(10,6),(11,5),(11,6)],12) [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[4,7,8,3,9,11,6,5,2,12,10,1]=>([(1,10),(1,11),(2,7),(2,8),(2,9),(3,5),(3,7),(3,8),(4,11),(5,6),(6,9),(7,10),(7,11),(8,10),(8,11),(9,4),(9,10)],12) [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[4,7,8,3,9,10,6,5,2,1,12,11]=>([(0,10),(0,11),(1,10),(1,11),(2,7),(2,8),(2,9),(3,4),(3,7),(3,8),(4,6),(5,10),(5,11),(6,9),(7,10),(7,11),(8,10),(8,11),(9,5)],12) [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>([(0,7),(0,8),(1,7),(1,8),(3,9),(3,10),(3,11),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,3),(7,4),(7,5),(7,6),(8,4),(8,5),(8,6),(11,2)],12) [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[3,7,2,8,10,11,6,5,12,9,4,1]=>([(1,5),(1,6),(1,7),(1,8),(2,6),(2,7),(2,8),(2,9),(3,4),(4,11),(5,9),(7,10),(7,11),(8,10),(8,11),(9,3),(9,10)],12) [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>([(0,4),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,7),(3,8),(4,9),(4,10),(4,11),(7,5),(7,6),(8,5),(8,6),(9,3),(10,7),(10,8),(11,7),(11,8)],12) [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[2,1,7,8,10,11,6,5,12,9,4,3]=>([(0,5),(0,6),(0,7),(0,8),(0,9),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,10),(3,11),(4,3),(7,2),(8,10),(8,11),(9,10),(9,11)],12) [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[3,4,2,1,7,8,6,5,11,12,10,9]=>([(0,5),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(4,6),(4,7),(4,8),(5,9),(5,10),(5,11),(8,3),(9,4),(10,6),(10,7),(10,8),(11,6),(11,7),(11,8)],12) [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[5,7,9,10,4,11,6,12,8,3,2,1]=>([(3,8),(3,11),(4,5),(4,8),(5,7),(5,10),(6,11),(7,6),(8,9),(8,10),(11,9)],12) [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[2,1,5,7,4,9,6,10,8,3,12,11]=>([(0,5),(0,7),(0,9),(1,5),(1,7),(1,9),(2,4),(2,6),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,3),(7,2),(7,8),(8,3),(8,4),(9,6),(9,8)],12) [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>([(1,3),(1,9),(2,9),(2,11),(3,10),(3,11),(6,5),(7,4),(7,6),(8,4),(8,5),(9,7),(9,10),(10,6),(10,8),(11,7),(11,8)],12) [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[3,5,2,7,4,9,6,10,8,1,12,11]=>([(0,10),(0,11),(1,3),(1,7),(2,7),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,5),(7,6),(7,8),(8,4),(8,5),(9,4),(9,6)],12) [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[2,1,5,7,4,9,6,11,8,12,10,3]=>([(0,5),(0,7),(0,11),(1,5),(1,7),(1,11),(2,9),(2,10),(6,4),(7,2),(7,8),(8,6),(8,10),(9,3),(9,6),(10,3),(10,4),(11,8),(11,9)],12) [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[5,7,8,10,4,11,6,3,12,9,2,1]=>([(2,10),(2,11),(3,8),(3,9),(4,5),(4,8),(5,7),(6,9),(7,6),(7,11),(8,10),(8,11),(9,10)],12) [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[2,1,5,7,4,8,6,3,10,9,12,11]=>([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,6),(3,10),(3,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(9,3),(9,6),(10,4),(10,5),(11,4),(11,5)],12) [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[5,7,8,9,4,11,6,3,2,12,10,1]=>([(1,10),(1,11),(2,10),(2,11),(3,8),(3,9),(4,5),(4,8),(5,7),(6,9),(6,11),(7,6),(8,10),(8,11),(9,10)],12) [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[5,7,8,9,4,10,6,3,2,1,12,11]=>([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,8),(3,9),(4,5),(4,8),(5,7),(6,9),(7,6),(8,10),(8,11),(9,10),(9,11)],12) [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[2,1,5,7,4,8,6,3,11,12,10,9]=>([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(3,5),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,3),(7,4),(8,4),(8,5),(11,2)],12) [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[3,5,2,7,4,10,6,11,12,9,8,1]=>([(1,4),(1,9),(2,9),(2,11),(4,10),(4,11),(7,3),(8,7),(9,8),(9,10),(10,5),(10,6),(10,7),(11,5),(11,6),(11,8)],12) [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[3,5,2,7,4,8,6,1,10,9,12,11]=>([(0,10),(0,11),(1,3),(1,9),(2,8),(2,9),(3,7),(3,8),(4,10),(4,11),(7,10),(7,11),(8,4),(9,4),(9,7),(10,5),(10,6),(11,5),(11,6)],12) [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[2,1,5,7,4,10,6,11,12,9,8,3]=>([(0,7),(0,9),(0,10),(1,7),(1,9),(1,10),(3,4),(3,5),(3,8),(6,2),(8,6),(9,3),(9,11),(10,8),(10,11),(11,4),(11,5),(11,6)],12) [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[3,5,2,7,4,8,6,1,11,12,10,9]=>([(0,9),(0,10),(0,11),(1,4),(1,8),(2,7),(2,8),(4,6),(4,7),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,5),(8,5),(8,6),(11,3)],12) [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[4,7,9,3,10,11,6,12,8,5,2,1]=>([(2,5),(2,7),(2,11),(3,7),(3,8),(3,11),(4,9),(5,6),(5,10),(6,8),(8,4),(11,9),(11,10)],12) [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[2,1,4,3,7,9,6,10,8,5,12,11]=>([(0,8),(0,9),(1,8),(1,9),(2,5),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,2),(6,4),(7,4),(7,5),(8,3),(8,6),(8,7),(9,3),(9,6),(9,7)],12) [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[4,5,7,3,2,9,6,11,8,12,10,1]=>([(1,10),(1,11),(2,10),(2,11),(3,4),(4,5),(4,11),(5,6),(5,10),(6,8),(6,9),(7,9),(10,7),(10,8),(11,6),(11,7)],12) [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[4,5,7,3,2,9,6,10,8,1,12,11]=>([(0,8),(0,11),(1,8),(1,11),(2,9),(2,10),(3,4),(4,5),(4,11),(5,7),(5,8),(6,9),(6,10),(7,9),(7,10),(8,6),(11,6),(11,7)],12) [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[2,1,4,3,7,9,6,11,8,12,10,5]=>([(0,10),(0,11),(1,10),(1,11),(2,5),(2,7),(6,2),(6,9),(7,3),(8,7),(8,9),(9,3),(9,5),(10,4),(10,6),(10,8),(11,4),(11,6),(11,8)],12) [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[3,7,2,9,10,11,6,12,8,5,4,1]=>([(1,5),(1,8),(1,9),(1,11),(2,8),(2,9),(2,10),(2,11),(3,4),(4,7),(5,6),(5,10),(10,3),(11,6),(11,7)],12) [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[3,4,2,1,7,9,6,10,8,5,12,11]=>([(0,4),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,6),(4,9),(4,10),(4,11),(5,7),(5,8),(6,7),(6,8),(9,5),(9,6),(10,3),(10,5),(11,7),(11,8)],12) [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[2,1,7,9,10,11,6,12,8,5,4,3]=>([(0,7),(0,8),(0,9),(0,10),(0,11),(1,7),(1,8),(1,9),(1,10),(1,11),(2,3),(3,4),(4,6),(10,2),(10,5),(11,5),(11,6)],12) [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[3,4,2,1,7,9,6,11,8,12,10,5]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,3),(3,9),(3,10),(3,11),(4,6),(4,7),(7,5),(8,5),(8,6),(10,7),(10,8),(11,4),(11,8)],12) [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[4,5,7,3,2,10,6,11,12,9,8,1]=>([(1,10),(1,11),(2,10),(2,11),(3,5),(5,6),(5,11),(6,7),(6,8),(6,10),(9,4),(10,9),(11,7),(11,8),(11,9)],12) [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[4,5,7,3,2,8,6,1,10,9,12,11]=>([(0,8),(0,11),(1,8),(1,11),(2,9),(2,10),(3,4),(4,5),(4,11),(5,8),(8,9),(8,10),(9,6),(9,7),(10,6),(10,7),(11,9),(11,10)],12) [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[2,1,4,3,7,10,6,11,12,9,8,5]=>([(0,10),(0,11),(1,10),(1,11),(3,7),(7,2),(8,3),(8,5),(8,6),(9,5),(9,6),(9,7),(10,4),(10,8),(10,9),(11,4),(11,8),(11,9)],12) [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[4,5,7,3,2,8,6,1,11,12,10,9]=>([(0,5),(1,10),(1,11),(2,10),(2,11),(3,7),(3,8),(3,9),(5,6),(5,11),(6,10),(9,4),(10,7),(10,8),(10,9),(11,7),(11,8),(11,9)],12) [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[3,4,2,1,7,10,6,11,12,9,8,5]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,5),(3,8),(5,9),(5,10),(5,11),(8,4),(10,6),(10,7),(10,8),(11,3),(11,6),(11,7)],12) [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[6,8,9,10,11,5,12,7,4,3,2,1]=>([(4,10),(4,11),(5,6),(5,10),(6,9),(7,11),(8,7),(9,8)],12) [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[2,1,6,8,9,5,10,7,4,3,12,11]=>([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,3),(3,5),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,4),(9,4),(9,5)],12) [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[3,6,2,8,9,5,11,7,4,12,10,1]=>([(1,4),(1,6),(1,9),(2,6),(2,7),(2,9),(3,8),(3,11),(4,5),(4,7),(5,10),(5,11),(6,10),(6,11),(7,3),(8,10),(9,5),(9,8)],12) [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[3,6,2,8,9,5,10,7,4,1,12,11]=>([(0,10),(0,11),(1,4),(1,6),(1,9),(2,6),(2,7),(2,9),(3,8),(4,5),(4,7),(5,10),(5,11),(6,10),(6,11),(7,3),(8,10),(8,11),(9,5),(9,8)],12) [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[2,1,6,8,9,5,11,7,4,12,10,3]=>([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,3),(3,4),(3,11),(4,10),(5,10),(5,11),(7,10),(7,11),(8,2),(8,5),(9,4),(9,5)],12) [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[4,6,8,3,10,5,11,7,12,9,2,1]=>([(2,4),(2,10),(3,9),(3,10),(4,5),(4,11),(5,7),(5,9),(8,6),(9,8),(10,8),(10,11),(11,6),(11,7)],12) [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>([(0,10),(0,11),(1,10),(1,11),(4,8),(4,9),(5,8),(5,9),(6,4),(6,5),(7,4),(7,5),(8,2),(8,3),(9,2),(9,3),(10,6),(10,7),(11,6),(11,7)],12) [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[4,6,8,3,9,5,11,7,2,12,10,1]=>([(1,10),(1,11),(2,6),(2,7),(3,4),(3,6),(4,5),(4,9),(5,7),(6,8),(6,9),(7,8),(7,11),(8,10),(9,10),(9,11)],12) [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[4,6,8,3,9,5,10,7,2,1,12,11]=>([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(3,4),(3,6),(4,5),(4,9),(5,7),(6,8),(6,9),(7,8),(8,10),(8,11),(9,10),(9,11)],12) [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>([(0,8),(0,9),(1,8),(1,9),(5,2),(6,10),(6,11),(7,10),(7,11),(8,6),(8,7),(9,6),(9,7),(10,3),(10,4),(10,5),(11,3),(11,4),(11,5)],12) [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[3,6,2,8,10,5,11,7,12,9,4,1]=>([(1,4),(1,7),(1,11),(2,7),(2,8),(2,11),(3,9),(4,8),(4,10),(8,3),(8,6),(9,5),(10,5),(10,6),(11,9),(11,10)],12) [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>([(0,10),(0,11),(1,10),(1,11),(2,3),(3,10),(3,11),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12) [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[2,1,6,8,10,5,11,7,12,9,4,3]=>([(0,6),(0,7),(0,9),(0,11),(1,6),(1,7),(1,9),(1,11),(2,3),(2,5),(3,8),(8,4),(9,2),(9,10),(10,4),(10,5),(11,8),(11,10)],12) [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[3,4,2,1,6,5,8,7,11,12,10,9]=>([(0,4),(1,10),(1,11),(2,10),(2,11),(4,10),(4,11),(7,3),(8,5),(8,6),(8,7),(9,5),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12) [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[6,7,9,10,11,5,4,12,8,3,2,1]=>([(3,6),(4,10),(4,11),(5,10),(5,11),(6,9),(6,10),(7,11),(8,7),(9,8)],12) [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[2,1,6,7,9,5,4,10,8,3,12,11]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,11),(3,8),(4,8),(4,11),(5,8),(5,11),(6,9),(6,10),(7,2),(8,9),(8,10),(11,9),(11,10)],12) [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[3,6,2,7,9,5,4,11,8,12,10,1]=>([(1,3),(1,5),(1,6),(2,5),(2,6),(2,9),(3,9),(4,8),(4,10),(5,10),(5,11),(6,10),(6,11),(9,4),(9,11),(10,7),(11,7),(11,8)],12) [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[3,6,2,7,9,5,4,10,8,1,12,11]=>([(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,8),(2,9),(3,5),(4,11),(5,4),(5,10),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8),(11,9)],12) [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[2,1,6,7,9,5,4,11,8,12,10,3]=>([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,3),(2,11),(3,4),(3,10),(7,10),(7,11),(8,10),(8,11),(9,2),(10,5),(11,4),(11,5)],12) [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[6,7,8,10,11,5,4,3,12,9,2,1]=>([(2,6),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,9),(7,11),(8,7),(9,8),(9,10)],12) [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[2,1,6,7,8,5,4,3,10,9,12,11]=>([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,3),(3,10),(3,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,2),(10,4),(10,5),(11,4),(11,5)],12) [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[6,7,8,9,11,5,4,3,2,12,10,1]=>([(1,6),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,8),(7,11),(8,9),(9,7),(9,10)],12) [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[6,7,8,9,10,5,4,3,2,1,12,11]=>([(0,6),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,9),(7,10),(7,11),(8,7),(9,8)],12) [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[2,1,6,7,8,5,4,3,11,12,10,9]=>([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(3,4),(4,9),(4,10),(4,11),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,3),(11,2)],12) [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[3,6,2,7,10,5,4,11,12,9,8,1]=>([(1,6),(1,7),(1,8),(2,4),(2,6),(2,7),(4,8),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,5),(8,9),(8,10),(11,3)],12) [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[3,6,2,7,8,5,4,1,10,9,12,11]=>([(0,10),(0,11),(1,4),(1,5),(1,6),(2,5),(2,6),(2,9),(3,10),(3,11),(4,9),(5,10),(5,11),(6,10),(6,11),(9,3),(10,7),(10,8),(11,7),(11,8)],12) [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[2,1,6,7,10,5,4,11,12,9,8,3]=>([(0,5),(0,6),(0,7),(0,8),(1,5),(1,6),(1,7),(1,8),(3,4),(3,10),(3,11),(4,9),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,3),(9,2)],12) [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[3,6,2,7,8,5,4,1,11,12,10,9]=>([(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(2,4),(2,6),(2,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,5),(11,3)],12) [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[4,6,9,3,10,5,11,12,8,7,2,1]=>([(2,6),(2,11),(3,10),(3,11),(5,10),(6,5),(6,7),(6,8),(9,4),(10,9),(11,7),(11,8),(11,9)],12) [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>([(0,6),(0,7),(1,6),(1,7),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,2),(6,8),(6,9),(7,8),(7,9),(8,3),(8,4),(8,5),(9,3),(9,4),(9,5)],12) [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[4,6,7,3,9,5,2,11,8,12,10,1]=>([(1,10),(1,11),(2,6),(2,7),(3,4),(3,7),(4,5),(5,6),(5,10),(6,9),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8)],12) [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[4,6,7,3,9,5,2,10,8,1,12,11]=>([(0,10),(0,11),(1,8),(1,9),(2,6),(2,7),(3,4),(3,6),(4,5),(5,7),(5,10),(6,10),(6,11),(7,11),(10,8),(10,9),(11,8),(11,9)],12) [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[2,1,4,3,6,5,9,11,8,12,10,7]=>([(0,8),(0,9),(1,8),(1,9),(2,5),(6,2),(6,4),(7,4),(7,5),(8,10),(8,11),(9,10),(9,11),(10,3),(10,6),(10,7),(11,3),(11,6),(11,7)],12) [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[3,6,2,9,10,5,11,12,8,7,4,1]=>([(1,5),(1,9),(1,11),(2,8),(2,9),(2,11),(4,10),(5,6),(5,7),(5,8),(8,4),(10,3),(11,6),(11,7),(11,10)],12) [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>([(0,4),(1,10),(1,11),(2,10),(2,11),(3,8),(3,9),(4,10),(4,11),(5,3),(6,8),(6,9),(7,8),(7,9),(10,5),(10,6),(10,7),(11,5),(11,6),(11,7)],12) [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[2,1,6,9,10,5,11,12,8,7,4,3]=>([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(3,4),(4,7),(7,2),(10,3),(10,5),(10,6),(11,5),(11,6),(11,7)],12) [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[3,4,2,1,6,5,9,11,8,12,10,7]=>([(0,10),(0,11),(1,10),(1,11),(2,3),(3,10),(3,11),(4,6),(8,4),(8,5),(9,5),(9,6),(10,7),(10,8),(10,9),(11,7),(11,8),(11,9)],12) [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[4,6,7,3,10,5,2,11,12,9,8,1]=>([(1,9),(1,10),(1,11),(2,7),(2,8),(3,5),(3,8),(5,6),(6,7),(6,9),(6,10),(7,11),(8,9),(8,10),(8,11),(11,4)],12) [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[4,6,7,3,8,5,2,1,10,9,12,11]=>([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(3,4),(3,6),(4,5),(5,7),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8),(11,9)],12) [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[2,1,4,3,6,5,10,11,12,9,8,7]=>([(0,8),(0,9),(1,8),(1,9),(2,3),(7,2),(8,10),(8,11),(9,10),(9,11),(10,4),(10,5),(10,6),(10,7),(11,4),(11,5),(11,6),(11,7)],12) [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[4,6,7,3,8,5,2,1,11,12,10,9]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,7),(2,8),(3,5),(3,7),(5,6),(6,8),(7,9),(7,10),(7,11),(8,9),(8,10),(8,11),(11,4)],12) [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[3,4,2,1,6,5,10,11,12,9,8,7]=>([(0,5),(1,10),(1,11),(2,10),(2,11),(3,4),(5,10),(5,11),(9,3),(10,6),(10,7),(10,8),(10,9),(11,6),(11,7),(11,8),(11,9)],12) [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[5,8,9,10,4,11,12,7,6,3,2,1]=>([(3,9),(3,10),(3,11),(4,6),(4,9),(4,10),(6,7),(7,8),(8,11),(11,5)],12) [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[2,1,5,8,4,9,10,7,6,3,12,11]=>([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,10),(2,11),(3,6),(4,10),(4,11),(5,10),(5,11),(6,2),(7,10),(7,11),(8,3),(8,4),(8,5),(9,4),(9,5),(9,6)],12) [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[3,5,2,8,4,9,11,7,6,12,10,1]=>([(1,4),(1,9),(2,8),(2,9),(3,11),(4,5),(4,6),(4,8),(5,10),(5,11),(6,10),(6,11),(7,3),(7,10),(8,7),(9,5),(9,6),(9,7)],12) [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[3,5,2,8,4,9,10,7,6,1,12,11]=>([(0,10),(0,11),(1,4),(1,9),(2,8),(2,9),(3,10),(3,11),(4,5),(4,6),(4,8),(5,10),(5,11),(6,10),(6,11),(7,3),(8,7),(9,5),(9,6),(9,7)],12) [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[2,1,5,8,4,9,11,7,6,12,10,3]=>([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(2,11),(3,6),(4,10),(4,11),(5,10),(5,11),(6,2),(6,10),(8,3),(8,4),(8,5),(9,4),(9,5),(9,6)],12) [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[5,6,8,10,4,3,11,7,12,9,2,1]=>([(2,5),(3,10),(3,11),(4,10),(4,11),(5,7),(5,10),(6,11),(7,6),(7,9),(10,8),(10,9),(11,8)],12) [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,10),(2,11),(5,10),(5,11),(6,10),(6,11),(7,2),(8,3),(8,4),(9,3),(9,4),(10,8),(10,9),(11,8),(11,9)],12) [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[5,6,8,9,4,3,11,7,2,12,10,1]=>([(1,9),(1,11),(2,5),(3,8),(3,10),(4,8),(4,10),(5,7),(5,8),(6,10),(6,11),(7,6),(8,9),(8,11),(10,9)],12) [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[5,6,8,9,4,3,10,7,2,1,12,11]=>([(0,5),(1,10),(1,11),(2,10),(2,11),(3,8),(3,9),(4,8),(4,9),(5,7),(5,8),(6,9),(7,6),(8,10),(8,11),(9,10),(9,11)],12) [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>([(0,7),(0,8),(0,9),(1,7),(1,8),(1,9),(3,10),(3,11),(6,2),(7,10),(7,11),(8,10),(8,11),(9,3),(10,4),(10,5),(10,6),(11,4),(11,5),(11,6)],12) [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[3,5,2,8,4,10,11,7,12,9,6,1]=>([(1,4),(1,11),(2,10),(2,11),(3,8),(4,6),(4,9),(4,10),(7,3),(9,5),(9,8),(10,5),(10,7),(11,6),(11,7),(11,9)],12) [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[3,5,2,6,4,1,8,7,10,9,12,11]=>([(0,10),(0,11),(1,3),(1,6),(2,6),(2,7),(3,7),(6,10),(6,11),(7,10),(7,11),(8,4),(8,5),(9,4),(9,5),(10,8),(10,9),(11,8),(11,9)],12) [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[2,1,5,8,4,10,11,7,12,9,6,3]=>([(0,8),(0,10),(0,11),(1,8),(1,10),(1,11),(2,7),(3,5),(3,6),(6,2),(9,5),(9,7),(10,3),(10,4),(10,9),(11,4),(11,6),(11,9)],12) [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[3,5,2,6,4,1,8,7,11,12,10,9]=>([(0,10),(0,11),(1,4),(1,6),(2,5),(2,6),(4,5),(5,10),(5,11),(6,10),(6,11),(9,3),(10,7),(10,8),(10,9),(11,7),(11,8),(11,9)],12) [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[4,8,9,3,10,11,12,7,6,5,2,1]=>([(2,8),(2,9),(2,10),(2,11),(3,5),(3,8),(3,9),(3,10),(4,6),(5,7),(7,11),(11,4)],12) [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[2,1,4,3,8,9,10,7,6,5,12,11]=>([(0,8),(0,9),(1,8),(1,9),(2,3),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,2),(8,4),(8,5),(8,6),(8,7),(9,4),(9,5),(9,6),(9,7)],12) [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[4,5,8,3,2,9,11,7,6,12,10,1]=>([(1,6),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,8),(5,9),(6,5),(6,10),(6,11),(9,4),(9,7),(10,7),(10,8),(11,7),(11,8)],12) [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[4,5,8,3,2,9,10,7,6,1,12,11]=>([(0,10),(0,11),(1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,5),(4,10),(4,11),(5,6),(5,8),(5,9),(6,7),(7,4),(8,10),(8,11),(9,10),(9,11)],12) [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[2,1,4,3,8,9,11,7,6,12,10,5]=>([(0,8),(0,9),(1,8),(1,9),(2,3),(2,11),(3,10),(5,10),(5,11),(6,10),(6,11),(7,2),(8,4),(8,5),(8,6),(8,7),(9,4),(9,5),(9,6),(9,7)],12) [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[3,8,2,9,10,11,12,7,6,5,4,1]=>([(1,6),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,5),(5,4),(6,7),(7,3)],12) [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[3,4,2,1,8,9,10,7,6,5,12,11]=>([(0,5),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,4),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,3)],12) [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[2,1,8,9,10,11,12,7,6,5,4,3]=>([(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,5),(4,3),(5,4),(11,2)],12) [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[3,4,2,1,8,9,11,7,6,12,10,5]=>([(0,5),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,4),(3,7),(4,6),(5,8),(5,9),(5,10),(5,11),(9,3),(10,6),(10,7),(11,6),(11,7)],12) [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[4,5,8,3,2,10,11,7,12,9,6,1]=>([(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,5),(4,8),(5,6),(5,10),(5,11),(6,7),(6,9),(9,4),(11,7),(11,8)],12) [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[4,5,6,3,2,1,8,7,10,9,12,11]=>([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,4),(4,5),(5,10),(5,11),(6,8),(6,9),(7,8),(7,9),(10,6),(10,7),(11,6),(11,7)],12) [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[2,1,4,3,8,10,11,7,12,9,6,5]=>([(0,10),(0,11),(1,10),(1,11),(2,3),(3,7),(8,2),(8,6),(9,6),(9,7),(10,4),(10,5),(10,8),(10,9),(11,4),(11,5),(11,8),(11,9)],12) [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[4,5,6,3,2,1,8,7,11,12,10,9]=>([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,5),(5,6),(6,10),(6,11),(9,4),(10,7),(10,8),(10,9),(11,7),(11,8),(11,9)],12) [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[3,4,2,1,8,10,11,7,12,9,6,5]=>([(0,5),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,4),(4,7),(5,8),(5,9),(5,10),(5,11),(10,6),(10,7),(11,3),(11,6)],12) [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[5,6,9,10,4,3,11,12,8,7,2,1]=>([(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,6),(6,7),(6,10),(6,11),(7,8),(8,9),(9,5)],12) [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,8),(2,9),(3,7),(3,10),(3,11),(4,3),(5,7),(5,10),(5,11),(6,7),(6,10),(6,11),(7,2),(10,8),(10,9),(11,8),(11,9)],12) [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[5,6,7,9,4,3,2,11,8,12,10,1]=>([(1,5),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,7),(6,9),(6,10),(7,6),(7,11),(10,8),(11,8),(11,9)],12) [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[5,6,7,9,4,3,2,10,8,1,12,11]=>([(0,5),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,8),(4,9),(5,7),(6,10),(7,6),(7,11),(10,8),(10,9),(11,8),(11,9)],12) [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[2,1,5,6,4,3,9,11,8,12,10,7]=>([(0,6),(0,7),(0,8),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(3,5),(6,9),(6,10),(6,11),(7,9),(7,10),(7,11),(8,2),(10,3),(10,4),(11,4),(11,5)],12) [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[3,5,2,9,4,10,11,12,8,7,6,1]=>([(1,5),(1,11),(2,10),(2,11),(3,4),(5,6),(5,7),(5,8),(5,10),(9,3),(10,9),(11,6),(11,7),(11,8),(11,9)],12) [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[3,5,2,6,4,1,9,10,8,7,12,11]=>([(0,5),(0,6),(1,3),(1,6),(2,9),(2,10),(2,11),(3,5),(4,7),(4,8),(5,9),(5,10),(5,11),(6,9),(6,10),(6,11),(9,4),(10,7),(10,8),(11,7),(11,8)],12) [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[2,1,5,9,4,10,11,12,8,7,6,3]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,3),(4,8),(8,2),(10,4),(10,5),(10,6),(10,7),(11,5),(11,6),(11,7),(11,8)],12) [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[3,5,2,6,4,1,9,11,8,12,10,7]=>([(0,9),(0,10),(0,11),(1,4),(1,6),(2,6),(2,8),(3,7),(4,8),(6,9),(6,10),(6,11),(8,9),(8,10),(8,11),(10,3),(10,5),(11,5),(11,7)],12) [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[5,6,7,10,4,3,2,11,12,9,8,1]=>([(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,6),(6,8),(7,11),(8,7),(8,9),(8,10),(11,5)],12) [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[5,6,7,8,4,3,2,1,10,9,12,11]=>([(0,5),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,7),(6,10),(6,11),(7,6),(10,8),(10,9),(11,8),(11,9)],12) [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[2,1,5,6,4,3,10,11,12,9,8,7]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(4,8),(4,9),(4,10),(4,11),(5,4),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(11,2)],12) [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[5,6,7,8,4,3,2,1,11,12,10,9]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,9),(3,10),(3,11),(4,6),(6,7),(7,8),(8,9),(8,10),(8,11),(11,5)],12) [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[3,5,2,6,4,1,10,11,12,9,8,7]=>([(0,5),(0,7),(1,6),(1,7),(2,8),(2,9),(2,10),(2,11),(3,4),(5,6),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(11,3)],12) [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[4,5,9,3,2,10,11,12,8,7,6,1]=>([(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,5),(4,6),(5,7),(5,9),(5,10),(5,11),(7,8),(8,4)],12) [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[4,5,6,3,2,1,9,10,8,7,12,11]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,4),(4,6),(5,7),(5,8),(6,9),(6,10),(6,11),(9,7),(9,8),(10,7),(10,8),(11,5)],12) [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[2,1,4,3,9,10,11,12,8,7,6,5]=>([(0,10),(0,11),(1,10),(1,11),(2,4),(4,3),(9,2),(10,5),(10,6),(10,7),(10,8),(10,9),(11,5),(11,6),(11,7),(11,8),(11,9)],12) [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[4,5,6,3,2,1,9,11,8,12,10,7]=>([(0,9),(0,10),(0,11),(1,9),(1,10),(1,11),(2,9),(2,10),(2,11),(3,5),(4,8),(5,6),(6,9),(6,10),(6,11),(10,7),(10,8),(11,4),(11,7)],12) [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[3,4,2,1,9,10,11,12,8,7,6,5]=>([(0,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,7),(2,8),(2,9),(2,10),(2,11),(3,5),(5,4),(6,7),(6,8),(6,9),(6,10),(6,11),(11,3)],12) [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[4,5,6,3,2,1,10,11,12,9,8,7]=>([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,4),(4,7),(5,6),(7,8),(7,9),(7,10),(7,11),(11,5)],12)
Map
reverse
Description
The reverse of a perfect matching of $\{1,2,...,n\}$.
This is the perfect matching obtained by replacing $i$ by $n+1-i$.
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$