Identifier
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0012;cc-rep-0
[(1,2)]=>[2,1]=>[2,1]=>[1,1] [(1,2),(3,4)]=>[2,1,4,3]=>[2,1,4,3]=>[1,2,1] [(1,3),(2,4)]=>[3,4,1,2]=>[4,3,2,1]=>[1,1,1,1] [(1,4),(2,3)]=>[3,4,2,1]=>[4,3,1,2]=>[1,1,2] [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,2,2,1] [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[4,3,2,1,6,5]=>[1,1,1,2,1] [(1,4),(2,3),(5,6)]=>[3,4,2,1,6,5]=>[4,3,1,2,6,5]=>[1,1,3,1] [(1,5),(2,3),(4,6)]=>[3,5,2,6,1,4]=>[6,3,1,5,4,2]=>[1,1,2,1,1] [(1,6),(2,3),(4,5)]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>[1,1,2,2] [(1,6),(2,4),(3,5)]=>[4,5,6,2,3,1]=>[6,5,4,2,1,3]=>[1,1,1,1,2] [(1,5),(2,4),(3,6)]=>[4,5,6,2,1,3]=>[6,5,4,2,3,1]=>[1,1,1,2,1] [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1] [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[6,3,2,5,4,1]=>[1,1,2,1,1] [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[2,1,6,5,4,3]=>[1,2,1,1,1] [(1,2),(3,6),(4,5)]=>[2,1,5,6,4,3]=>[2,1,6,5,3,4]=>[1,2,1,2] [(1,3),(2,6),(4,5)]=>[3,5,1,6,4,2]=>[6,3,2,5,1,4]=>[1,1,2,2] [(1,4),(2,6),(3,5)]=>[4,5,6,1,3,2]=>[6,5,4,3,1,2]=>[1,1,1,1,2] [(1,5),(2,6),(3,4)]=>[4,5,6,3,1,2]=>[6,5,4,1,3,2]=>[1,1,1,2,1] [(1,6),(2,5),(3,4)]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,1,1,3] [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1] [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1] [(1,4),(2,3),(5,6),(7,8)]=>[3,4,2,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[1,1,3,2,1] [(1,5),(2,3),(4,6),(7,8)]=>[3,5,2,6,1,4,8,7]=>[6,3,1,5,4,2,8,7]=>[1,1,2,1,2,1] [(1,6),(2,3),(4,5),(7,8)]=>[3,5,2,6,4,1,8,7]=>[6,3,1,5,2,4,8,7]=>[1,1,2,3,1] [(1,7),(2,3),(4,5),(6,8)]=>[3,5,2,7,4,8,1,6]=>[8,3,1,5,2,7,6,4]=>[1,1,2,2,1,1] [(1,8),(2,3),(4,5),(6,7)]=>[3,5,2,7,4,8,6,1]=>[8,3,1,5,2,7,4,6]=>[1,1,2,2,2] [(1,8),(2,4),(3,5),(6,7)]=>[4,5,7,2,3,8,6,1]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,2,2] [(1,7),(2,4),(3,5),(6,8)]=>[4,5,7,2,3,8,1,6]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,2,1,1] [(1,6),(2,4),(3,5),(7,8)]=>[4,5,6,2,3,1,8,7]=>[6,5,4,2,1,3,8,7]=>[1,1,1,1,3,1] [(1,5),(2,4),(3,6),(7,8)]=>[4,5,6,2,1,3,8,7]=>[6,5,4,2,3,1,8,7]=>[1,1,1,2,2,1] [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1] [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[6,3,2,5,4,1,8,7]=>[1,1,2,1,2,1] [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1] [(1,2),(3,6),(4,5),(7,8)]=>[2,1,5,6,4,3,8,7]=>[2,1,6,5,3,4,8,7]=>[1,2,1,3,1] [(1,3),(2,6),(4,5),(7,8)]=>[3,5,1,6,4,2,8,7]=>[6,3,2,5,1,4,8,7]=>[1,1,2,3,1] [(1,4),(2,6),(3,5),(7,8)]=>[4,5,6,1,3,2,8,7]=>[6,5,4,3,1,2,8,7]=>[1,1,1,1,3,1] [(1,5),(2,6),(3,4),(7,8)]=>[4,5,6,3,1,2,8,7]=>[6,5,4,1,3,2,8,7]=>[1,1,1,2,2,1] [(1,6),(2,5),(3,4),(7,8)]=>[4,5,6,3,2,1,8,7]=>[6,5,4,1,2,3,8,7]=>[1,1,1,4,1] [(1,7),(2,5),(3,4),(6,8)]=>[4,5,7,3,2,8,1,6]=>[8,5,4,1,2,7,6,3]=>[1,1,1,3,1,1] [(1,8),(2,5),(3,4),(6,7)]=>[4,5,7,3,2,8,6,1]=>[8,5,4,1,2,7,3,6]=>[1,1,1,3,2] [(1,8),(2,6),(3,4),(5,7)]=>[4,6,7,3,8,2,5,1]=>[8,7,4,1,6,3,2,5]=>[1,1,1,2,1,2] [(1,7),(2,6),(3,4),(5,8)]=>[4,6,7,3,8,2,1,5]=>[8,7,4,1,6,3,5,2]=>[1,1,1,2,2,1] [(1,6),(2,7),(3,4),(5,8)]=>[4,6,7,3,8,1,2,5]=>[8,7,4,1,6,5,3,2]=>[1,1,1,2,1,1,1] [(1,5),(2,7),(3,4),(6,8)]=>[4,5,7,3,1,8,2,6]=>[8,5,4,1,3,7,6,2]=>[1,1,1,3,1,1] [(1,4),(2,7),(3,5),(6,8)]=>[4,5,7,1,3,8,2,6]=>[8,5,4,3,1,7,6,2]=>[1,1,1,1,2,1,1] [(1,3),(2,7),(4,5),(6,8)]=>[3,5,1,7,4,8,2,6]=>[8,3,2,5,1,7,6,4]=>[1,1,2,2,1,1] [(1,2),(3,7),(4,5),(6,8)]=>[2,1,5,7,4,8,3,6]=>[2,1,8,5,3,7,6,4]=>[1,2,1,2,1,1] [(1,2),(3,8),(4,5),(6,7)]=>[2,1,5,7,4,8,6,3]=>[2,1,8,5,3,7,4,6]=>[1,2,1,2,2] [(1,3),(2,8),(4,5),(6,7)]=>[3,5,1,7,4,8,6,2]=>[8,3,2,5,1,7,4,6]=>[1,1,2,2,2] [(1,4),(2,8),(3,5),(6,7)]=>[4,5,7,1,3,8,6,2]=>[8,5,4,3,1,7,2,6]=>[1,1,1,1,2,2] [(1,5),(2,8),(3,4),(6,7)]=>[4,5,7,3,1,8,6,2]=>[8,5,4,1,3,7,2,6]=>[1,1,1,3,2] [(1,6),(2,8),(3,4),(5,7)]=>[4,6,7,3,8,1,5,2]=>[8,7,4,1,6,5,2,3]=>[1,1,1,2,1,2] [(1,7),(2,8),(3,4),(5,6)]=>[4,6,7,3,8,5,1,2]=>[8,7,4,1,6,2,5,3]=>[1,1,1,2,2,1] [(1,8),(2,7),(3,4),(5,6)]=>[4,6,7,3,8,5,2,1]=>[8,7,4,1,6,2,3,5]=>[1,1,1,2,3] [(1,8),(2,7),(3,5),(4,6)]=>[5,6,7,8,3,4,2,1]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3] [(1,7),(2,8),(3,5),(4,6)]=>[5,6,7,8,3,4,1,2]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,2,1] [(1,6),(2,8),(3,5),(4,7)]=>[5,6,7,8,3,1,4,2]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,2,2] [(1,5),(2,8),(3,6),(4,7)]=>[5,6,7,8,1,3,4,2]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2] [(1,4),(2,8),(3,6),(5,7)]=>[4,6,7,1,8,3,5,2]=>[8,7,4,3,6,2,1,5]=>[1,1,1,2,1,2] [(1,3),(2,8),(4,6),(5,7)]=>[3,6,1,7,8,4,5,2]=>[8,3,2,7,6,4,1,5]=>[1,1,2,1,1,2] [(1,2),(3,8),(4,6),(5,7)]=>[2,1,6,7,8,4,5,3]=>[2,1,8,7,6,4,3,5]=>[1,2,1,1,1,2] [(1,2),(3,7),(4,6),(5,8)]=>[2,1,6,7,8,4,3,5]=>[2,1,8,7,6,4,5,3]=>[1,2,1,1,2,1] [(1,3),(2,7),(4,6),(5,8)]=>[3,6,1,7,8,4,2,5]=>[8,3,2,7,6,4,5,1]=>[1,1,2,1,2,1] [(1,4),(2,7),(3,6),(5,8)]=>[4,6,7,1,8,3,2,5]=>[8,7,4,3,6,2,5,1]=>[1,1,1,2,2,1] [(1,5),(2,7),(3,6),(4,8)]=>[5,6,7,8,1,3,2,4]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1] [(1,6),(2,7),(3,5),(4,8)]=>[5,6,7,8,3,1,2,4]=>[8,7,6,5,2,4,3,1]=>[1,1,1,1,2,1,1] [(1,7),(2,6),(3,5),(4,8)]=>[5,6,7,8,3,2,1,4]=>[8,7,6,5,2,3,4,1]=>[1,1,1,1,3,1] [(1,8),(2,6),(3,5),(4,7)]=>[5,6,7,8,3,2,4,1]=>[8,7,6,5,2,3,1,4]=>[1,1,1,1,2,2] [(1,8),(2,5),(3,6),(4,7)]=>[5,6,7,8,2,3,4,1]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2] [(1,7),(2,5),(3,6),(4,8)]=>[5,6,7,8,2,3,1,4]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,2,1] [(1,6),(2,5),(3,7),(4,8)]=>[5,6,7,8,2,1,3,4]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1] [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1] [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[8,7,4,3,6,5,2,1]=>[1,1,1,2,1,1,1] [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[8,3,2,7,6,5,4,1]=>[1,1,2,1,1,1,1] [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1] [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[2,1,8,5,4,7,6,3]=>[1,2,1,2,1,1] [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[8,3,2,5,4,7,6,1]=>[1,1,2,2,1,1] [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,2,1,1] [(1,5),(2,4),(3,7),(6,8)]=>[4,5,7,2,1,8,3,6]=>[8,5,4,2,3,7,6,1]=>[1,1,1,3,1,1] [(1,6),(2,4),(3,7),(5,8)]=>[4,6,7,2,8,1,3,5]=>[8,7,4,2,6,5,3,1]=>[1,1,1,2,1,1,1] [(1,7),(2,4),(3,6),(5,8)]=>[4,6,7,2,8,3,1,5]=>[8,7,4,2,6,3,5,1]=>[1,1,1,2,2,1] [(1,8),(2,4),(3,6),(5,7)]=>[4,6,7,2,8,3,5,1]=>[8,7,4,2,6,3,1,5]=>[1,1,1,2,1,2] [(1,8),(2,3),(4,6),(5,7)]=>[3,6,2,7,8,4,5,1]=>[8,3,1,7,6,4,2,5]=>[1,1,2,1,1,2] [(1,7),(2,3),(4,6),(5,8)]=>[3,6,2,7,8,4,1,5]=>[8,3,1,7,6,4,5,2]=>[1,1,2,1,2,1] [(1,6),(2,3),(4,7),(5,8)]=>[3,6,2,7,8,1,4,5]=>[8,3,1,7,6,5,4,2]=>[1,1,2,1,1,1,1] [(1,5),(2,3),(4,7),(6,8)]=>[3,5,2,7,1,8,4,6]=>[8,3,1,5,4,7,6,2]=>[1,1,2,2,1,1] [(1,4),(2,3),(5,7),(6,8)]=>[3,4,2,1,7,8,5,6]=>[4,3,1,2,8,7,6,5]=>[1,1,3,1,1,1] [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1] [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1] [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,7,5,6]=>[1,2,2,1,2] [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,7,8,6,5]=>[4,3,2,1,8,7,5,6]=>[1,1,1,2,1,2] [(1,4),(2,3),(5,8),(6,7)]=>[3,4,2,1,7,8,6,5]=>[4,3,1,2,8,7,5,6]=>[1,1,3,1,2] [(1,5),(2,3),(4,8),(6,7)]=>[3,5,2,7,1,8,6,4]=>[8,3,1,5,4,7,2,6]=>[1,1,2,2,2] [(1,6),(2,3),(4,8),(5,7)]=>[3,6,2,7,8,1,5,4]=>[8,3,1,7,6,5,2,4]=>[1,1,2,1,1,2] [(1,7),(2,3),(4,8),(5,6)]=>[3,6,2,7,8,5,1,4]=>[8,3,1,7,6,2,5,4]=>[1,1,2,1,2,1] [(1,8),(2,3),(4,7),(5,6)]=>[3,6,2,7,8,5,4,1]=>[8,3,1,7,6,2,4,5]=>[1,1,2,1,3] [(1,8),(2,4),(3,7),(5,6)]=>[4,6,7,2,8,5,3,1]=>[8,7,4,2,6,1,3,5]=>[1,1,1,2,3] [(1,7),(2,4),(3,8),(5,6)]=>[4,6,7,2,8,5,1,3]=>[8,7,4,2,6,1,5,3]=>[1,1,1,2,2,1] [(1,6),(2,4),(3,8),(5,7)]=>[4,6,7,2,8,1,5,3]=>[8,7,4,2,6,5,1,3]=>[1,1,1,2,1,2] [(1,5),(2,4),(3,8),(6,7)]=>[4,5,7,2,1,8,6,3]=>[8,5,4,2,3,7,1,6]=>[1,1,1,3,2] [(1,4),(2,5),(3,8),(6,7)]=>[4,5,7,1,2,8,6,3]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,2,2] [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,7,2,8,6,4]=>[8,3,2,5,4,7,1,6]=>[1,1,2,2,2] [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,7,3,8,6,4]=>[2,1,8,5,4,7,3,6]=>[1,2,1,2,2] [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,7,8,3,5,4]=>[2,1,8,7,6,5,3,4]=>[1,2,1,1,1,2] [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,7,8,2,5,4]=>[8,3,2,7,6,5,1,4]=>[1,1,2,1,1,2] [(1,4),(2,6),(3,8),(5,7)]=>[4,6,7,1,8,2,5,3]=>[8,7,4,3,6,5,1,2]=>[1,1,1,2,1,2] [(1,5),(2,6),(3,8),(4,7)]=>[5,6,7,8,1,2,4,3]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2] [(1,6),(2,5),(3,8),(4,7)]=>[5,6,7,8,2,1,4,3]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2] [(1,7),(2,5),(3,8),(4,6)]=>[5,6,7,8,2,4,1,3]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,2,1] [(1,8),(2,5),(3,7),(4,6)]=>[5,6,7,8,2,4,3,1]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3] [(1,8),(2,6),(3,7),(4,5)]=>[5,6,7,8,4,2,3,1]=>[8,7,6,5,1,3,2,4]=>[1,1,1,1,2,2] [(1,7),(2,6),(3,8),(4,5)]=>[5,6,7,8,4,2,1,3]=>[8,7,6,5,1,3,4,2]=>[1,1,1,1,3,1] [(1,6),(2,7),(3,8),(4,5)]=>[5,6,7,8,4,1,2,3]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1] [(1,5),(2,7),(3,8),(4,6)]=>[5,6,7,8,1,4,2,3]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1] [(1,4),(2,7),(3,8),(5,6)]=>[4,6,7,1,8,5,2,3]=>[8,7,4,3,6,1,5,2]=>[1,1,1,2,2,1] [(1,3),(2,7),(4,8),(5,6)]=>[3,6,1,7,8,5,2,4]=>[8,3,2,7,6,1,5,4]=>[1,1,2,1,2,1] [(1,2),(3,7),(4,8),(5,6)]=>[2,1,6,7,8,5,3,4]=>[2,1,8,7,6,3,5,4]=>[1,2,1,1,2,1] [(1,2),(3,8),(4,7),(5,6)]=>[2,1,6,7,8,5,4,3]=>[2,1,8,7,6,3,4,5]=>[1,2,1,1,3] [(1,3),(2,8),(4,7),(5,6)]=>[3,6,1,7,8,5,4,2]=>[8,3,2,7,6,1,4,5]=>[1,1,2,1,3] [(1,4),(2,8),(3,7),(5,6)]=>[4,6,7,1,8,5,3,2]=>[8,7,4,3,6,1,2,5]=>[1,1,1,2,3] [(1,5),(2,8),(3,7),(4,6)]=>[5,6,7,8,1,4,3,2]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3] [(1,6),(2,8),(3,7),(4,5)]=>[5,6,7,8,4,1,3,2]=>[8,7,6,5,1,4,2,3]=>[1,1,1,1,2,2] [(1,7),(2,8),(3,6),(4,5)]=>[5,6,7,8,4,3,1,2]=>[8,7,6,5,1,2,4,3]=>[1,1,1,1,3,1] [(1,8),(2,7),(3,6),(4,5)]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4] [(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[1,2,2,2,2,1] [(1,3),(2,4),(5,6),(7,8),(9,10)]=>[3,4,1,2,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[1,1,1,2,2,2,1] [(1,4),(2,3),(5,6),(7,8),(9,10)]=>[3,4,2,1,6,5,8,7,10,9]=>[4,3,1,2,6,5,8,7,10,9]=>[1,1,3,2,2,1] [(1,6),(2,3),(4,5),(7,8),(9,10)]=>[3,5,2,6,4,1,8,7,10,9]=>[6,3,1,5,2,4,8,7,10,9]=>[1,1,2,3,2,1] [(1,8),(2,3),(4,5),(6,7),(9,10)]=>[3,5,2,7,4,8,6,1,10,9]=>[8,3,1,5,2,7,4,6,10,9]=>[1,1,2,2,3,1] [(1,10),(2,3),(4,5),(6,7),(8,9)]=>[3,5,2,7,4,9,6,10,8,1]=>[10,3,1,5,2,7,4,9,6,8]=>[1,1,2,2,2,2] [(1,4),(2,5),(3,6),(7,8),(9,10)]=>[4,5,6,1,2,3,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[1,1,1,1,1,2,2,1] [(1,3),(2,5),(4,6),(7,8),(9,10)]=>[3,5,1,6,2,4,8,7,10,9]=>[6,3,2,5,4,1,8,7,10,9]=>[1,1,2,1,2,2,1] [(1,2),(3,5),(4,6),(7,8),(9,10)]=>[2,1,5,6,3,4,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[1,2,1,1,2,2,1] [(1,2),(3,6),(4,5),(7,8),(9,10)]=>[2,1,5,6,4,3,8,7,10,9]=>[2,1,6,5,3,4,8,7,10,9]=>[1,2,1,3,2,1] [(1,6),(2,5),(3,4),(7,8),(9,10)]=>[4,5,6,3,2,1,8,7,10,9]=>[6,5,4,1,2,3,8,7,10,9]=>[1,1,1,4,2,1] [(1,8),(2,5),(3,4),(6,7),(9,10)]=>[4,5,7,3,2,8,6,1,10,9]=>[8,5,4,1,2,7,3,6,10,9]=>[1,1,1,3,3,1] [(1,10),(2,5),(3,4),(6,7),(8,9)]=>[4,5,7,3,2,9,6,10,8,1]=>[10,5,4,1,2,7,3,9,6,8]=>[1,1,1,3,2,2] [(1,2),(3,8),(4,5),(6,7),(9,10)]=>[2,1,5,7,4,8,6,3,10,9]=>[2,1,8,5,3,7,4,6,10,9]=>[1,2,1,2,3,1] [(1,8),(2,7),(3,4),(5,6),(9,10)]=>[4,6,7,3,8,5,2,1,10,9]=>[8,7,4,1,6,2,3,5,10,9]=>[1,1,1,2,4,1] [(1,10),(2,7),(3,4),(5,6),(8,9)]=>[4,6,7,3,9,5,2,10,8,1]=>[10,7,4,1,6,2,3,9,5,8]=>[1,1,1,2,3,2] [(1,2),(3,10),(4,5),(6,7),(8,9)]=>[2,1,5,7,4,9,6,10,8,3]=>[2,1,10,5,3,7,4,9,6,8]=>[1,2,1,2,2,2] [(1,10),(2,9),(3,4),(5,6),(7,8)]=>[4,6,8,3,9,5,10,7,2,1]=>[10,9,4,1,6,2,8,3,5,7]=>[1,1,1,2,2,3] [(1,5),(2,6),(3,7),(4,8),(9,10)]=>[5,6,7,8,1,2,3,4,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[1,1,1,1,1,1,1,2,1] [(1,4),(2,6),(3,7),(5,8),(9,10)]=>[4,6,7,1,8,2,3,5,10,9]=>[8,7,4,3,6,5,2,1,10,9]=>[1,1,1,2,1,1,2,1] [(1,3),(2,6),(4,7),(5,8),(9,10)]=>[3,6,1,7,8,2,4,5,10,9]=>[8,3,2,7,6,5,4,1,10,9]=>[1,1,2,1,1,1,2,1] [(1,2),(3,6),(4,7),(5,8),(9,10)]=>[2,1,6,7,8,3,4,5,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[1,2,1,1,1,1,2,1] [(1,2),(3,5),(4,7),(6,8),(9,10)]=>[2,1,5,7,3,8,4,6,10,9]=>[2,1,8,5,4,7,6,3,10,9]=>[1,2,1,2,1,2,1] [(1,3),(2,5),(4,7),(6,8),(9,10)]=>[3,5,1,7,2,8,4,6,10,9]=>[8,3,2,5,4,7,6,1,10,9]=>[1,1,2,2,1,2,1] [(1,4),(2,5),(3,7),(6,8),(9,10)]=>[4,5,7,1,2,8,3,6,10,9]=>[8,5,4,3,2,7,6,1,10,9]=>[1,1,1,1,2,1,2,1] [(1,3),(2,4),(5,7),(6,8),(9,10)]=>[3,4,1,2,7,8,5,6,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[1,1,1,2,1,1,2,1] [(1,2),(3,4),(5,7),(6,8),(9,10)]=>[2,1,4,3,7,8,5,6,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[1,2,2,1,1,2,1] [(1,2),(3,4),(5,8),(6,7),(9,10)]=>[2,1,4,3,7,8,6,5,10,9]=>[2,1,4,3,8,7,5,6,10,9]=>[1,2,2,1,3,1] [(1,4),(2,3),(5,8),(6,7),(9,10)]=>[3,4,2,1,7,8,6,5,10,9]=>[4,3,1,2,8,7,5,6,10,9]=>[1,1,3,1,3,1] [(1,8),(2,3),(4,7),(5,6),(9,10)]=>[3,6,2,7,8,5,4,1,10,9]=>[8,3,1,7,6,2,4,5,10,9]=>[1,1,2,1,4,1] [(1,10),(2,3),(4,7),(5,6),(8,9)]=>[3,6,2,7,9,5,4,10,8,1]=>[10,3,1,7,6,2,4,9,5,8]=>[1,1,2,1,3,2] [(1,2),(3,8),(4,7),(5,6),(9,10)]=>[2,1,6,7,8,5,4,3,10,9]=>[2,1,8,7,6,3,4,5,10,9]=>[1,2,1,1,4,1] [(1,8),(2,7),(3,6),(4,5),(9,10)]=>[5,6,7,8,4,3,2,1,10,9]=>[8,7,6,5,1,2,3,4,10,9]=>[1,1,1,1,5,1] [(1,10),(2,7),(3,6),(4,5),(8,9)]=>[5,6,7,9,4,3,2,10,8,1]=>[10,7,6,5,1,2,3,9,4,8]=>[1,1,1,1,4,2] [(1,2),(3,10),(4,7),(5,6),(8,9)]=>[2,1,6,7,9,5,4,10,8,3]=>[2,1,10,7,6,3,4,9,5,8]=>[1,2,1,1,3,2] [(1,10),(2,9),(3,6),(4,5),(7,8)]=>[5,6,8,9,4,3,10,7,2,1]=>[10,9,6,5,1,2,8,3,4,7]=>[1,1,1,1,3,3] [(1,2),(3,4),(5,10),(6,7),(8,9)]=>[2,1,4,3,7,9,6,10,8,5]=>[2,1,4,3,10,7,5,9,6,8]=>[1,2,2,1,2,2] [(1,4),(2,3),(5,10),(6,7),(8,9)]=>[3,4,2,1,7,9,6,10,8,5]=>[4,3,1,2,10,7,5,9,6,8]=>[1,1,3,1,2,2] [(1,10),(2,3),(4,9),(5,6),(7,8)]=>[3,6,2,8,9,5,10,7,4,1]=>[10,3,1,9,6,2,8,4,5,7]=>[1,1,2,1,2,3] [(1,2),(3,10),(4,9),(5,6),(7,8)]=>[2,1,6,8,9,5,10,7,4,3]=>[2,1,10,9,6,3,8,4,5,7]=>[1,2,1,1,2,3] [(1,10),(2,9),(3,8),(4,5),(6,7)]=>[5,7,8,9,4,10,6,3,2,1]=>[10,9,8,5,1,7,2,3,4,6]=>[1,1,1,1,2,4] [(1,6),(2,9),(3,10),(4,7),(5,8)]=>[6,7,8,9,10,1,4,5,2,3]=>[10,9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,1,2,1] [(1,6),(2,10),(3,7),(4,8),(5,9)]=>[6,7,8,9,10,1,3,4,5,2]=>[10,9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,2] [(1,2),(3,7),(4,8),(5,9),(6,10)]=>[2,1,7,8,9,10,3,4,5,6]=>[2,1,10,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1,1] [(1,3),(2,7),(4,8),(5,9),(6,10)]=>[3,7,1,8,9,10,2,4,5,6]=>[10,3,2,9,8,7,6,5,4,1]=>[1,1,2,1,1,1,1,1,1] [(1,4),(2,7),(3,8),(5,9),(6,10)]=>[4,7,8,1,9,10,2,3,5,6]=>[10,9,4,3,8,7,6,5,2,1]=>[1,1,1,2,1,1,1,1,1] [(1,5),(2,7),(3,8),(4,9),(6,10)]=>[5,7,8,9,1,10,2,3,4,6]=>[10,9,8,5,4,7,6,3,2,1]=>[1,1,1,1,2,1,1,1,1] [(1,6),(2,7),(3,8),(4,9),(5,10)]=>[6,7,8,9,10,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1] [(1,10),(2,6),(3,7),(4,8),(5,9)]=>[6,7,8,9,10,2,3,4,5,1]=>[10,9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,2] [(1,5),(2,6),(3,8),(4,9),(7,10)]=>[5,6,8,9,1,2,10,3,4,7]=>[10,9,6,5,4,3,8,7,2,1]=>[1,1,1,1,1,2,1,1,1] [(1,4),(2,6),(3,8),(5,9),(7,10)]=>[4,6,8,1,9,2,10,3,5,7]=>[10,9,4,3,6,5,8,7,2,1]=>[1,1,1,2,2,1,1,1] [(1,3),(2,6),(4,8),(5,9),(7,10)]=>[3,6,1,8,9,2,10,4,5,7]=>[10,3,2,9,6,5,8,7,4,1]=>[1,1,2,1,2,1,1,1] [(1,2),(3,6),(4,8),(5,9),(7,10)]=>[2,1,6,8,9,3,10,4,5,7]=>[2,1,10,9,6,5,8,7,4,3]=>[1,2,1,1,2,1,1,1] [(1,2),(3,5),(4,8),(6,9),(7,10)]=>[2,1,5,8,3,9,10,4,6,7]=>[2,1,10,5,4,9,8,7,6,3]=>[1,2,1,2,1,1,1,1] [(1,3),(2,5),(4,8),(6,9),(7,10)]=>[3,5,1,8,2,9,10,4,6,7]=>[10,3,2,5,4,9,8,7,6,1]=>[1,1,2,2,1,1,1,1] [(1,4),(2,5),(3,8),(6,9),(7,10)]=>[4,5,8,1,2,9,10,3,6,7]=>[10,5,4,3,2,9,8,7,6,1]=>[1,1,1,1,2,1,1,1,1] [(1,3),(2,4),(5,8),(6,9),(7,10)]=>[3,4,1,2,8,9,10,5,6,7]=>[4,3,2,1,10,9,8,7,6,5]=>[1,1,1,2,1,1,1,1,1] [(1,2),(3,4),(5,8),(6,9),(7,10)]=>[2,1,4,3,8,9,10,5,6,7]=>[2,1,4,3,10,9,8,7,6,5]=>[1,2,2,1,1,1,1,1] [(1,2),(3,4),(5,7),(6,9),(8,10)]=>[2,1,4,3,7,9,5,10,6,8]=>[2,1,4,3,10,7,6,9,8,5]=>[1,2,2,1,2,1,1] [(1,3),(2,4),(5,7),(6,9),(8,10)]=>[3,4,1,2,7,9,5,10,6,8]=>[4,3,2,1,10,7,6,9,8,5]=>[1,1,1,2,1,2,1,1] [(1,4),(2,5),(3,7),(6,9),(8,10)]=>[4,5,7,1,2,9,3,10,6,8]=>[10,5,4,3,2,7,6,9,8,1]=>[1,1,1,1,2,2,1,1] [(1,3),(2,5),(4,7),(6,9),(8,10)]=>[3,5,1,7,2,9,4,10,6,8]=>[10,3,2,5,4,7,6,9,8,1]=>[1,1,2,2,2,1,1] [(1,2),(3,5),(4,7),(6,9),(8,10)]=>[2,1,5,7,3,9,4,10,6,8]=>[2,1,10,5,4,7,6,9,8,3]=>[1,2,1,2,2,1,1] [(1,2),(3,6),(4,7),(5,9),(8,10)]=>[2,1,6,7,9,3,4,10,5,8]=>[2,1,10,7,6,5,4,9,8,3]=>[1,2,1,1,1,2,1,1] [(1,3),(2,6),(4,7),(5,9),(8,10)]=>[3,6,1,7,9,2,4,10,5,8]=>[10,3,2,7,6,5,4,9,8,1]=>[1,1,2,1,1,2,1,1] [(1,4),(2,6),(3,7),(5,9),(8,10)]=>[4,6,7,1,9,2,3,10,5,8]=>[10,7,4,3,6,5,2,9,8,1]=>[1,1,1,2,1,2,1,1] [(1,5),(2,6),(3,7),(4,9),(8,10)]=>[5,6,7,9,1,2,3,10,4,8]=>[10,7,6,5,4,3,2,9,8,1]=>[1,1,1,1,1,1,2,1,1] [(1,2),(3,5),(4,6),(7,9),(8,10)]=>[2,1,5,6,3,4,9,10,7,8]=>[2,1,6,5,4,3,10,9,8,7]=>[1,2,1,1,2,1,1,1] [(1,3),(2,5),(4,6),(7,9),(8,10)]=>[3,5,1,6,2,4,9,10,7,8]=>[6,3,2,5,4,1,10,9,8,7]=>[1,1,2,1,2,1,1,1] [(1,4),(2,5),(3,6),(7,9),(8,10)]=>[4,5,6,1,2,3,9,10,7,8]=>[6,5,4,3,2,1,10,9,8,7]=>[1,1,1,1,1,2,1,1,1] [(1,3),(2,4),(5,6),(7,9),(8,10)]=>[3,4,1,2,6,5,9,10,7,8]=>[4,3,2,1,6,5,10,9,8,7]=>[1,1,1,2,2,1,1,1] [(1,2),(3,4),(5,6),(7,9),(8,10)]=>[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,10,9,8,7]=>[1,2,2,2,1,1,1] [(1,2),(3,4),(5,6),(7,10),(8,9)]=>[2,1,4,3,6,5,9,10,8,7]=>[2,1,4,3,6,5,10,9,7,8]=>[1,2,2,2,1,2] [(1,4),(2,3),(5,6),(7,10),(8,9)]=>[3,4,2,1,6,5,9,10,8,7]=>[4,3,1,2,6,5,10,9,7,8]=>[1,1,3,2,1,2] [(1,6),(2,3),(4,5),(7,10),(8,9)]=>[3,5,2,6,4,1,9,10,8,7]=>[6,3,1,5,2,4,10,9,7,8]=>[1,1,2,3,1,2] [(1,10),(2,3),(4,5),(6,9),(7,8)]=>[3,5,2,8,4,9,10,7,6,1]=>[10,3,1,5,2,9,8,4,6,7]=>[1,1,2,2,1,3] [(1,2),(3,6),(4,5),(7,10),(8,9)]=>[2,1,5,6,4,3,9,10,8,7]=>[2,1,6,5,3,4,10,9,7,8]=>[1,2,1,3,1,2] [(1,6),(2,5),(3,4),(7,10),(8,9)]=>[4,5,6,3,2,1,9,10,8,7]=>[6,5,4,1,2,3,10,9,7,8]=>[1,1,1,4,1,2] [(1,10),(2,5),(3,4),(6,9),(7,8)]=>[4,5,8,3,2,9,10,7,6,1]=>[10,5,4,1,2,9,8,3,6,7]=>[1,1,1,3,1,3] [(1,2),(3,10),(4,5),(6,9),(7,8)]=>[2,1,5,8,4,9,10,7,6,3]=>[2,1,10,5,3,9,8,4,6,7]=>[1,2,1,2,1,3] [(1,10),(2,9),(3,4),(5,8),(6,7)]=>[4,7,8,3,9,10,6,5,2,1]=>[10,9,4,1,8,7,2,3,5,6]=>[1,1,1,2,1,4] [(1,2),(3,4),(5,10),(6,9),(7,8)]=>[2,1,4,3,8,9,10,7,6,5]=>[2,1,4,3,10,9,8,5,6,7]=>[1,2,2,1,1,3] [(1,4),(2,3),(5,10),(6,9),(7,8)]=>[3,4,2,1,8,9,10,7,6,5]=>[4,3,1,2,10,9,8,5,6,7]=>[1,1,3,1,1,3] [(1,10),(2,3),(4,9),(5,8),(6,7)]=>[3,7,2,8,9,10,6,5,4,1]=>[10,3,1,9,8,7,2,4,5,6]=>[1,1,2,1,1,4] [(1,2),(3,10),(4,9),(5,8),(6,7)]=>[2,1,7,8,9,10,6,5,4,3]=>[2,1,10,9,8,7,3,4,5,6]=>[1,2,1,1,1,4] [(1,6),(2,10),(3,9),(4,8),(5,7)]=>[6,7,8,9,10,1,5,4,3,2]=>[10,9,8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,4] [(1,10),(2,9),(3,8),(4,7),(5,6)]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>[1,1,1,1,1,5] [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>[12,11,10,9,8,7,1,2,3,4,5,6]=>[1,1,1,1,1,1,6] [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[2,1,7,8,9,10,6,5,4,3,12,11]=>[2,1,10,9,8,7,3,4,5,6,12,11]=>[1,2,1,1,1,5,1] [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>[3,7,2,8,9,11,6,5,4,12,10,1]=>[12,3,1,9,8,7,2,4,5,11,6,10]=>[1,1,2,1,1,4,2] [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[2,1,7,8,9,11,6,5,4,12,10,3]=>[2,1,12,9,8,7,3,4,5,11,6,10]=>[1,2,1,1,1,4,2] [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[3,7,2,8,9,10,6,5,4,1,12,11]=>[10,3,1,9,8,7,2,4,5,6,12,11]=>[1,1,2,1,1,5,1] [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[4,7,8,3,10,11,6,5,12,9,2,1]=>[12,11,4,1,8,7,2,3,10,5,6,9]=>[1,1,1,2,1,3,3] [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>[2,1,4,3,8,7,5,6,10,9,12,11]=>[1,2,2,1,3,2,1] [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>[3,7,2,8,10,11,6,5,12,9,4,1]=>[12,3,1,11,8,7,2,4,10,5,6,9]=>[1,1,2,1,1,3,3] [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[2,1,7,8,10,11,6,5,12,9,4,3]=>[2,1,12,11,8,7,3,4,10,5,6,9]=>[1,2,1,1,1,3,3] [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>[4,3,1,2,8,7,5,6,10,9,12,11]=>[1,1,3,1,3,2,1] [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[4,7,8,3,9,11,6,5,2,12,10,1]=>[12,9,4,1,8,7,2,3,5,11,6,10]=>[1,1,1,2,1,4,2] [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>[2,1,4,3,8,7,5,6,12,11,9,10]=>[1,2,2,1,3,1,2] [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>[4,7,8,3,9,10,6,5,2,1,12,11]=>[10,9,4,1,8,7,2,3,5,6,12,11]=>[1,1,1,2,1,5,1] [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>[3,4,2,1,7,8,6,5,11,12,10,9]=>[4,3,1,2,8,7,5,6,12,11,9,10]=>[1,1,3,1,3,1,2] [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[5,7,9,10,4,11,6,12,8,3,2,1]=>[12,11,10,5,1,7,2,9,3,4,6,8]=>[1,1,1,1,2,2,4] [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[2,1,5,7,4,9,6,10,8,3,12,11]=>[2,1,10,5,3,7,4,9,6,8,12,11]=>[1,2,1,2,2,3,1] [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>[12,3,1,5,2,7,4,9,6,11,8,10]=>[1,1,2,2,2,2,2] [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[2,1,5,7,4,9,6,11,8,12,10,3]=>[2,1,12,5,3,7,4,9,6,11,8,10]=>[1,2,1,2,2,2,2] [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[3,5,2,7,4,9,6,10,8,1,12,11]=>[10,3,1,5,2,7,4,9,6,8,12,11]=>[1,1,2,2,2,3,1] [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[4,7,9,3,10,11,6,12,8,5,2,1]=>[12,11,4,1,10,7,2,9,3,5,6,8]=>[1,1,1,2,1,2,4] [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[2,1,4,3,7,9,6,10,8,5,12,11]=>[2,1,4,3,10,7,5,9,6,8,12,11]=>[1,2,2,1,2,3,1] [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>[3,7,2,9,10,11,6,12,8,5,4,1]=>[12,3,1,11,10,7,2,9,4,5,6,8]=>[1,1,2,1,1,2,4] [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[2,1,7,9,10,11,6,12,8,5,4,3]=>[2,1,12,11,10,7,3,9,4,5,6,8]=>[1,2,1,1,1,2,4] [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[3,4,2,1,7,9,6,10,8,5,12,11]=>[4,3,1,2,10,7,5,9,6,8,12,11]=>[1,1,3,1,2,3,1] [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[4,5,7,3,2,9,6,11,8,12,10,1]=>[12,5,4,1,2,7,3,9,6,11,8,10]=>[1,1,1,3,2,2,2] [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[2,1,4,3,7,9,6,11,8,12,10,5]=>[2,1,4,3,12,7,5,9,6,11,8,10]=>[1,2,2,1,2,2,2] [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>[4,5,7,3,2,9,6,10,8,1,12,11]=>[10,5,4,1,2,7,3,9,6,8,12,11]=>[1,1,1,3,2,3,1] [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>[3,4,2,1,7,9,6,11,8,12,10,5]=>[4,3,1,2,12,7,5,9,6,11,8,10]=>[1,1,3,1,2,2,2] [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[5,7,8,10,4,11,6,3,12,9,2,1]=>[12,11,8,5,1,7,2,3,10,4,6,9]=>[1,1,1,1,2,3,3] [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[2,1,5,7,4,8,6,3,10,9,12,11]=>[2,1,8,5,3,7,4,6,10,9,12,11]=>[1,2,1,2,3,2,1] [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>[3,5,2,7,4,10,6,11,12,9,8,1]=>[12,3,1,5,2,7,4,11,10,6,8,9]=>[1,1,2,2,2,1,3] [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[2,1,5,7,4,10,6,11,12,9,8,3]=>[2,1,12,5,3,7,4,11,10,6,8,9]=>[1,2,1,2,2,1,3] [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[3,5,2,7,4,8,6,1,10,9,12,11]=>[8,3,1,5,2,7,4,6,10,9,12,11]=>[1,1,2,2,3,2,1] [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[5,7,8,9,4,11,6,3,2,12,10,1]=>[12,9,8,5,1,7,2,3,4,11,6,10]=>[1,1,1,1,2,4,2] [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[2,1,5,7,4,8,6,3,11,12,10,9]=>[2,1,8,5,3,7,4,6,12,11,9,10]=>[1,2,1,2,3,1,2] [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[5,7,8,9,4,10,6,3,2,1,12,11]=>[10,9,8,5,1,7,2,3,4,6,12,11]=>[1,1,1,1,2,5,1] [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>[3,5,2,7,4,8,6,1,11,12,10,9]=>[8,3,1,5,2,7,4,6,12,11,9,10]=>[1,1,2,2,3,1,2] [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>[4,5,7,3,2,10,6,11,12,9,8,1]=>[12,5,4,1,2,7,3,11,10,6,8,9]=>[1,1,1,3,2,1,3] [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[2,1,4,3,7,10,6,11,12,9,8,5]=>[2,1,4,3,12,7,5,11,10,6,8,9]=>[1,2,2,1,2,1,3] [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[4,5,7,3,2,8,6,1,10,9,12,11]=>[8,5,4,1,2,7,3,6,10,9,12,11]=>[1,1,1,3,3,2,1] [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>[3,4,2,1,7,10,6,11,12,9,8,5]=>[4,3,1,2,12,7,5,11,10,6,8,9]=>[1,1,3,1,2,1,3] [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[4,5,7,3,2,8,6,1,11,12,10,9]=>[8,5,4,1,2,7,3,6,12,11,9,10]=>[1,1,1,3,3,1,2] [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[6,8,9,10,11,5,12,7,4,3,2,1]=>[12,11,10,9,6,1,8,2,3,4,5,7]=>[1,1,1,1,1,2,5] [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[2,1,6,8,9,5,10,7,4,3,12,11]=>[2,1,10,9,6,3,8,4,5,7,12,11]=>[1,2,1,1,2,4,1] [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>[3,6,2,8,9,5,11,7,4,12,10,1]=>[12,3,1,9,6,2,8,4,5,11,7,10]=>[1,1,2,1,2,3,2] [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[2,1,6,8,9,5,11,7,4,12,10,3]=>[2,1,12,9,6,3,8,4,5,11,7,10]=>[1,2,1,1,2,3,2] [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[3,6,2,8,9,5,10,7,4,1,12,11]=>[10,3,1,9,6,2,8,4,5,7,12,11]=>[1,1,2,1,2,4,1] [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[4,6,8,3,10,5,11,7,12,9,2,1]=>[12,11,4,1,6,2,8,3,10,5,7,9]=>[1,1,1,2,2,2,3] [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[1,2,2,2,2,2,1] [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>[3,6,2,8,10,5,11,7,12,9,4,1]=>[12,3,1,11,6,2,8,4,10,5,7,9]=>[1,1,2,1,2,2,3] [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[2,1,6,8,10,5,11,7,12,9,4,3]=>[2,1,12,11,6,3,8,4,10,5,7,9]=>[1,2,1,1,2,2,3] [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>[4,3,1,2,6,5,8,7,10,9,12,11]=>[1,1,3,2,2,2,1] [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[4,6,8,3,9,5,11,7,2,12,10,1]=>[12,9,4,1,6,2,8,3,5,11,7,10]=>[1,1,1,2,2,3,2] [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>[2,1,4,3,6,5,8,7,12,11,9,10]=>[1,2,2,2,2,1,2] [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>[4,6,8,3,9,5,10,7,2,1,12,11]=>[10,9,4,1,6,2,8,3,5,7,12,11]=>[1,1,1,2,2,4,1] [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>[3,4,2,1,6,5,8,7,11,12,10,9]=>[4,3,1,2,6,5,8,7,12,11,9,10]=>[1,1,3,2,2,1,2] [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[5,8,9,10,4,11,12,7,6,3,2,1]=>[12,11,10,5,1,9,8,2,3,4,6,7]=>[1,1,1,1,2,1,5] [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[2,1,5,8,4,9,10,7,6,3,12,11]=>[2,1,10,5,3,9,8,4,6,7,12,11]=>[1,2,1,2,1,4,1] [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>[3,5,2,8,4,9,11,7,6,12,10,1]=>[12,3,1,5,2,9,8,4,6,11,7,10]=>[1,1,2,2,1,3,2] [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[2,1,5,8,4,9,11,7,6,12,10,3]=>[2,1,12,5,3,9,8,4,6,11,7,10]=>[1,2,1,2,1,3,2] [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[3,5,2,8,4,9,10,7,6,1,12,11]=>[10,3,1,5,2,9,8,4,6,7,12,11]=>[1,1,2,2,1,4,1] [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[4,8,9,3,10,11,12,7,6,5,2,1]=>[12,11,4,1,10,9,8,2,3,5,6,7]=>[1,1,1,2,1,1,5] [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[2,1,4,3,8,9,10,7,6,5,12,11]=>[2,1,4,3,10,9,8,5,6,7,12,11]=>[1,2,2,1,1,4,1] [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>[3,8,2,9,10,11,12,7,6,5,4,1]=>[12,3,1,11,10,9,8,2,4,5,6,7]=>[1,1,2,1,1,1,5] [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[2,1,8,9,10,11,12,7,6,5,4,3]=>[2,1,12,11,10,9,8,3,4,5,6,7]=>[1,2,1,1,1,1,5] [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[3,4,2,1,8,9,10,7,6,5,12,11]=>[4,3,1,2,10,9,8,5,6,7,12,11]=>[1,1,3,1,1,4,1] [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[4,5,8,3,2,9,11,7,6,12,10,1]=>[12,5,4,1,2,9,8,3,6,11,7,10]=>[1,1,1,3,1,3,2] [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[2,1,4,3,8,9,11,7,6,12,10,5]=>[2,1,4,3,12,9,8,5,6,11,7,10]=>[1,2,2,1,1,3,2] [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>[4,5,8,3,2,9,10,7,6,1,12,11]=>[10,5,4,1,2,9,8,3,6,7,12,11]=>[1,1,1,3,1,4,1] [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>[3,4,2,1,8,9,11,7,6,12,10,5]=>[4,3,1,2,12,9,8,5,6,11,7,10]=>[1,1,3,1,1,3,2] [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[5,6,8,10,4,3,11,7,12,9,2,1]=>[12,11,6,5,1,2,8,3,10,4,7,9]=>[1,1,1,1,3,2,3] [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>[2,1,6,5,3,4,8,7,10,9,12,11]=>[1,2,1,3,2,2,1] [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>[3,5,2,8,4,10,11,7,12,9,6,1]=>[12,3,1,5,2,11,8,4,10,6,7,9]=>[1,1,2,2,1,2,3] [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[2,1,5,8,4,10,11,7,12,9,6,3]=>[2,1,12,5,3,11,8,4,10,6,7,9]=>[1,2,1,2,1,2,3] [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[3,5,2,6,4,1,8,7,10,9,12,11]=>[6,3,1,5,2,4,8,7,10,9,12,11]=>[1,1,2,3,2,2,1] [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[5,6,8,9,4,3,11,7,2,12,10,1]=>[12,9,6,5,1,2,8,3,4,11,7,10]=>[1,1,1,1,3,3,2] [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>[2,1,6,5,3,4,8,7,12,11,9,10]=>[1,2,1,3,2,1,2] [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[5,6,8,9,4,3,10,7,2,1,12,11]=>[10,9,6,5,1,2,8,3,4,7,12,11]=>[1,1,1,1,3,4,1] [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>[3,5,2,6,4,1,8,7,11,12,10,9]=>[6,3,1,5,2,4,8,7,12,11,9,10]=>[1,1,2,3,2,1,2] [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>[4,5,8,3,2,10,11,7,12,9,6,1]=>[12,5,4,1,2,11,8,3,10,6,7,9]=>[1,1,1,3,1,2,3] [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[2,1,4,3,8,10,11,7,12,9,6,5]=>[2,1,4,3,12,11,8,5,10,6,7,9]=>[1,2,2,1,1,2,3] [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[4,5,6,3,2,1,8,7,10,9,12,11]=>[6,5,4,1,2,3,8,7,10,9,12,11]=>[1,1,1,4,2,2,1] [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>[3,4,2,1,8,10,11,7,12,9,6,5]=>[4,3,1,2,12,11,8,5,10,6,7,9]=>[1,1,3,1,1,2,3] [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[4,5,6,3,2,1,8,7,11,12,10,9]=>[6,5,4,1,2,3,8,7,12,11,9,10]=>[1,1,1,4,2,1,2] [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[6,7,9,10,11,5,4,12,8,3,2,1]=>[12,11,10,7,6,1,2,9,3,4,5,8]=>[1,1,1,1,1,3,4] [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[2,1,6,7,9,5,4,10,8,3,12,11]=>[2,1,10,7,6,3,4,9,5,8,12,11]=>[1,2,1,1,3,3,1] [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>[3,6,2,7,9,5,4,11,8,12,10,1]=>[12,3,1,7,6,2,4,9,5,11,8,10]=>[1,1,2,1,3,2,2] [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[2,1,6,7,9,5,4,11,8,12,10,3]=>[2,1,12,7,6,3,4,9,5,11,8,10]=>[1,2,1,1,3,2,2] [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[3,6,2,7,9,5,4,10,8,1,12,11]=>[10,3,1,7,6,2,4,9,5,8,12,11]=>[1,1,2,1,3,3,1] [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[4,6,9,3,10,5,11,12,8,7,2,1]=>[12,11,4,1,6,2,10,9,3,5,7,8]=>[1,1,1,2,2,1,4] [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>[2,1,4,3,6,5,10,9,7,8,12,11]=>[1,2,2,2,1,3,1] [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>[3,6,2,9,10,5,11,12,8,7,4,1]=>[12,3,1,11,6,2,10,9,4,5,7,8]=>[1,1,2,1,2,1,4] [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[2,1,6,9,10,5,11,12,8,7,4,3]=>[2,1,12,11,6,3,10,9,4,5,7,8]=>[1,2,1,1,2,1,4] [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>[4,3,1,2,6,5,10,9,7,8,12,11]=>[1,1,3,2,1,3,1] [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[4,6,7,3,9,5,2,11,8,12,10,1]=>[12,7,4,1,6,2,3,9,5,11,8,10]=>[1,1,1,2,3,2,2] [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[2,1,4,3,6,5,9,11,8,12,10,7]=>[2,1,4,3,6,5,12,9,7,11,8,10]=>[1,2,2,2,1,2,2] [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>[4,6,7,3,9,5,2,10,8,1,12,11]=>[10,7,4,1,6,2,3,9,5,8,12,11]=>[1,1,1,2,3,3,1] [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>[3,4,2,1,6,5,9,11,8,12,10,7]=>[4,3,1,2,6,5,12,9,7,11,8,10]=>[1,1,3,2,1,2,2] [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[6,7,8,10,11,5,4,3,12,9,2,1]=>[12,11,8,7,6,1,2,3,10,4,5,9]=>[1,1,1,1,1,4,3] [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[2,1,6,7,8,5,4,3,10,9,12,11]=>[2,1,8,7,6,3,4,5,10,9,12,11]=>[1,2,1,1,4,2,1] [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>[3,6,2,7,10,5,4,11,12,9,8,1]=>[12,3,1,7,6,2,4,11,10,5,8,9]=>[1,1,2,1,3,1,3] [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[2,1,6,7,10,5,4,11,12,9,8,3]=>[2,1,12,7,6,3,4,11,10,5,8,9]=>[1,2,1,1,3,1,3] [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[3,6,2,7,8,5,4,1,10,9,12,11]=>[8,3,1,7,6,2,4,5,10,9,12,11]=>[1,1,2,1,4,2,1] [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>[6,7,8,9,11,5,4,3,2,12,10,1]=>[12,9,8,7,6,1,2,3,4,11,5,10]=>[1,1,1,1,1,5,2] [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[2,1,6,7,8,5,4,3,11,12,10,9]=>[2,1,8,7,6,3,4,5,12,11,9,10]=>[1,2,1,1,4,1,2] [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[6,7,8,9,10,5,4,3,2,1,12,11]=>[10,9,8,7,6,1,2,3,4,5,12,11]=>[1,1,1,1,1,6,1] [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>[3,6,2,7,8,5,4,1,11,12,10,9]=>[8,3,1,7,6,2,4,5,12,11,9,10]=>[1,1,2,1,4,1,2] [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>[4,6,7,3,10,5,2,11,12,9,8,1]=>[12,7,4,1,6,2,3,11,10,5,8,9]=>[1,1,1,2,3,1,3] [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[2,1,4,3,6,5,10,11,12,9,8,7]=>[2,1,4,3,6,5,12,11,10,7,8,9]=>[1,2,2,2,1,1,3] [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[4,6,7,3,8,5,2,1,10,9,12,11]=>[8,7,4,1,6,2,3,5,10,9,12,11]=>[1,1,1,2,4,2,1] [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>[3,4,2,1,6,5,10,11,12,9,8,7]=>[4,3,1,2,6,5,12,11,10,7,8,9]=>[1,1,3,2,1,1,3] [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[4,6,7,3,8,5,2,1,11,12,10,9]=>[8,7,4,1,6,2,3,5,12,11,9,10]=>[1,1,1,2,4,1,2] [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[5,6,9,10,4,3,11,12,8,7,2,1]=>[12,11,6,5,1,2,10,9,3,4,7,8]=>[1,1,1,1,3,1,4] [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>[2,1,6,5,3,4,10,9,7,8,12,11]=>[1,2,1,3,1,3,1] [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>[3,5,2,9,4,10,11,12,8,7,6,1]=>[12,3,1,5,2,11,10,9,4,6,7,8]=>[1,1,2,2,1,1,4] [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[2,1,5,9,4,10,11,12,8,7,6,3]=>[2,1,12,5,3,11,10,9,4,6,7,8]=>[1,2,1,2,1,1,4] [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[3,5,2,6,4,1,9,10,8,7,12,11]=>[6,3,1,5,2,4,10,9,7,8,12,11]=>[1,1,2,3,1,3,1] [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>[5,6,7,9,4,3,2,11,8,12,10,1]=>[12,7,6,5,1,2,3,9,4,11,8,10]=>[1,1,1,1,4,2,2] [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[2,1,5,6,4,3,9,11,8,12,10,7]=>[2,1,6,5,3,4,12,9,7,11,8,10]=>[1,2,1,3,1,2,2] [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[5,6,7,9,4,3,2,10,8,1,12,11]=>[10,7,6,5,1,2,3,9,4,8,12,11]=>[1,1,1,1,4,3,1] [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>[3,5,2,6,4,1,9,11,8,12,10,7]=>[6,3,1,5,2,4,12,9,7,11,8,10]=>[1,1,2,3,1,2,2] [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>[4,5,9,3,2,10,11,12,8,7,6,1]=>[12,5,4,1,2,11,10,9,3,6,7,8]=>[1,1,1,3,1,1,4] [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[2,1,4,3,9,10,11,12,8,7,6,5]=>[2,1,4,3,12,11,10,9,5,6,7,8]=>[1,2,2,1,1,1,4] [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[4,5,6,3,2,1,9,10,8,7,12,11]=>[6,5,4,1,2,3,10,9,7,8,12,11]=>[1,1,1,4,1,3,1] [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>[3,4,2,1,9,10,11,12,8,7,6,5]=>[4,3,1,2,12,11,10,9,5,6,7,8]=>[1,1,3,1,1,1,4] [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[4,5,6,3,2,1,9,11,8,12,10,7]=>[6,5,4,1,2,3,12,9,7,11,8,10]=>[1,1,1,4,1,2,2] [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[5,6,7,10,4,3,2,11,12,9,8,1]=>[12,7,6,5,1,2,3,11,10,4,8,9]=>[1,1,1,1,4,1,3] [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[2,1,5,6,4,3,10,11,12,9,8,7]=>[2,1,6,5,3,4,12,11,10,7,8,9]=>[1,2,1,3,1,1,3] [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>[5,6,7,8,4,3,2,1,10,9,12,11]=>[8,7,6,5,1,2,3,4,10,9,12,11]=>[1,1,1,1,5,2,1] [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>[3,5,2,6,4,1,10,11,12,9,8,7]=>[6,3,1,5,2,4,12,11,10,7,8,9]=>[1,1,2,3,1,1,3] [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>[5,6,7,8,4,3,2,1,11,12,10,9]=>[8,7,6,5,1,2,3,4,12,11,9,10]=>[1,1,1,1,5,1,2] [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>[4,5,6,3,2,1,10,11,12,9,8,7]=>[6,5,4,1,2,3,12,11,10,7,8,9]=>[1,1,1,4,1,1,3] [(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)]=>[2,1,4,3,6,5,8,7,11,12,9,10]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[1,2,2,2,2,1,1,1] [(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]=>[2,1,4,3,6,5,9,10,7,8,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[1,2,2,2,1,1,2,1] [(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)]=>[2,1,4,3,6,5,9,11,7,12,8,10]=>[2,1,4,3,6,5,12,9,8,11,10,7]=>[1,2,2,2,1,2,1,1] [(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)]=>[2,1,4,3,6,5,10,11,12,7,8,9]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[1,2,2,2,1,1,1,1,1] [(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)]=>[2,1,4,3,7,8,5,6,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[1,2,2,1,1,2,2,1] [(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)]=>[2,1,4,3,7,8,5,6,11,12,9,10]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[1,2,2,1,1,2,1,1,1] [(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)]=>[2,1,4,3,7,9,5,10,6,8,12,11]=>[2,1,4,3,10,7,6,9,8,5,12,11]=>[1,2,2,1,2,1,2,1] [(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)]=>[2,1,4,3,7,9,5,11,6,12,8,10]=>[2,1,4,3,12,7,6,9,8,11,10,5]=>[1,2,2,1,2,2,1,1] [(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)]=>[2,1,4,3,7,10,5,11,12,6,8,9]=>[2,1,4,3,12,7,6,11,10,9,8,5]=>[1,2,2,1,2,1,1,1,1] [(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)]=>[2,1,4,3,8,9,10,5,6,7,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[1,2,2,1,1,1,1,2,1] [(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)]=>[2,1,4,3,8,9,11,5,6,12,7,10]=>[2,1,4,3,12,9,8,7,6,11,10,5]=>[1,2,2,1,1,1,2,1,1] [(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)]=>[2,1,4,3,8,10,11,5,12,6,7,9]=>[2,1,4,3,12,11,8,7,10,9,6,5]=>[1,2,2,1,1,2,1,1,1] [(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)]=>[2,1,4,3,9,10,11,12,5,6,7,8]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[1,2,2,1,1,1,1,1,1,1] [(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)]=>[2,1,5,6,3,4,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[1,2,1,1,2,2,2,1] [(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)]=>[2,1,5,6,3,4,8,7,11,12,9,10]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[1,2,1,1,2,2,1,1,1] [(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)]=>[2,1,5,6,3,4,9,10,7,8,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[1,2,1,1,2,1,1,2,1] [(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)]=>[2,1,5,6,3,4,9,11,7,12,8,10]=>[2,1,6,5,4,3,12,9,8,11,10,7]=>[1,2,1,1,2,1,2,1,1] [(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)]=>[2,1,5,6,3,4,10,11,12,7,8,9]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[1,2,1,1,2,1,1,1,1,1] [(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)]=>[2,1,5,7,3,8,4,6,10,9,12,11]=>[2,1,8,5,4,7,6,3,10,9,12,11]=>[1,2,1,2,1,2,2,1] [(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)]=>[2,1,5,7,3,8,4,6,11,12,9,10]=>[2,1,8,5,4,7,6,3,12,11,10,9]=>[1,2,1,2,1,2,1,1,1] [(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)]=>[2,1,5,7,3,9,4,10,6,8,12,11]=>[2,1,10,5,4,7,6,9,8,3,12,11]=>[1,2,1,2,2,1,2,1] [(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)]=>[2,1,5,7,3,9,4,11,6,12,8,10]=>[2,1,12,5,4,7,6,9,8,11,10,3]=>[1,2,1,2,2,2,1,1] [(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)]=>[2,1,5,7,3,10,4,11,12,6,8,9]=>[2,1,12,5,4,7,6,11,10,9,8,3]=>[1,2,1,2,2,1,1,1,1] [(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)]=>[2,1,5,8,3,9,10,4,6,7,12,11]=>[2,1,10,5,4,9,8,7,6,3,12,11]=>[1,2,1,2,1,1,1,2,1] [(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)]=>[2,1,5,8,3,9,11,4,6,12,7,10]=>[2,1,12,5,4,9,8,7,6,11,10,3]=>[1,2,1,2,1,1,2,1,1] [(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)]=>[2,1,5,8,3,10,11,4,12,6,7,9]=>[2,1,12,5,4,11,8,7,10,9,6,3]=>[1,2,1,2,1,2,1,1,1] [(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)]=>[2,1,5,9,3,10,11,12,4,6,7,8]=>[2,1,12,5,4,11,10,9,8,7,6,3]=>[1,2,1,2,1,1,1,1,1,1] [(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)]=>[2,1,6,7,8,3,4,5,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[1,2,1,1,1,1,2,2,1] [(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)]=>[2,1,6,7,8,3,4,5,11,12,9,10]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[1,2,1,1,1,1,2,1,1,1] [(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)]=>[2,1,6,7,9,3,4,10,5,8,12,11]=>[2,1,10,7,6,5,4,9,8,3,12,11]=>[1,2,1,1,1,2,1,2,1] [(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)]=>[2,1,6,7,9,3,4,11,5,12,8,10]=>[2,1,12,7,6,5,4,9,8,11,10,3]=>[1,2,1,1,1,2,2,1,1] [(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)]=>[2,1,6,7,10,3,4,11,12,5,8,9]=>[2,1,12,7,6,5,4,11,10,9,8,3]=>[1,2,1,1,1,2,1,1,1,1] [(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)]=>[2,1,6,8,9,3,10,4,5,7,12,11]=>[2,1,10,9,6,5,8,7,4,3,12,11]=>[1,2,1,1,2,1,1,2,1] [(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)]=>[2,1,6,8,9,3,11,4,5,12,7,10]=>[2,1,12,9,6,5,8,7,4,11,10,3]=>[1,2,1,1,2,1,2,1,1] [(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)]=>[2,1,6,8,10,3,11,4,12,5,7,9]=>[2,1,12,11,6,5,8,7,10,9,4,3]=>[1,2,1,1,2,2,1,1,1] [(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)]=>[2,1,6,9,10,3,11,12,4,5,7,8]=>[2,1,12,11,6,5,10,9,8,7,4,3]=>[1,2,1,1,2,1,1,1,1,1] [(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)]=>[2,1,7,8,9,10,3,4,5,6,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[1,2,1,1,1,1,1,1,2,1] [(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)]=>[2,1,7,8,9,11,3,4,5,12,6,10]=>[2,1,12,9,8,7,6,5,4,11,10,3]=>[1,2,1,1,1,1,1,2,1,1] [(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)]=>[2,1,7,8,10,11,3,4,12,5,6,9]=>[2,1,12,11,8,7,6,5,10,9,4,3]=>[1,2,1,1,1,1,2,1,1,1] [(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)]=>[2,1,7,9,10,11,3,12,4,5,6,8]=>[2,1,12,11,10,7,6,9,8,5,4,3]=>[1,2,1,1,1,2,1,1,1,1] [(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)]=>[2,1,8,9,10,11,12,3,4,5,6,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1,1,1,1] [(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)]=>[3,4,1,2,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[1,1,1,2,2,2,2,1] [(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)]=>[3,4,1,2,6,5,8,7,11,12,9,10]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[1,1,1,2,2,2,1,1,1] [(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)]=>[3,4,1,2,6,5,9,10,7,8,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[1,1,1,2,2,1,1,2,1] [(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)]=>[3,4,1,2,6,5,9,11,7,12,8,10]=>[4,3,2,1,6,5,12,9,8,11,10,7]=>[1,1,1,2,2,1,2,1,1] [(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)]=>[3,4,1,2,6,5,10,11,12,7,8,9]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[1,1,1,2,2,1,1,1,1,1] [(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)]=>[3,4,1,2,7,8,5,6,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[1,1,1,2,1,1,2,2,1] [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)]=>[3,4,1,2,7,8,5,6,11,12,9,10]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[1,1,1,2,1,1,2,1,1,1] [(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)]=>[3,4,1,2,7,9,5,10,6,8,12,11]=>[4,3,2,1,10,7,6,9,8,5,12,11]=>[1,1,1,2,1,2,1,2,1] [(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)]=>[3,4,1,2,7,9,5,11,6,12,8,10]=>[4,3,2,1,12,7,6,9,8,11,10,5]=>[1,1,1,2,1,2,2,1,1] [(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)]=>[3,4,1,2,7,10,5,11,12,6,8,9]=>[4,3,2,1,12,7,6,11,10,9,8,5]=>[1,1,1,2,1,2,1,1,1,1] [(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)]=>[3,4,1,2,8,9,10,5,6,7,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[1,1,1,2,1,1,1,1,2,1] [(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)]=>[3,4,1,2,8,9,11,5,6,12,7,10]=>[4,3,2,1,12,9,8,7,6,11,10,5]=>[1,1,1,2,1,1,1,2,1,1] [(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)]=>[3,4,1,2,8,10,11,5,12,6,7,9]=>[4,3,2,1,12,11,8,7,10,9,6,5]=>[1,1,1,2,1,1,2,1,1,1] [(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)]=>[3,4,1,2,9,10,11,12,5,6,7,8]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[1,1,1,2,1,1,1,1,1,1,1] [(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)]=>[3,5,1,6,2,4,8,7,10,9,12,11]=>[6,3,2,5,4,1,8,7,10,9,12,11]=>[1,1,2,1,2,2,2,1] [(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)]=>[3,5,1,6,2,4,8,7,11,12,9,10]=>[6,3,2,5,4,1,8,7,12,11,10,9]=>[1,1,2,1,2,2,1,1,1] [(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)]=>[3,5,1,6,2,4,9,10,7,8,12,11]=>[6,3,2,5,4,1,10,9,8,7,12,11]=>[1,1,2,1,2,1,1,2,1] [(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)]=>[3,5,1,6,2,4,9,11,7,12,8,10]=>[6,3,2,5,4,1,12,9,8,11,10,7]=>[1,1,2,1,2,1,2,1,1] [(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)]=>[3,5,1,6,2,4,10,11,12,7,8,9]=>[6,3,2,5,4,1,12,11,10,9,8,7]=>[1,1,2,1,2,1,1,1,1,1] [(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)]=>[3,5,1,7,2,8,4,6,10,9,12,11]=>[8,3,2,5,4,7,6,1,10,9,12,11]=>[1,1,2,2,1,2,2,1] [(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)]=>[3,5,1,7,2,8,4,6,11,12,9,10]=>[8,3,2,5,4,7,6,1,12,11,10,9]=>[1,1,2,2,1,2,1,1,1] [(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)]=>[3,5,1,7,2,9,4,10,6,8,12,11]=>[10,3,2,5,4,7,6,9,8,1,12,11]=>[1,1,2,2,2,1,2,1] [(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)]=>[3,5,1,7,2,9,4,11,6,12,8,10]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>[1,1,2,2,2,2,1,1] [(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)]=>[3,5,1,7,2,10,4,11,12,6,8,9]=>[12,3,2,5,4,7,6,11,10,9,8,1]=>[1,1,2,2,2,1,1,1,1] [(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)]=>[3,5,1,8,2,9,10,4,6,7,12,11]=>[10,3,2,5,4,9,8,7,6,1,12,11]=>[1,1,2,2,1,1,1,2,1] [(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)]=>[3,5,1,8,2,9,11,4,6,12,7,10]=>[12,3,2,5,4,9,8,7,6,11,10,1]=>[1,1,2,2,1,1,2,1,1] [(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)]=>[3,5,1,8,2,10,11,4,12,6,7,9]=>[12,3,2,5,4,11,8,7,10,9,6,1]=>[1,1,2,2,1,2,1,1,1] [(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)]=>[3,5,1,9,2,10,11,12,4,6,7,8]=>[12,3,2,5,4,11,10,9,8,7,6,1]=>[1,1,2,2,1,1,1,1,1,1] [(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)]=>[3,6,1,7,8,2,4,5,10,9,12,11]=>[8,3,2,7,6,5,4,1,10,9,12,11]=>[1,1,2,1,1,1,2,2,1] [(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)]=>[3,6,1,7,8,2,4,5,11,12,9,10]=>[8,3,2,7,6,5,4,1,12,11,10,9]=>[1,1,2,1,1,1,2,1,1,1] [(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)]=>[3,6,1,7,9,2,4,10,5,8,12,11]=>[10,3,2,7,6,5,4,9,8,1,12,11]=>[1,1,2,1,1,2,1,2,1] [(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)]=>[3,6,1,7,9,2,4,11,5,12,8,10]=>[12,3,2,7,6,5,4,9,8,11,10,1]=>[1,1,2,1,1,2,2,1,1] [(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)]=>[3,6,1,7,10,2,4,11,12,5,8,9]=>[12,3,2,7,6,5,4,11,10,9,8,1]=>[1,1,2,1,1,2,1,1,1,1] [(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)]=>[3,6,1,8,9,2,10,4,5,7,12,11]=>[10,3,2,9,6,5,8,7,4,1,12,11]=>[1,1,2,1,2,1,1,2,1] [(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)]=>[3,6,1,8,9,2,11,4,5,12,7,10]=>[12,3,2,9,6,5,8,7,4,11,10,1]=>[1,1,2,1,2,1,2,1,1] [(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)]=>[3,6,1,8,10,2,11,4,12,5,7,9]=>[12,3,2,11,6,5,8,7,10,9,4,1]=>[1,1,2,1,2,2,1,1,1] [(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)]=>[3,6,1,9,10,2,11,12,4,5,7,8]=>[12,3,2,11,6,5,10,9,8,7,4,1]=>[1,1,2,1,2,1,1,1,1,1] [(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)]=>[3,7,1,8,9,10,2,4,5,6,12,11]=>[10,3,2,9,8,7,6,5,4,1,12,11]=>[1,1,2,1,1,1,1,1,2,1] [(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)]=>[3,7,1,8,9,11,2,4,5,12,6,10]=>[12,3,2,9,8,7,6,5,4,11,10,1]=>[1,1,2,1,1,1,1,2,1,1] [(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)]=>[3,7,1,8,10,11,2,4,12,5,6,9]=>[12,3,2,11,8,7,6,5,10,9,4,1]=>[1,1,2,1,1,1,2,1,1,1] [(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)]=>[3,7,1,9,10,11,2,12,4,5,6,8]=>[12,3,2,11,10,7,6,9,8,5,4,1]=>[1,1,2,1,1,2,1,1,1,1] [(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)]=>[3,8,1,9,10,11,12,2,4,5,6,7]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[1,1,2,1,1,1,1,1,1,1,1] [(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)]=>[4,5,6,1,2,3,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[1,1,1,1,1,2,2,2,1] [(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)]=>[4,5,6,1,2,3,8,7,11,12,9,10]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[1,1,1,1,1,2,2,1,1,1] [(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)]=>[4,5,6,1,2,3,9,10,7,8,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[1,1,1,1,1,2,1,1,2,1] [(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)]=>[4,5,6,1,2,3,9,11,7,12,8,10]=>[6,5,4,3,2,1,12,9,8,11,10,7]=>[1,1,1,1,1,2,1,2,1,1] [(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)]=>[4,5,6,1,2,3,10,11,12,7,8,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[1,1,1,1,1,2,1,1,1,1,1] [(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)]=>[4,5,7,1,2,8,3,6,10,9,12,11]=>[8,5,4,3,2,7,6,1,10,9,12,11]=>[1,1,1,1,2,1,2,2,1] [(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)]=>[4,5,7,1,2,8,3,6,11,12,9,10]=>[8,5,4,3,2,7,6,1,12,11,10,9]=>[1,1,1,1,2,1,2,1,1,1] [(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)]=>[4,5,7,1,2,9,3,10,6,8,12,11]=>[10,5,4,3,2,7,6,9,8,1,12,11]=>[1,1,1,1,2,2,1,2,1] [(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)]=>[4,5,7,1,2,9,3,11,6,12,8,10]=>[12,5,4,3,2,7,6,9,8,11,10,1]=>[1,1,1,1,2,2,2,1,1] [(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)]=>[4,5,7,1,2,10,3,11,12,6,8,9]=>[12,5,4,3,2,7,6,11,10,9,8,1]=>[1,1,1,1,2,2,1,1,1,1] [(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)]=>[4,5,8,1,2,9,10,3,6,7,12,11]=>[10,5,4,3,2,9,8,7,6,1,12,11]=>[1,1,1,1,2,1,1,1,2,1] [(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)]=>[4,5,8,1,2,9,11,3,6,12,7,10]=>[12,5,4,3,2,9,8,7,6,11,10,1]=>[1,1,1,1,2,1,1,2,1,1] [(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)]=>[4,5,8,1,2,10,11,3,12,6,7,9]=>[12,5,4,3,2,11,8,7,10,9,6,1]=>[1,1,1,1,2,1,2,1,1,1] [(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)]=>[4,5,9,1,2,10,11,12,3,6,7,8]=>[12,5,4,3,2,11,10,9,8,7,6,1]=>[1,1,1,1,2,1,1,1,1,1,1] [(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)]=>[4,6,7,1,8,2,3,5,10,9,12,11]=>[8,7,4,3,6,5,2,1,10,9,12,11]=>[1,1,1,2,1,1,2,2,1] [(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)]=>[4,6,7,1,8,2,3,5,11,12,9,10]=>[8,7,4,3,6,5,2,1,12,11,10,9]=>[1,1,1,2,1,1,2,1,1,1] [(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)]=>[4,6,7,1,9,2,3,10,5,8,12,11]=>[10,7,4,3,6,5,2,9,8,1,12,11]=>[1,1,1,2,1,2,1,2,1] [(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)]=>[4,6,7,1,9,2,3,11,5,12,8,10]=>[12,7,4,3,6,5,2,9,8,11,10,1]=>[1,1,1,2,1,2,2,1,1] [(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)]=>[4,6,7,1,10,2,3,11,12,5,8,9]=>[12,7,4,3,6,5,2,11,10,9,8,1]=>[1,1,1,2,1,2,1,1,1,1] [(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)]=>[4,6,8,1,9,2,10,3,5,7,12,11]=>[10,9,4,3,6,5,8,7,2,1,12,11]=>[1,1,1,2,2,1,1,2,1] [(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)]=>[4,6,8,1,9,2,11,3,5,12,7,10]=>[12,9,4,3,6,5,8,7,2,11,10,1]=>[1,1,1,2,2,1,2,1,1] [(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)]=>[4,6,8,1,10,2,11,3,12,5,7,9]=>[12,11,4,3,6,5,8,7,10,9,2,1]=>[1,1,1,2,2,2,1,1,1] [(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)]=>[4,6,9,1,10,2,11,12,3,5,7,8]=>[12,11,4,3,6,5,10,9,8,7,2,1]=>[1,1,1,2,2,1,1,1,1,1] [(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)]=>[4,7,8,1,9,10,2,3,5,6,12,11]=>[10,9,4,3,8,7,6,5,2,1,12,11]=>[1,1,1,2,1,1,1,1,2,1] [(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)]=>[4,7,8,1,9,11,2,3,5,12,6,10]=>[12,9,4,3,8,7,6,5,2,11,10,1]=>[1,1,1,2,1,1,1,2,1,1] [(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)]=>[4,7,8,1,10,11,2,3,12,5,6,9]=>[12,11,4,3,8,7,6,5,10,9,2,1]=>[1,1,1,2,1,1,2,1,1,1] [(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)]=>[4,7,9,1,10,11,2,12,3,5,6,8]=>[12,11,4,3,10,7,6,9,8,5,2,1]=>[1,1,1,2,1,2,1,1,1,1] [(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)]=>[4,8,9,1,10,11,12,2,3,5,6,7]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[1,1,1,2,1,1,1,1,1,1,1] [(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)]=>[5,6,7,8,1,2,3,4,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[1,1,1,1,1,1,1,2,2,1] [(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)]=>[5,6,7,8,1,2,3,4,11,12,9,10]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[1,1,1,1,1,1,1,2,1,1,1] [(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)]=>[5,6,7,9,1,2,3,10,4,8,12,11]=>[10,7,6,5,4,3,2,9,8,1,12,11]=>[1,1,1,1,1,1,2,1,2,1] [(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)]=>[5,6,7,9,1,2,3,11,4,12,8,10]=>[12,7,6,5,4,3,2,9,8,11,10,1]=>[1,1,1,1,1,1,2,2,1,1] [(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)]=>[5,6,7,10,1,2,3,11,12,4,8,9]=>[12,7,6,5,4,3,2,11,10,9,8,1]=>[1,1,1,1,1,1,2,1,1,1,1] [(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)]=>[5,6,8,9,1,2,10,3,4,7,12,11]=>[10,9,6,5,4,3,8,7,2,1,12,11]=>[1,1,1,1,1,2,1,1,2,1] [(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)]=>[5,6,8,9,1,2,11,3,4,12,7,10]=>[12,9,6,5,4,3,8,7,2,11,10,1]=>[1,1,1,1,1,2,1,2,1,1] [(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)]=>[5,6,8,10,1,2,11,3,12,4,7,9]=>[12,11,6,5,4,3,8,7,10,9,2,1]=>[1,1,1,1,1,2,2,1,1,1] [(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)]=>[5,6,9,10,1,2,11,12,3,4,7,8]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[1,1,1,1,1,2,1,1,1,1,1] [(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)]=>[5,7,8,9,1,10,2,3,4,6,12,11]=>[10,9,8,5,4,7,6,3,2,1,12,11]=>[1,1,1,1,2,1,1,1,2,1] [(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)]=>[5,7,8,9,1,11,2,3,4,12,6,10]=>[12,9,8,5,4,7,6,3,2,11,10,1]=>[1,1,1,1,2,1,1,2,1,1] [(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)]=>[5,7,8,10,1,11,2,3,12,4,6,9]=>[12,11,8,5,4,7,6,3,10,9,2,1]=>[1,1,1,1,2,1,2,1,1,1] [(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)]=>[5,7,9,10,1,11,2,12,3,4,6,8]=>[12,11,10,5,4,7,6,9,8,3,2,1]=>[1,1,1,1,2,2,1,1,1,1] [(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)]=>[5,8,9,10,1,11,12,2,3,4,6,7]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[1,1,1,1,2,1,1,1,1,1,1] [(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)]=>[6,7,8,9,10,1,2,3,4,5,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[1,1,1,1,1,1,1,1,1,2,1] [(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)]=>[6,7,8,9,11,1,2,3,4,12,5,10]=>[12,9,8,7,6,5,4,3,2,11,10,1]=>[1,1,1,1,1,1,1,1,2,1,1] [(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)]=>[6,7,8,10,11,1,2,3,12,4,5,9]=>[12,11,8,7,6,5,4,3,10,9,2,1]=>[1,1,1,1,1,1,1,2,1,1,1] [(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)]=>[6,7,9,10,11,1,2,12,3,4,5,8]=>[12,11,10,7,6,5,4,9,8,3,2,1]=>[1,1,1,1,1,1,2,1,1,1,1] [(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)]=>[6,8,9,10,11,1,12,2,3,4,5,7]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[1,1,1,1,1,2,1,1,1,1,1] [(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]
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
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.