Identifier
Mp00283:
Perfect matchings
—non-nesting-exceedence permutation⟶
Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Images
=>
Cc0012;cc-rep-0Cc0009;cc-rep-2Cc0009;cc-rep-3
[(1,2)]=>[2,1]=>{{1,2}}=>{{1,2}}
[(1,2),(3,4)]=>[2,1,4,3]=>{{1,2},{3,4}}=>{{1,2,4},{3}}
[(1,3),(2,4)]=>[3,4,1,2]=>{{1,3},{2,4}}=>{{1,4},{2,3}}
[(1,4),(2,3)]=>[3,4,2,1]=>{{1,3},{2,4}}=>{{1,4},{2,3}}
[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}=>{{1,2,4},{3,6},{5}}
[(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3,6},{5}}
[(1,4),(2,3),(5,6)]=>[3,4,2,1,6,5]=>{{1,3},{2,4},{5,6}}=>{{1,4},{2,3,6},{5}}
[(1,5),(2,3),(4,6)]=>[3,5,2,6,1,4]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3,5},{4}}
[(1,6),(2,3),(4,5)]=>[3,5,2,6,4,1]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3,5},{4}}
[(1,6),(2,4),(3,5)]=>[4,5,6,2,3,1]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[(1,5),(2,4),(3,6)]=>[4,5,6,2,1,3]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3,5},{4}}
[(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}=>{{1,2,6},{3,5},{4}}
[(1,2),(3,6),(4,5)]=>[2,1,5,6,4,3]=>{{1,2},{3,5},{4,6}}=>{{1,2,6},{3,5},{4}}
[(1,3),(2,6),(4,5)]=>[3,5,1,6,4,2]=>{{1,3},{2,5},{4,6}}=>{{1,6},{2,3,5},{4}}
[(1,4),(2,6),(3,5)]=>[4,5,6,1,3,2]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[(1,5),(2,6),(3,4)]=>[4,5,6,3,1,2]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[(1,6),(2,5),(3,4)]=>[4,5,6,3,2,1]=>{{1,4},{2,5},{3,6}}=>{{1,6},{2,5},{3,4}}
[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}=>{{1,2,4,8},{3,6},{5},{7}}
[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,4,8},{2,3,6},{5},{7}}
[(1,4),(2,3),(5,6),(7,8)]=>[3,4,2,1,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}=>{{1,4,8},{2,3,6},{5},{7}}
[(1,5),(2,3),(4,6),(7,8)]=>[3,5,2,6,1,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3,5},{4,8},{7}}
[(1,6),(2,3),(4,5),(7,8)]=>[3,5,2,6,4,1,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3,5},{4,8},{7}}
[(1,7),(2,3),(4,5),(6,8)]=>[3,5,2,7,4,8,1,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,8),(2,3),(4,5),(6,7)]=>[3,5,2,7,4,8,6,1]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,8),(2,4),(3,5),(6,7)]=>[4,5,7,2,3,8,6,1]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,7),(2,4),(3,5),(6,8)]=>[4,5,7,2,3,8,1,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,6),(2,4),(3,5),(7,8)]=>[4,5,6,2,3,1,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4,8},{7}}
[(1,5),(2,4),(3,6),(7,8)]=>[4,5,6,2,1,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4,8},{7}}
[(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4,8},{7}}
[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3,5},{4,8},{7}}
[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2,6},{3,5},{4,8},{7}}
[(1,2),(3,6),(4,5),(7,8)]=>[2,1,5,6,4,3,8,7]=>{{1,2},{3,5},{4,6},{7,8}}=>{{1,2,6},{3,5},{4,8},{7}}
[(1,3),(2,6),(4,5),(7,8)]=>[3,5,1,6,4,2,8,7]=>{{1,3},{2,5},{4,6},{7,8}}=>{{1,6},{2,3,5},{4,8},{7}}
[(1,4),(2,6),(3,5),(7,8)]=>[4,5,6,1,3,2,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4,8},{7}}
[(1,5),(2,6),(3,4),(7,8)]=>[4,5,6,3,1,2,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4,8},{7}}
[(1,6),(2,5),(3,4),(7,8)]=>[4,5,6,3,2,1,8,7]=>{{1,4},{2,5},{3,6},{7,8}}=>{{1,6},{2,5},{3,4,8},{7}}
[(1,7),(2,5),(3,4),(6,8)]=>[4,5,7,3,2,8,1,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,8),(2,5),(3,4),(6,7)]=>[4,5,7,3,2,8,6,1]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,8),(2,6),(3,4),(5,7)]=>[4,6,7,3,8,2,5,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,7),(2,6),(3,4),(5,8)]=>[4,6,7,3,8,2,1,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,6),(2,7),(3,4),(5,8)]=>[4,6,7,3,8,1,2,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,5),(2,7),(3,4),(6,8)]=>[4,5,7,3,1,8,2,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,4),(2,7),(3,5),(6,8)]=>[4,5,7,1,3,8,2,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,3),(2,7),(4,5),(6,8)]=>[3,5,1,7,4,8,2,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,2),(3,7),(4,5),(6,8)]=>[2,1,5,7,4,8,3,6]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2,8},{3,5},{4,7},{6}}
[(1,2),(3,8),(4,5),(6,7)]=>[2,1,5,7,4,8,6,3]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2,8},{3,5},{4,7},{6}}
[(1,3),(2,8),(4,5),(6,7)]=>[3,5,1,7,4,8,6,2]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,4),(2,8),(3,5),(6,7)]=>[4,5,7,1,3,8,6,2]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,5),(2,8),(3,4),(6,7)]=>[4,5,7,3,1,8,6,2]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,6),(2,8),(3,4),(5,7)]=>[4,6,7,3,8,1,5,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,7),(2,8),(3,4),(5,6)]=>[4,6,7,3,8,5,1,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,8),(2,7),(3,4),(5,6)]=>[4,6,7,3,8,5,2,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,8),(2,7),(3,5),(4,6)]=>[5,6,7,8,3,4,2,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,7),(2,8),(3,5),(4,6)]=>[5,6,7,8,3,4,1,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,6),(2,8),(3,5),(4,7)]=>[5,6,7,8,3,1,4,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,5),(2,8),(3,6),(4,7)]=>[5,6,7,8,1,3,4,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,4),(2,8),(3,6),(5,7)]=>[4,6,7,1,8,3,5,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,3),(2,8),(4,6),(5,7)]=>[3,6,1,7,8,4,5,2]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,2),(3,8),(4,6),(5,7)]=>[2,1,6,7,8,4,5,3]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2,8},{3,7},{4,6},{5}}
[(1,2),(3,7),(4,6),(5,8)]=>[2,1,6,7,8,4,3,5]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2,8},{3,7},{4,6},{5}}
[(1,3),(2,7),(4,6),(5,8)]=>[3,6,1,7,8,4,2,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,4),(2,7),(3,6),(5,8)]=>[4,6,7,1,8,3,2,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,5),(2,7),(3,6),(4,8)]=>[5,6,7,8,1,3,2,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,6),(2,7),(3,5),(4,8)]=>[5,6,7,8,3,1,2,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,7),(2,6),(3,5),(4,8)]=>[5,6,7,8,3,2,1,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,8),(2,6),(3,5),(4,7)]=>[5,6,7,8,3,2,4,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,8),(2,5),(3,6),(4,7)]=>[5,6,7,8,2,3,4,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,7),(2,5),(3,6),(4,8)]=>[5,6,7,8,2,3,1,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,6),(2,5),(3,7),(4,8)]=>[5,6,7,8,2,1,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2,8},{3,7},{4,6},{5}}
[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2,8},{3,5},{4,7},{6}}
[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,5),(2,4),(3,7),(6,8)]=>[4,5,7,2,1,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,6),(2,4),(3,7),(5,8)]=>[4,6,7,2,8,1,3,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,7),(2,4),(3,6),(5,8)]=>[4,6,7,2,8,3,1,5]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,8),(2,4),(3,6),(5,7)]=>[4,6,7,2,8,3,5,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,8),(2,3),(4,6),(5,7)]=>[3,6,2,7,8,4,5,1]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,7),(2,3),(4,6),(5,8)]=>[3,6,2,7,8,4,1,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,6),(2,3),(4,7),(5,8)]=>[3,6,2,7,8,1,4,5]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,5),(2,3),(4,7),(6,8)]=>[3,5,2,7,1,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,4),(2,3),(5,7),(6,8)]=>[3,4,2,1,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4,7},{2,3,8},{5},{6}}
[(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4,7},{2,3,8},{5},{6}}
[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,2,4,7},{3,8},{5},{6}}
[(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,7,8,6,5]=>{{1,2},{3,4},{5,7},{6,8}}=>{{1,2,4,7},{3,8},{5},{6}}
[(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,7,8,6,5]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4,7},{2,3,8},{5},{6}}
[(1,4),(2,3),(5,8),(6,7)]=>[3,4,2,1,7,8,6,5]=>{{1,3},{2,4},{5,7},{6,8}}=>{{1,4,7},{2,3,8},{5},{6}}
[(1,5),(2,3),(4,8),(6,7)]=>[3,5,2,7,1,8,6,4]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,6),(2,3),(4,8),(5,7)]=>[3,6,2,7,8,1,5,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,7),(2,3),(4,8),(5,6)]=>[3,6,2,7,8,5,1,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,8),(2,3),(4,7),(5,6)]=>[3,6,2,7,8,5,4,1]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,8),(2,4),(3,7),(5,6)]=>[4,6,7,2,8,5,3,1]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,7),(2,4),(3,8),(5,6)]=>[4,6,7,2,8,5,1,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,6),(2,4),(3,8),(5,7)]=>[4,6,7,2,8,1,5,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,5),(2,4),(3,8),(6,7)]=>[4,5,7,2,1,8,6,3]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,4),(2,5),(3,8),(6,7)]=>[4,5,7,1,2,8,6,3]=>{{1,4},{2,5},{3,7},{6,8}}=>{{1,8},{2,5},{3,4,7},{6}}
[(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,7,2,8,6,4]=>{{1,3},{2,5},{4,7},{6,8}}=>{{1,8},{2,3,5},{4,7},{6}}
[(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,7,3,8,6,4]=>{{1,2},{3,5},{4,7},{6,8}}=>{{1,2,8},{3,5},{4,7},{6}}
[(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,7,8,3,5,4]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2,8},{3,7},{4,6},{5}}
[(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,7,8,2,5,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,4),(2,6),(3,8),(5,7)]=>[4,6,7,1,8,2,5,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,5),(2,6),(3,8),(4,7)]=>[5,6,7,8,1,2,4,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,6),(2,5),(3,8),(4,7)]=>[5,6,7,8,2,1,4,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,7),(2,5),(3,8),(4,6)]=>[5,6,7,8,2,4,1,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,8),(2,5),(3,7),(4,6)]=>[5,6,7,8,2,4,3,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,8),(2,6),(3,7),(4,5)]=>[5,6,7,8,4,2,3,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,7),(2,6),(3,8),(4,5)]=>[5,6,7,8,4,2,1,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,6),(2,7),(3,8),(4,5)]=>[5,6,7,8,4,1,2,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,5),(2,7),(3,8),(4,6)]=>[5,6,7,8,1,4,2,3]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,4),(2,7),(3,8),(5,6)]=>[4,6,7,1,8,5,2,3]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,3),(2,7),(4,8),(5,6)]=>[3,6,1,7,8,5,2,4]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,2),(3,7),(4,8),(5,6)]=>[2,1,6,7,8,5,3,4]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2,8},{3,7},{4,6},{5}}
[(1,2),(3,8),(4,7),(5,6)]=>[2,1,6,7,8,5,4,3]=>{{1,2},{3,6},{4,7},{5,8}}=>{{1,2,8},{3,7},{4,6},{5}}
[(1,3),(2,8),(4,7),(5,6)]=>[3,6,1,7,8,5,4,2]=>{{1,3},{2,6},{4,7},{5,8}}=>{{1,8},{2,3,7},{4,6},{5}}
[(1,4),(2,8),(3,7),(5,6)]=>[4,6,7,1,8,5,3,2]=>{{1,4},{2,6},{3,7},{5,8}}=>{{1,8},{2,7},{3,4,6},{5}}
[(1,5),(2,8),(3,7),(4,6)]=>[5,6,7,8,1,4,3,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,6),(2,8),(3,7),(4,5)]=>[5,6,7,8,4,1,3,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,7),(2,8),(3,6),(4,5)]=>[5,6,7,8,4,3,1,2]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,8),(2,7),(3,6),(4,5)]=>[5,6,7,8,4,3,2,1]=>{{1,5},{2,6},{3,7},{4,8}}=>{{1,8},{2,7},{3,6},{4,5}}
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>{{1,2,4,8},{3,6},{5,10},{7},{9}}
[(1,4),(2,3),(5,6),(7,8),(9,10)]=>[3,4,2,1,6,5,8,7,10,9]=>{{1,3},{2,4},{5,6},{7,8},{9,10}}=>{{1,4,8},{2,3,6},{5,10},{7},{9}}
[(1,6),(2,3),(4,5),(7,8),(9,10)]=>[3,5,2,6,4,1,8,7,10,9]=>{{1,3},{2,5},{4,6},{7,8},{9,10}}=>{{1,6},{2,3,5,10},{4,8},{7},{9}}
[(1,8),(2,3),(4,5),(6,7),(9,10)]=>[3,5,2,7,4,8,6,1,10,9]=>{{1,3},{2,5},{4,7},{6,8},{9,10}}=>{{1,8},{2,3,5,10},{4,7},{6},{9}}
[(1,10),(2,3),(4,5),(6,7),(8,9)]=>[3,5,2,7,4,9,6,10,8,1]=>{{1,3},{2,5},{4,7},{6,9},{8,10}}=>{{1,10},{2,3,5,9},{4,7},{6},{8}}
[(1,2),(3,6),(4,5),(7,8),(9,10)]=>[2,1,5,6,4,3,8,7,10,9]=>{{1,2},{3,5},{4,6},{7,8},{9,10}}=>{{1,2,6},{3,5,10},{4,8},{7},{9}}
[(1,6),(2,5),(3,4),(7,8),(9,10)]=>[4,5,6,3,2,1,8,7,10,9]=>{{1,4},{2,5},{3,6},{7,8},{9,10}}=>{{1,6},{2,5,10},{3,4,8},{7},{9}}
[(1,8),(2,5),(3,4),(6,7),(9,10)]=>[4,5,7,3,2,8,6,1,10,9]=>{{1,4},{2,5},{3,7},{6,8},{9,10}}=>{{1,8},{2,5,10},{3,4,7},{6},{9}}
[(1,10),(2,5),(3,4),(6,7),(8,9)]=>[4,5,7,3,2,9,6,10,8,1]=>{{1,4},{2,5},{3,7},{6,9},{8,10}}=>{{1,10},{2,5,9},{3,4,7},{6},{8}}
[(1,2),(3,8),(4,5),(6,7),(9,10)]=>[2,1,5,7,4,8,6,3,10,9]=>{{1,2},{3,5},{4,7},{6,8},{9,10}}=>{{1,2,8},{3,5,10},{4,7},{6},{9}}
[(1,8),(2,7),(3,4),(5,6),(9,10)]=>[4,6,7,3,8,5,2,1,10,9]=>{{1,4},{2,6},{3,7},{5,8},{9,10}}=>{{1,8},{2,7},{3,4,6},{5,10},{9}}
[(1,10),(2,7),(3,4),(5,6),(8,9)]=>[4,6,7,3,9,5,2,10,8,1]=>{{1,4},{2,6},{3,7},{5,9},{8,10}}=>{{1,10},{2,7},{3,4,6},{5,9},{8}}
[(1,2),(3,10),(4,5),(6,7),(8,9)]=>[2,1,5,7,4,9,6,10,8,3]=>{{1,2},{3,5},{4,7},{6,9},{8,10}}=>{{1,2,10},{3,5,9},{4,7},{6},{8}}
[(1,10),(2,9),(3,4),(5,6),(7,8)]=>[4,6,8,3,9,5,10,7,2,1]=>{{1,4},{2,6},{3,8},{5,9},{7,10}}=>{{1,10},{2,9},{3,4,6},{5,8},{7}}
[(1,2),(3,4),(5,8),(6,7),(9,10)]=>[2,1,4,3,7,8,6,5,10,9]=>{{1,2},{3,4},{5,7},{6,8},{9,10}}=>{{1,2,4,7},{3,8},{5,10},{6},{9}}
[(1,4),(2,3),(5,8),(6,7),(9,10)]=>[3,4,2,1,7,8,6,5,10,9]=>{{1,3},{2,4},{5,7},{6,8},{9,10}}=>{{1,4,7},{2,3,8},{5,10},{6},{9}}
[(1,8),(2,3),(4,7),(5,6),(9,10)]=>[3,6,2,7,8,5,4,1,10,9]=>{{1,3},{2,6},{4,7},{5,8},{9,10}}=>{{1,8},{2,3,7},{4,6},{5,10},{9}}
[(1,10),(2,3),(4,7),(5,6),(8,9)]=>[3,6,2,7,9,5,4,10,8,1]=>{{1,3},{2,6},{4,7},{5,9},{8,10}}=>{{1,10},{2,3,7},{4,6},{5,9},{8}}
[(1,2),(3,8),(4,7),(5,6),(9,10)]=>[2,1,6,7,8,5,4,3,10,9]=>{{1,2},{3,6},{4,7},{5,8},{9,10}}=>{{1,2,8},{3,7},{4,6},{5,10},{9}}
[(1,8),(2,7),(3,6),(4,5),(9,10)]=>[5,6,7,8,4,3,2,1,10,9]=>{{1,5},{2,6},{3,7},{4,8},{9,10}}=>{{1,8},{2,7},{3,6},{4,5,10},{9}}
[(1,10),(2,7),(3,6),(4,5),(8,9)]=>[5,6,7,9,4,3,2,10,8,1]=>{{1,5},{2,6},{3,7},{4,9},{8,10}}=>{{1,10},{2,7},{3,6},{4,5,9},{8}}
[(1,2),(3,10),(4,7),(5,6),(8,9)]=>[2,1,6,7,9,5,4,10,8,3]=>{{1,2},{3,6},{4,7},{5,9},{8,10}}=>{{1,2,10},{3,7},{4,6},{5,9},{8}}
[(1,10),(2,9),(3,6),(4,5),(7,8)]=>[5,6,8,9,4,3,10,7,2,1]=>{{1,5},{2,6},{3,8},{4,9},{7,10}}=>{{1,10},{2,9},{3,6},{4,5,8},{7}}
[(1,2),(3,4),(5,10),(6,7),(8,9)]=>[2,1,4,3,7,9,6,10,8,5]=>{{1,2},{3,4},{5,7},{6,9},{8,10}}=>{{1,2,4,7},{3,10},{5,9},{6},{8}}
[(1,4),(2,3),(5,10),(6,7),(8,9)]=>[3,4,2,1,7,9,6,10,8,5]=>{{1,3},{2,4},{5,7},{6,9},{8,10}}=>{{1,4,7},{2,3,10},{5,9},{6},{8}}
[(1,10),(2,3),(4,9),(5,6),(7,8)]=>[3,6,2,8,9,5,10,7,4,1]=>{{1,3},{2,6},{4,8},{5,9},{7,10}}=>{{1,10},{2,3,9},{4,6},{5,8},{7}}
[(1,2),(3,10),(4,9),(5,6),(7,8)]=>[2,1,6,8,9,5,10,7,4,3]=>{{1,2},{3,6},{4,8},{5,9},{7,10}}=>{{1,2,10},{3,9},{4,6},{5,8},{7}}
[(1,10),(2,9),(3,8),(4,5),(6,7)]=>[5,7,8,9,4,10,6,3,2,1]=>{{1,5},{2,7},{3,8},{4,9},{6,10}}=>{{1,10},{2,9},{3,8},{4,5,7},{6}}
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>[6,7,8,9,10,1,2,3,4,5]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}=>{{1,10},{2,9},{3,8},{4,7},{5,6}}
[(1,2),(3,4),(5,6),(7,10),(8,9)]=>[2,1,4,3,6,5,9,10,8,7]=>{{1,2},{3,4},{5,6},{7,9},{8,10}}=>{{1,2,4,10},{3,6},{5,9},{7},{8}}
[(1,4),(2,3),(5,6),(7,10),(8,9)]=>[3,4,2,1,6,5,9,10,8,7]=>{{1,3},{2,4},{5,6},{7,9},{8,10}}=>{{1,4,10},{2,3,6},{5,9},{7},{8}}
[(1,6),(2,3),(4,5),(7,10),(8,9)]=>[3,5,2,6,4,1,9,10,8,7]=>{{1,3},{2,5},{4,6},{7,9},{8,10}}=>{{1,6},{2,3,5,9},{4,10},{7},{8}}
[(1,10),(2,3),(4,5),(6,9),(7,8)]=>[3,5,2,8,4,9,10,7,6,1]=>{{1,3},{2,5},{4,8},{6,9},{7,10}}=>{{1,10},{2,3,5,8},{4,9},{6},{7}}
[(1,2),(3,6),(4,5),(7,10),(8,9)]=>[2,1,5,6,4,3,9,10,8,7]=>{{1,2},{3,5},{4,6},{7,9},{8,10}}=>{{1,2,6},{3,5,9},{4,10},{7},{8}}
[(1,6),(2,5),(3,4),(7,10),(8,9)]=>[4,5,6,3,2,1,9,10,8,7]=>{{1,4},{2,5},{3,6},{7,9},{8,10}}=>{{1,6},{2,5,9},{3,4,10},{7},{8}}
[(1,10),(2,5),(3,4),(6,9),(7,8)]=>[4,5,8,3,2,9,10,7,6,1]=>{{1,4},{2,5},{3,8},{6,9},{7,10}}=>{{1,10},{2,5,8},{3,4,9},{6},{7}}
[(1,2),(3,10),(4,5),(6,9),(7,8)]=>[2,1,5,8,4,9,10,7,6,3]=>{{1,2},{3,5},{4,8},{6,9},{7,10}}=>{{1,2,10},{3,5,8},{4,9},{6},{7}}
[(1,10),(2,9),(3,4),(5,8),(6,7)]=>[4,7,8,3,9,10,6,5,2,1]=>{{1,4},{2,7},{3,8},{5,9},{6,10}}=>{{1,10},{2,9},{3,4,8},{5,7},{6}}
[(1,2),(3,4),(5,10),(6,9),(7,8)]=>[2,1,4,3,8,9,10,7,6,5]=>{{1,2},{3,4},{5,8},{6,9},{7,10}}=>{{1,2,4,9},{3,10},{5,8},{6},{7}}
[(1,4),(2,3),(5,10),(6,9),(7,8)]=>[3,4,2,1,8,9,10,7,6,5]=>{{1,3},{2,4},{5,8},{6,9},{7,10}}=>{{1,4,9},{2,3,10},{5,8},{6},{7}}
[(1,10),(2,3),(4,9),(5,8),(6,7)]=>[3,7,2,8,9,10,6,5,4,1]=>{{1,3},{2,7},{4,8},{5,9},{6,10}}=>{{1,10},{2,3,9},{4,8},{5,7},{6}}
[(1,2),(3,10),(4,9),(5,8),(6,7)]=>[2,1,7,8,9,10,6,5,4,3]=>{{1,2},{3,7},{4,8},{5,9},{6,10}}=>{{1,2,10},{3,9},{4,8},{5,7},{6}}
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[6,7,8,9,10,5,4,3,2,1]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}=>{{1,10},{2,9},{3,8},{4,7},{5,6}}
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}=>{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>[2,1,7,8,9,10,6,5,4,3,12,11]=>{{1,2},{3,7},{4,8},{5,9},{6,10},{11,12}}=>{{1,2,10},{3,9},{4,8},{5,7},{6,12},{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]=>{{1,3},{2,7},{4,8},{5,9},{6,11},{10,12}}=>{{1,12},{2,3,9},{4,8},{5,7},{6,11},{10}}
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>[2,1,7,8,9,11,6,5,4,12,10,3]=>{{1,2},{3,7},{4,8},{5,9},{6,11},{10,12}}=>{{1,2,12},{3,9},{4,8},{5,7},{6,11},{10}}
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>[3,7,2,8,9,10,6,5,4,1,12,11]=>{{1,3},{2,7},{4,8},{5,9},{6,10},{11,12}}=>{{1,10},{2,3,9},{4,8},{5,7},{6,12},{11}}
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>[4,7,8,3,10,11,6,5,12,9,2,1]=>{{1,4},{2,7},{3,8},{5,10},{6,11},{9,12}}=>{{1,12},{2,11},{3,4,8},{5,7},{6,10},{9}}
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>{{1,2},{3,4},{5,7},{6,8},{9,10},{11,12}}=>{{1,2,4,7},{3,8},{5,10},{6,12},{9},{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]=>{{1,3},{2,7},{4,8},{5,10},{6,11},{9,12}}=>{{1,12},{2,3,11},{4,8},{5,7},{6,10},{9}}
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>[2,1,7,8,10,11,6,5,12,9,4,3]=>{{1,2},{3,7},{4,8},{5,10},{6,11},{9,12}}=>{{1,2,12},{3,11},{4,8},{5,7},{6,10},{9}}
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>{{1,3},{2,4},{5,7},{6,8},{9,10},{11,12}}=>{{1,4,7},{2,3,8},{5,10},{6,12},{9},{11}}
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>[4,7,8,3,9,11,6,5,2,12,10,1]=>{{1,4},{2,7},{3,8},{5,9},{6,11},{10,12}}=>{{1,12},{2,9},{3,4,8},{5,7},{6,11},{10}}
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>{{1,2},{3,4},{5,7},{6,8},{9,11},{10,12}}=>{{1,2,4,7},{3,8},{5,12},{6,11},{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]=>{{1,4},{2,7},{3,8},{5,9},{6,10},{11,12}}=>{{1,10},{2,9},{3,4,8},{5,7},{6,12},{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]=>{{1,3},{2,4},{5,7},{6,8},{9,11},{10,12}}=>{{1,4,7},{2,3,8},{5,12},{6,11},{9},{10}}
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>[5,7,9,10,4,11,6,12,8,3,2,1]=>{{1,5},{2,7},{3,9},{4,10},{6,11},{8,12}}=>{{1,12},{2,11},{3,10},{4,5,7},{6,9},{8}}
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>[2,1,5,7,4,9,6,10,8,3,12,11]=>{{1,2},{3,5},{4,7},{6,9},{8,10},{11,12}}=>{{1,2,10},{3,5,9},{4,7},{6,12},{8},{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},{2,5},{4,7},{6,9},{8,11},{10,12}}=>{{1,12},{2,3,5,9},{4,7},{6,11},{8},{10}}
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>[2,1,5,7,4,9,6,11,8,12,10,3]=>{{1,2},{3,5},{4,7},{6,9},{8,11},{10,12}}=>{{1,2,12},{3,5,9},{4,7},{6,11},{8},{10}}
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>[3,5,2,7,4,9,6,10,8,1,12,11]=>{{1,3},{2,5},{4,7},{6,9},{8,10},{11,12}}=>{{1,10},{2,3,5,9},{4,7},{6,12},{8},{11}}
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>[4,7,9,3,10,11,6,12,8,5,2,1]=>{{1,4},{2,7},{3,9},{5,10},{6,11},{8,12}}=>{{1,12},{2,11},{3,4,10},{5,7},{6,9},{8}}
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>[2,1,4,3,7,9,6,10,8,5,12,11]=>{{1,2},{3,4},{5,7},{6,9},{8,10},{11,12}}=>{{1,2,4,7},{3,10},{5,9},{6,12},{8},{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]=>{{1,3},{2,7},{4,9},{5,10},{6,11},{8,12}}=>{{1,12},{2,3,11},{4,10},{5,7},{6,9},{8}}
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>[2,1,7,9,10,11,6,12,8,5,4,3]=>{{1,2},{3,7},{4,9},{5,10},{6,11},{8,12}}=>{{1,2,12},{3,11},{4,10},{5,7},{6,9},{8}}
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>[3,4,2,1,7,9,6,10,8,5,12,11]=>{{1,3},{2,4},{5,7},{6,9},{8,10},{11,12}}=>{{1,4,7},{2,3,10},{5,9},{6,12},{8},{11}}
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>[4,5,7,3,2,9,6,11,8,12,10,1]=>{{1,4},{2,5},{3,7},{6,9},{8,11},{10,12}}=>{{1,12},{2,5,9},{3,4,7},{6,11},{8},{10}}
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>[2,1,4,3,7,9,6,11,8,12,10,5]=>{{1,2},{3,4},{5,7},{6,9},{8,11},{10,12}}=>{{1,2,4,7},{3,12},{5,9},{6,11},{8},{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]=>{{1,4},{2,5},{3,7},{6,9},{8,10},{11,12}}=>{{1,10},{2,5,9},{3,4,7},{6,12},{8},{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]=>{{1,3},{2,4},{5,7},{6,9},{8,11},{10,12}}=>{{1,4,7},{2,3,12},{5,9},{6,11},{8},{10}}
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>[5,7,8,10,4,11,6,3,12,9,2,1]=>{{1,5},{2,7},{3,8},{4,10},{6,11},{9,12}}=>{{1,12},{2,11},{3,8},{4,5,7},{6,10},{9}}
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>[2,1,5,7,4,8,6,3,10,9,12,11]=>{{1,2},{3,5},{4,7},{6,8},{9,10},{11,12}}=>{{1,2,8},{3,5,10},{4,7},{6,12},{9},{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]=>{{1,3},{2,5},{4,7},{6,10},{8,11},{9,12}}=>{{1,12},{2,3,5,11},{4,7},{6,10},{8},{9}}
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>[2,1,5,7,4,10,6,11,12,9,8,3]=>{{1,2},{3,5},{4,7},{6,10},{8,11},{9,12}}=>{{1,2,12},{3,5,11},{4,7},{6,10},{8},{9}}
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>[3,5,2,7,4,8,6,1,10,9,12,11]=>{{1,3},{2,5},{4,7},{6,8},{9,10},{11,12}}=>{{1,8},{2,3,5,10},{4,7},{6,12},{9},{11}}
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>[5,7,8,9,4,11,6,3,2,12,10,1]=>{{1,5},{2,7},{3,8},{4,9},{6,11},{10,12}}=>{{1,12},{2,9},{3,8},{4,5,7},{6,11},{10}}
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>[2,1,5,7,4,8,6,3,11,12,10,9]=>{{1,2},{3,5},{4,7},{6,8},{9,11},{10,12}}=>{{1,2,8},{3,5,12},{4,7},{6,11},{9},{10}}
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>[5,7,8,9,4,10,6,3,2,1,12,11]=>{{1,5},{2,7},{3,8},{4,9},{6,10},{11,12}}=>{{1,10},{2,9},{3,8},{4,5,7},{6,12},{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]=>{{1,3},{2,5},{4,7},{6,8},{9,11},{10,12}}=>{{1,8},{2,3,5,12},{4,7},{6,11},{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]=>{{1,4},{2,5},{3,7},{6,10},{8,11},{9,12}}=>{{1,12},{2,5,11},{3,4,7},{6,10},{8},{9}}
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>[2,1,4,3,7,10,6,11,12,9,8,5]=>{{1,2},{3,4},{5,7},{6,10},{8,11},{9,12}}=>{{1,2,4,7},{3,12},{5,11},{6,10},{8},{9}}
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>[4,5,7,3,2,8,6,1,10,9,12,11]=>{{1,4},{2,5},{3,7},{6,8},{9,10},{11,12}}=>{{1,8},{2,5,10},{3,4,7},{6,12},{9},{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]=>{{1,3},{2,4},{5,7},{6,10},{8,11},{9,12}}=>{{1,4,7},{2,3,12},{5,11},{6,10},{8},{9}}
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>[4,5,7,3,2,8,6,1,11,12,10,9]=>{{1,4},{2,5},{3,7},{6,8},{9,11},{10,12}}=>{{1,8},{2,5,12},{3,4,7},{6,11},{9},{10}}
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>[6,8,9,10,11,5,12,7,4,3,2,1]=>{{1,6},{2,8},{3,9},{4,10},{5,11},{7,12}}=>{{1,12},{2,11},{3,10},{4,9},{5,6,8},{7}}
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>[2,1,6,8,9,5,10,7,4,3,12,11]=>{{1,2},{3,6},{4,8},{5,9},{7,10},{11,12}}=>{{1,2,10},{3,9},{4,6,12},{5,8},{7},{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]=>{{1,3},{2,6},{4,8},{5,9},{7,11},{10,12}}=>{{1,12},{2,3,9},{4,6,11},{5,8},{7},{10}}
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>[2,1,6,8,9,5,11,7,4,12,10,3]=>{{1,2},{3,6},{4,8},{5,9},{7,11},{10,12}}=>{{1,2,12},{3,9},{4,6,11},{5,8},{7},{10}}
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>[3,6,2,8,9,5,10,7,4,1,12,11]=>{{1,3},{2,6},{4,8},{5,9},{7,10},{11,12}}=>{{1,10},{2,3,9},{4,6,12},{5,8},{7},{11}}
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>[4,6,8,3,10,5,11,7,12,9,2,1]=>{{1,4},{2,6},{3,8},{5,10},{7,11},{9,12}}=>{{1,12},{2,11},{3,4,6,10},{5,8},{7},{9}}
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,2,4,8},{3,6,12},{5,10},{7},{9},{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]=>{{1,3},{2,6},{4,8},{5,10},{7,11},{9,12}}=>{{1,12},{2,3,11},{4,6,10},{5,8},{7},{9}}
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>[2,1,6,8,10,5,11,7,12,9,4,3]=>{{1,2},{3,6},{4,8},{5,10},{7,11},{9,12}}=>{{1,2,12},{3,11},{4,6,10},{5,8},{7},{9}}
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>{{1,3},{2,4},{5,6},{7,8},{9,10},{11,12}}=>{{1,4,8},{2,3,6,12},{5,10},{7},{9},{11}}
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>[4,6,8,3,9,5,11,7,2,12,10,1]=>{{1,4},{2,6},{3,8},{5,9},{7,11},{10,12}}=>{{1,12},{2,9},{3,4,6,11},{5,8},{7},{10}}
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,11},{10,12}}=>{{1,2,4,8},{3,6,11},{5,12},{7},{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]=>{{1,4},{2,6},{3,8},{5,9},{7,10},{11,12}}=>{{1,10},{2,9},{3,4,6,12},{5,8},{7},{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]=>{{1,3},{2,4},{5,6},{7,8},{9,11},{10,12}}=>{{1,4,8},{2,3,6,11},{5,12},{7},{9},{10}}
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>[5,8,9,10,4,11,12,7,6,3,2,1]=>{{1,5},{2,8},{3,9},{4,10},{6,11},{7,12}}=>{{1,12},{2,11},{3,10},{4,5,9},{6,8},{7}}
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>[2,1,5,8,4,9,10,7,6,3,12,11]=>{{1,2},{3,5},{4,8},{6,9},{7,10},{11,12}}=>{{1,2,10},{3,5,8},{4,9},{6,12},{7},{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]=>{{1,3},{2,5},{4,8},{6,9},{7,11},{10,12}}=>{{1,12},{2,3,5,8},{4,9},{6,11},{7},{10}}
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>[2,1,5,8,4,9,11,7,6,12,10,3]=>{{1,2},{3,5},{4,8},{6,9},{7,11},{10,12}}=>{{1,2,12},{3,5,8},{4,9},{6,11},{7},{10}}
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>[3,5,2,8,4,9,10,7,6,1,12,11]=>{{1,3},{2,5},{4,8},{6,9},{7,10},{11,12}}=>{{1,10},{2,3,5,8},{4,9},{6,12},{7},{11}}
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>[4,8,9,3,10,11,12,7,6,5,2,1]=>{{1,4},{2,8},{3,9},{5,10},{6,11},{7,12}}=>{{1,12},{2,11},{3,4,10},{5,9},{6,8},{7}}
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>[2,1,4,3,8,9,10,7,6,5,12,11]=>{{1,2},{3,4},{5,8},{6,9},{7,10},{11,12}}=>{{1,2,4,9},{3,10},{5,8},{6,12},{7},{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]=>{{1,3},{2,8},{4,9},{5,10},{6,11},{7,12}}=>{{1,12},{2,3,11},{4,10},{5,9},{6,8},{7}}
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>[2,1,8,9,10,11,12,7,6,5,4,3]=>{{1,2},{3,8},{4,9},{5,10},{6,11},{7,12}}=>{{1,2,12},{3,11},{4,10},{5,9},{6,8},{7}}
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>[3,4,2,1,8,9,10,7,6,5,12,11]=>{{1,3},{2,4},{5,8},{6,9},{7,10},{11,12}}=>{{1,4,9},{2,3,10},{5,8},{6,12},{7},{11}}
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>[4,5,8,3,2,9,11,7,6,12,10,1]=>{{1,4},{2,5},{3,8},{6,9},{7,11},{10,12}}=>{{1,12},{2,5,8},{3,4,9},{6,11},{7},{10}}
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>[2,1,4,3,8,9,11,7,6,12,10,5]=>{{1,2},{3,4},{5,8},{6,9},{7,11},{10,12}}=>{{1,2,4,9},{3,12},{5,8},{6,11},{7},{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]=>{{1,4},{2,5},{3,8},{6,9},{7,10},{11,12}}=>{{1,10},{2,5,8},{3,4,9},{6,12},{7},{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]=>{{1,3},{2,4},{5,8},{6,9},{7,11},{10,12}}=>{{1,4,9},{2,3,12},{5,8},{6,11},{7},{10}}
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>[5,6,8,10,4,3,11,7,12,9,2,1]=>{{1,5},{2,6},{3,8},{4,10},{7,11},{9,12}}=>{{1,12},{2,11},{3,6,10},{4,5,8},{7},{9}}
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>{{1,2},{3,5},{4,6},{7,8},{9,10},{11,12}}=>{{1,2,6,12},{3,5,10},{4,8},{7},{9},{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]=>{{1,3},{2,5},{4,8},{6,10},{7,11},{9,12}}=>{{1,12},{2,3,5,8},{4,11},{6,10},{7},{9}}
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>[2,1,5,8,4,10,11,7,12,9,6,3]=>{{1,2},{3,5},{4,8},{6,10},{7,11},{9,12}}=>{{1,2,12},{3,5,8},{4,11},{6,10},{7},{9}}
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>[3,5,2,6,4,1,8,7,10,9,12,11]=>{{1,3},{2,5},{4,6},{7,8},{9,10},{11,12}}=>{{1,6,12},{2,3,5,10},{4,8},{7},{9},{11}}
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>[5,6,8,9,4,3,11,7,2,12,10,1]=>{{1,5},{2,6},{3,8},{4,9},{7,11},{10,12}}=>{{1,12},{2,9},{3,6,11},{4,5,8},{7},{10}}
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>{{1,2},{3,5},{4,6},{7,8},{9,11},{10,12}}=>{{1,2,6,11},{3,5,12},{4,8},{7},{9},{10}}
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>[5,6,8,9,4,3,10,7,2,1,12,11]=>{{1,5},{2,6},{3,8},{4,9},{7,10},{11,12}}=>{{1,10},{2,9},{3,6,12},{4,5,8},{7},{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]=>{{1,3},{2,5},{4,6},{7,8},{9,11},{10,12}}=>{{1,6,11},{2,3,5,12},{4,8},{7},{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]=>{{1,4},{2,5},{3,8},{6,10},{7,11},{9,12}}=>{{1,12},{2,5,8},{3,4,11},{6,10},{7},{9}}
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>[2,1,4,3,8,10,11,7,12,9,6,5]=>{{1,2},{3,4},{5,8},{6,10},{7,11},{9,12}}=>{{1,2,4,11},{3,12},{5,8},{6,10},{7},{9}}
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>[4,5,6,3,2,1,8,7,10,9,12,11]=>{{1,4},{2,5},{3,6},{7,8},{9,10},{11,12}}=>{{1,6,12},{2,5,10},{3,4,8},{7},{9},{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]=>{{1,3},{2,4},{5,8},{6,10},{7,11},{9,12}}=>{{1,4,11},{2,3,12},{5,8},{6,10},{7},{9}}
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>[4,5,6,3,2,1,8,7,11,12,10,9]=>{{1,4},{2,5},{3,6},{7,8},{9,11},{10,12}}=>{{1,6,11},{2,5,12},{3,4,8},{7},{9},{10}}
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>[6,7,9,10,11,5,4,12,8,3,2,1]=>{{1,6},{2,7},{3,9},{4,10},{5,11},{8,12}}=>{{1,12},{2,11},{3,10},{4,7},{5,6,9},{8}}
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>[2,1,6,7,9,5,4,10,8,3,12,11]=>{{1,2},{3,6},{4,7},{5,9},{8,10},{11,12}}=>{{1,2,10},{3,7},{4,6,12},{5,9},{8},{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},{2,6},{4,7},{5,9},{8,11},{10,12}}=>{{1,12},{2,3,7},{4,6,11},{5,9},{8},{10}}
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>[2,1,6,7,9,5,4,11,8,12,10,3]=>{{1,2},{3,6},{4,7},{5,9},{8,11},{10,12}}=>{{1,2,12},{3,7},{4,6,11},{5,9},{8},{10}}
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>[3,6,2,7,9,5,4,10,8,1,12,11]=>{{1,3},{2,6},{4,7},{5,9},{8,10},{11,12}}=>{{1,10},{2,3,7},{4,6,12},{5,9},{8},{11}}
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>[4,6,9,3,10,5,11,12,8,7,2,1]=>{{1,4},{2,6},{3,9},{5,10},{7,11},{8,12}}=>{{1,12},{2,11},{3,4,6,9},{5,10},{7},{8}}
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>{{1,2},{3,4},{5,6},{7,9},{8,10},{11,12}}=>{{1,2,4,10},{3,6,12},{5,9},{7},{8},{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]=>{{1,3},{2,6},{4,9},{5,10},{7,11},{8,12}}=>{{1,12},{2,3,11},{4,6,9},{5,10},{7},{8}}
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>[2,1,6,9,10,5,11,12,8,7,4,3]=>{{1,2},{3,6},{4,9},{5,10},{7,11},{8,12}}=>{{1,2,12},{3,11},{4,6,9},{5,10},{7},{8}}
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>{{1,3},{2,4},{5,6},{7,9},{8,10},{11,12}}=>{{1,4,10},{2,3,6,12},{5,9},{7},{8},{11}}
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>[4,6,7,3,9,5,2,11,8,12,10,1]=>{{1,4},{2,6},{3,7},{5,9},{8,11},{10,12}}=>{{1,12},{2,7},{3,4,6,11},{5,9},{8},{10}}
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>[2,1,4,3,6,5,9,11,8,12,10,7]=>{{1,2},{3,4},{5,6},{7,9},{8,11},{10,12}}=>{{1,2,4,12},{3,6,11},{5,9},{7},{8},{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]=>{{1,4},{2,6},{3,7},{5,9},{8,10},{11,12}}=>{{1,10},{2,7},{3,4,6,12},{5,9},{8},{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]=>{{1,3},{2,4},{5,6},{7,9},{8,11},{10,12}}=>{{1,4,12},{2,3,6,11},{5,9},{7},{8},{10}}
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>[6,7,8,10,11,5,4,3,12,9,2,1]=>{{1,6},{2,7},{3,8},{4,10},{5,11},{9,12}}=>{{1,12},{2,11},{3,8},{4,7},{5,6,10},{9}}
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>[2,1,6,7,8,5,4,3,10,9,12,11]=>{{1,2},{3,6},{4,7},{5,8},{9,10},{11,12}}=>{{1,2,8},{3,7},{4,6,12},{5,10},{9},{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]=>{{1,3},{2,6},{4,7},{5,10},{8,11},{9,12}}=>{{1,12},{2,3,7},{4,6,10},{5,11},{8},{9}}
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>[2,1,6,7,10,5,4,11,12,9,8,3]=>{{1,2},{3,6},{4,7},{5,10},{8,11},{9,12}}=>{{1,2,12},{3,7},{4,6,10},{5,11},{8},{9}}
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>[3,6,2,7,8,5,4,1,10,9,12,11]=>{{1,3},{2,6},{4,7},{5,8},{9,10},{11,12}}=>{{1,8},{2,3,7},{4,6,12},{5,10},{9},{11}}
[(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},{2,7},{3,8},{4,9},{5,11},{10,12}}=>{{1,12},{2,9},{3,8},{4,7},{5,6,11},{10}}
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>[2,1,6,7,8,5,4,3,11,12,10,9]=>{{1,2},{3,6},{4,7},{5,8},{9,11},{10,12}}=>{{1,2,8},{3,7},{4,6,11},{5,12},{9},{10}}
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>[6,7,8,9,10,5,4,3,2,1,12,11]=>{{1,6},{2,7},{3,8},{4,9},{5,10},{11,12}}=>{{1,10},{2,9},{3,8},{4,7},{5,6,12},{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]=>{{1,3},{2,6},{4,7},{5,8},{9,11},{10,12}}=>{{1,8},{2,3,7},{4,6,11},{5,12},{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]=>{{1,4},{2,6},{3,7},{5,10},{8,11},{9,12}}=>{{1,12},{2,7},{3,4,6,10},{5,11},{8},{9}}
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>[2,1,4,3,6,5,10,11,12,9,8,7]=>{{1,2},{3,4},{5,6},{7,10},{8,11},{9,12}}=>{{1,2,4,12},{3,6,10},{5,11},{7},{8},{9}}
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>[4,6,7,3,8,5,2,1,10,9,12,11]=>{{1,4},{2,6},{3,7},{5,8},{9,10},{11,12}}=>{{1,8},{2,7},{3,4,6,12},{5,10},{9},{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]=>{{1,3},{2,4},{5,6},{7,10},{8,11},{9,12}}=>{{1,4,12},{2,3,6,10},{5,11},{7},{8},{9}}
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>[4,6,7,3,8,5,2,1,11,12,10,9]=>{{1,4},{2,6},{3,7},{5,8},{9,11},{10,12}}=>{{1,8},{2,7},{3,4,6,11},{5,12},{9},{10}}
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>[5,6,9,10,4,3,11,12,8,7,2,1]=>{{1,5},{2,6},{3,9},{4,10},{7,11},{8,12}}=>{{1,12},{2,11},{3,6,9},{4,5,10},{7},{8}}
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>{{1,2},{3,5},{4,6},{7,9},{8,10},{11,12}}=>{{1,2,6,12},{3,5,9},{4,10},{7},{8},{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]=>{{1,3},{2,5},{4,9},{6,10},{7,11},{8,12}}=>{{1,12},{2,3,5,10},{4,11},{6,9},{7},{8}}
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>[2,1,5,9,4,10,11,12,8,7,6,3]=>{{1,2},{3,5},{4,9},{6,10},{7,11},{8,12}}=>{{1,2,12},{3,5,10},{4,11},{6,9},{7},{8}}
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>[3,5,2,6,4,1,9,10,8,7,12,11]=>{{1,3},{2,5},{4,6},{7,9},{8,10},{11,12}}=>{{1,6,12},{2,3,5,9},{4,10},{7},{8},{11}}
[(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},{2,6},{3,7},{4,9},{8,11},{10,12}}=>{{1,12},{2,7},{3,6,11},{4,5,9},{8},{10}}
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>[2,1,5,6,4,3,9,11,8,12,10,7]=>{{1,2},{3,5},{4,6},{7,9},{8,11},{10,12}}=>{{1,2,6,11},{3,5,9},{4,12},{7},{8},{10}}
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>[5,6,7,9,4,3,2,10,8,1,12,11]=>{{1,5},{2,6},{3,7},{4,9},{8,10},{11,12}}=>{{1,10},{2,7},{3,6,12},{4,5,9},{8},{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]=>{{1,3},{2,5},{4,6},{7,9},{8,11},{10,12}}=>{{1,6,11},{2,3,5,9},{4,12},{7},{8},{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]=>{{1,4},{2,5},{3,9},{6,10},{7,11},{8,12}}=>{{1,12},{2,5,10},{3,4,11},{6,9},{7},{8}}
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>[2,1,4,3,9,10,11,12,8,7,6,5]=>{{1,2},{3,4},{5,9},{6,10},{7,11},{8,12}}=>{{1,2,4,11},{3,12},{5,10},{6,9},{7},{8}}
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>[4,5,6,3,2,1,9,10,8,7,12,11]=>{{1,4},{2,5},{3,6},{7,9},{8,10},{11,12}}=>{{1,6,12},{2,5,9},{3,4,10},{7},{8},{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]=>{{1,3},{2,4},{5,9},{6,10},{7,11},{8,12}}=>{{1,4,11},{2,3,12},{5,10},{6,9},{7},{8}}
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>[4,5,6,3,2,1,9,11,8,12,10,7]=>{{1,4},{2,5},{3,6},{7,9},{8,11},{10,12}}=>{{1,6,11},{2,5,9},{3,4,12},{7},{8},{10}}
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>[5,6,7,10,4,3,2,11,12,9,8,1]=>{{1,5},{2,6},{3,7},{4,10},{8,11},{9,12}}=>{{1,12},{2,7},{3,6,10},{4,5,11},{8},{9}}
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>[2,1,5,6,4,3,10,11,12,9,8,7]=>{{1,2},{3,5},{4,6},{7,10},{8,11},{9,12}}=>{{1,2,6,10},{3,5,11},{4,12},{7},{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]=>{{1,5},{2,6},{3,7},{4,8},{9,10},{11,12}}=>{{1,8},{2,7},{3,6,12},{4,5,10},{9},{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]=>{{1,3},{2,5},{4,6},{7,10},{8,11},{9,12}}=>{{1,6,10},{2,3,5,11},{4,12},{7},{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]=>{{1,5},{2,6},{3,7},{4,8},{9,11},{10,12}}=>{{1,8},{2,7},{3,6,11},{4,5,12},{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]=>{{1,4},{2,5},{3,6},{7,10},{8,11},{9,12}}=>{{1,6,10},{2,5,11},{3,4,12},{7},{8},{9}}
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}=>{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}
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.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
Map
dual major index to intertwining number
Description
A bijection sending the dual major index of a set partition to its intertwining number.
More precisely, St000493The los statistic of a set partition.$(P) = $St000490The intertwining number of a set partition.$(\phi(P))$ for all set partitions $P$.
This is the inverse of Mp00171intertwining number to dual major index.
More precisely, St000493The los statistic of a set partition.$(P) = $St000490The intertwining number of a set partition.$(\phi(P))$ for all set partitions $P$.
This is the inverse of Mp00171intertwining number to dual major index.
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