- FindStat

Identifier

Mp00113: Perfect matchings —reverse⟶ Perfect matchings
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets

Images

[(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)] => [4,3,2,1] => ([],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)] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)

[(1,5),(2,3),(4,6)] => [(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)

[(1,6),(2,3),(4,5)] => [(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6)

[(1,6),(2,4),(3,5)] => [(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6)

[(1,5),(2,4),(3,6)] => [(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => ([(0,4),(0,5),(1,2),(1,3)],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)] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)

[(1,3),(2,6),(4,5)] => [(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)

[(1,4),(2,6),(3,5)] => [(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6)

[(1,5),(2,6),(3,4)] => [(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6)

[(1,6),(2,5),(3,4)] => [(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => ([],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)] => [2,1,4,3,8,7,6,5] => ([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8)

[(1,5),(2,3),(4,6),(7,8)] => [(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => ([(0,6),(0,7),(1,6),(1,7),(6,3),(6,4),(6,5),(7,2),(7,4),(7,5)],8)

[(1,6),(2,3),(4,5),(7,8)] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8)

[(1,7),(2,3),(4,5),(6,8)] => [(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(6,4),(6,5),(7,4),(7,5)],8)

[(1,8),(2,3),(4,5),(6,7)] => [(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => ([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)

[(1,8),(2,4),(3,5),(6,7)] => [(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => ([(2,6),(2,7),(3,6),(3,7),(6,5),(7,4)],8)

[(1,7),(2,4),(3,5),(6,8)] => [(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(6,3),(7,2)],8)

[(1,6),(2,4),(3,5),(7,8)] => [(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,3),(7,2)],8)

[(1,5),(2,4),(3,6),(7,8)] => [(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => ([(0,6),(0,7),(1,6),(1,7),(6,4),(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)] => [2,1,6,5,4,3,8,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[(1,3),(2,6),(4,5),(7,8)] => [(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)

[(1,4),(2,6),(3,5),(7,8)] => [(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(4,3),(5,3),(6,2),(7,2)],8)

[(1,5),(2,6),(3,4),(7,8)] => [(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,3),(7,2)],8)

[(1,6),(2,5),(3,4),(7,8)] => [(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)

[(1,7),(2,5),(3,4),(6,8)] => [(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7)],8)

[(1,8),(2,5),(3,4),(6,7)] => [(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[(1,8),(2,6),(3,4),(5,7)] => [(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8)

[(1,7),(2,6),(3,4),(5,8)] => [(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7)],8)

[(1,6),(2,7),(3,4),(5,8)] => [(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(4,2),(5,3)],8)

[(1,5),(2,7),(3,4),(6,8)] => [(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => ([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,5),(3,4)],8)

[(1,4),(2,7),(3,5),(6,8)] => [(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => ([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(3,5),(6,4),(7,5)],8)

[(1,3),(2,7),(4,5),(6,8)] => [(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[(1,2),(3,7),(4,5),(6,8)] => [(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(2,7),(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)] => [6,3,2,5,4,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(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)] => [7,3,2,5,4,8,1,6] => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)

[(1,4),(2,8),(3,5),(6,7)] => [(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,7)],8)

[(1,5),(2,8),(3,4),(6,7)] => [(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => ([(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[(1,6),(2,8),(3,4),(5,7)] => [(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => ([(0,5),(1,4),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8)

[(1,7),(2,8),(3,4),(5,6)] => [(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)

[(1,8),(2,7),(3,4),(5,6)] => [(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => ([(4,6),(4,7),(5,6),(5,7)],8)

[(1,8),(2,7),(3,5),(4,6)] => [(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => ([(4,7),(5,6)],8)

[(1,7),(2,8),(3,5),(4,6)] => [(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8)

[(1,6),(2,8),(3,5),(4,7)] => [(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)

[(1,5),(2,8),(3,6),(4,7)] => [(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8)

[(1,4),(2,8),(3,6),(5,7)] => [(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,6),(5,7)],8)

[(1,3),(2,8),(4,6),(5,7)] => [(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => ([(0,7),(1,6),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8)

[(1,2),(3,8),(4,6),(5,7)] => [(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(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)] => [4,6,5,1,3,2,8,7] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[(1,3),(2,7),(4,6),(5,8)] => [(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => ([(0,3),(0,5),(1,2),(1,4),(2,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[(1,4),(2,7),(3,6),(5,8)] => [(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => ([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,7),(3,7),(4,6),(5,6)],8)

[(1,5),(2,7),(3,6),(4,8)] => [(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,7),(5,7)],8)

[(1,6),(2,7),(3,5),(4,8)] => [(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => ([(0,5),(0,7),(1,4),(1,6),(6,2),(7,3)],8)

[(1,7),(2,6),(3,5),(4,8)] => [(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4)],8)

[(1,8),(2,6),(3,5),(4,7)] => [(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => ([(2,6),(2,7),(3,4),(3,5)],8)

[(1,8),(2,5),(3,6),(4,7)] => [(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => ([(2,5),(3,4),(4,6),(5,7)],8)

[(1,7),(2,5),(3,6),(4,8)] => [(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => ([(0,5),(0,7),(1,4),(1,6),(6,2),(7,3)],8)

[(1,6),(2,5),(3,7),(4,8)] => [(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => ([(0,7),(1,6),(6,2),(6,3),(7,4),(7,5)],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)] => [3,6,1,8,7,2,5,4] => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5)],8)

[(1,6),(2,4),(3,7),(5,8)] => [(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => ([(0,5),(0,7),(1,4),(1,6),(4,2),(4,7),(5,3),(5,6)],8)

[(1,7),(2,4),(3,6),(5,8)] => [(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => ([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(4,7),(5,6)],8)

[(1,8),(2,4),(3,6),(5,7)] => [(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => ([(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8)

[(1,8),(2,3),(4,6),(5,7)] => [(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => ([(2,5),(3,4),(4,6),(4,7),(5,6),(5,7)],8)

[(1,7),(2,3),(4,6),(5,8)] => [(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => ([(0,3),(0,5),(1,2),(1,4),(4,6),(4,7),(5,6),(5,7)],8)

[(1,6),(2,3),(4,7),(5,8)] => [(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => ([(0,5),(1,4),(4,2),(4,6),(4,7),(5,3),(5,6),(5,7)],8)

[(1,5),(2,3),(4,7),(6,8)] => [(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => ([(0,3),(0,7),(1,2),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6)],8)

[(1,4),(2,3),(5,7),(6,8)] => [(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => ([(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[(1,3),(2,4),(5,7),(6,8)] => [(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => ([(0,5),(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)] => [4,3,2,1,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(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)] => [4,3,2,1,7,8,5,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(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)] => [4,3,2,1,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[(1,5),(2,3),(4,8),(6,7)] => [(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => ([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[(1,6),(2,3),(4,8),(5,7)] => [(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7)],8)

[(1,7),(2,3),(4,8),(5,6)] => [(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7)],8)

[(1,8),(2,3),(4,7),(5,6)] => [(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[(1,8),(2,4),(3,7),(5,6)] => [(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)

[(1,7),(2,4),(3,8),(5,6)] => [(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6)],8)

[(1,6),(2,4),(3,8),(5,7)] => [(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => ([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8)

[(1,5),(2,4),(3,8),(6,7)] => [(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)

[(1,4),(2,5),(3,8),(6,7)] => [(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(6,4),(7,5)],8)

>>> Load all 477 entries. <<<

[(1,3),(2,5),(4,8),(6,7)] => [(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(6,5),(7,4)],8)

[(1,2),(3,5),(4,8),(6,7)] => [(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(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)] => [5,4,6,2,1,3,8,7] => ([(0,5),(1,5),(2,4),(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)] => [5,4,7,2,1,8,3,6] => ([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(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)] => [6,4,7,2,8,1,3,5] => ([(0,5),(1,4),(2,4),(2,7),(3,5),(3,6),(4,6),(5,7)],8)

[(1,5),(2,6),(3,8),(4,7)] => [(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => ([(0,6),(1,6),(2,7),(3,7),(6,5),(7,4)],8)

[(1,6),(2,5),(3,8),(4,7)] => [(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7)],8)

[(1,7),(2,5),(3,8),(4,6)] => [(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => ([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)

[(1,8),(2,5),(3,7),(4,6)] => [(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8)

[(1,8),(2,6),(3,7),(4,5)] => [(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => ([(4,7),(5,6)],8)

[(1,7),(2,6),(3,8),(4,5)] => [(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => ([(2,6),(2,7),(3,4),(3,5)],8)

[(1,6),(2,7),(3,8),(4,5)] => [(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8)

[(1,5),(2,7),(3,8),(4,6)] => [(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8)

[(1,4),(2,7),(3,8),(5,6)] => [(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,6),(5,7)],8)

[(1,3),(2,7),(4,8),(5,6)] => [(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8)

[(1,2),(3,7),(4,8),(5,6)] => [(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(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)] => [6,5,4,3,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[(1,3),(2,8),(4,7),(5,6)] => [(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => ([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)

[(1,4),(2,8),(3,7),(5,6)] => [(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8)

[(1,5),(2,8),(3,7),(4,6)] => [(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)

[(1,6),(2,8),(3,7),(4,5)] => [(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => ([(2,7),(3,7),(4,6),(5,6)],8)

[(1,7),(2,8),(3,6),(4,5)] => [(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => ([(4,7),(5,6)],8)

[(1,8),(2,7),(3,6),(4,5)] => [(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => ([],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)

[(1,3),(2,4),(5,6),(7,8),(9,10)] => [(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => ([(0,8),(0,9),(1,8),(1,9),(4,3),(5,2),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[(1,4),(2,3),(5,6),(7,8),(9,10)] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => ([(0,6),(0,7),(1,6),(1,7),(6,8),(6,9),(7,8),(7,9),(8,2),(8,3),(8,4),(8,5),(9,2),(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)] => [2,1,4,3,10,7,6,9,8,5] => ([(0,8),(0,9),(1,8),(1,9),(6,4),(6,5),(7,4),(7,5),(8,2),(8,3),(8,6),(8,7),(9,2),(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)] => [2,1,10,5,4,7,6,9,8,3] => ([(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(6,2),(6,3),(7,2),(7,3),(8,6),(8,7),(9,6),(9,7)],10)

[(1,10),(2,3),(4,5),(6,7),(8,9)] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => ([(2,8),(2,9),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[(1,4),(2,5),(3,6),(7,8),(9,10)] => [(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => ([(0,8),(0,9),(1,8),(1,9),(4,3),(5,2),(6,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[(1,3),(2,5),(4,6),(7,8),(9,10)] => [(1,2),(3,4),(5,7),(6,9),(8,10)] => [2,1,4,3,7,9,5,10,6,8] => ([(0,8),(0,9),(1,8),(1,9),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4),(8,6),(8,7),(9,6),(9,7)],10)

[(1,2),(3,5),(4,6),(7,8),(9,10)] => [(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(8,4),(8,5),(9,4),(9,5)],10)

[(1,2),(3,6),(4,5),(7,8),(9,10)] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => ([(0,6),(0,7),(1,6),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,2),(6,3),(6,4),(6,5),(7,2),(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)] => [2,1,4,3,10,9,8,7,6,5] => ([(0,8),(0,9),(1,8),(1,9),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(9,2),(9,3),(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)] => [2,1,10,5,4,9,8,7,6,3] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(8,2),(8,3),(8,4),(8,5),(9,2),(9,3),(9,4),(9,5)],10)

[(1,10),(2,5),(3,4),(6,7),(8,9)] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => ([(2,8),(2,9),(3,8),(3,9),(8,4),(8,5),(8,6),(8,7),(9,4),(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)] => [2,1,8,5,4,7,6,3,10,9] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,2),(6,3),(7,2),(7,3)],10)

[(1,8),(2,7),(3,4),(5,6),(9,10)] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(8,2),(8,3),(9,2),(9,3)],10)

[(1,10),(2,7),(3,4),(5,6),(8,9)] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => ([(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(8,4),(8,5),(9,4),(9,5)],10)

[(1,2),(3,10),(4,5),(6,7),(8,9)] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9)],10)

[(1,10),(2,9),(3,4),(5,6),(7,8)] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => ([(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9)],10)

[(1,5),(2,6),(3,7),(4,8),(9,10)] => [(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => ([(0,8),(0,9),(1,8),(1,9),(4,3),(5,2),(6,4),(7,5),(8,6),(9,7)],10)

[(1,4),(2,6),(3,7),(5,8),(9,10)] => [(1,2),(3,6),(4,8),(5,9),(7,10)] => [2,1,6,8,9,3,10,4,5,7] => ([(0,8),(0,9),(1,8),(1,9),(2,7),(3,6),(4,3),(5,2),(8,5),(8,6),(9,4),(9,7)],10)

[(1,3),(2,6),(4,7),(5,8),(9,10)] => [(1,2),(3,6),(4,7),(5,9),(8,10)] => [2,1,6,7,9,3,4,10,5,8] => ([(0,8),(0,9),(1,8),(1,9),(2,7),(3,6),(4,3),(4,7),(5,2),(5,6),(8,4),(9,5)],10)

[(1,2),(3,6),(4,7),(5,8),(9,10)] => [(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(8,4),(9,5)],10)

[(1,2),(3,5),(4,7),(6,8),(9,10)] => [(1,2),(3,5),(4,7),(6,8),(9,10)] => [2,1,5,7,3,8,4,6,10,9] => ([(0,6),(0,7),(1,6),(1,7),(2,9),(3,8),(6,3),(6,9),(7,2),(7,8),(8,4),(8,5),(9,4),(9,5)],10)

[(1,3),(2,5),(4,7),(6,8),(9,10)] => [(1,2),(3,5),(4,7),(6,9),(8,10)] => [2,1,5,7,3,9,4,10,6,8] => ([(0,8),(0,9),(1,8),(1,9),(2,5),(2,7),(3,4),(3,6),(6,5),(7,4),(8,3),(8,7),(9,2),(9,6)],10)

[(1,4),(2,5),(3,7),(6,8),(9,10)] => [(1,2),(3,5),(4,8),(6,9),(7,10)] => [2,1,5,8,3,9,10,4,6,7] => ([(0,8),(0,9),(1,8),(1,9),(2,7),(3,6),(6,4),(7,5),(8,3),(8,7),(9,2),(9,6)],10)

[(1,3),(2,4),(5,7),(6,8),(9,10)] => [(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => ([(0,8),(0,9),(1,8),(1,9),(2,6),(2,7),(3,6),(3,7),(6,5),(7,4),(8,3),(9,2)],10)

[(1,2),(3,4),(5,7),(6,8),(9,10)] => [(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => ([(0,6),(0,7),(1,6),(1,7),(2,8),(2,9),(3,8),(3,9),(6,3),(7,2),(8,4),(8,5),(9,4),(9,5)],10)

[(1,2),(3,4),(5,8),(6,7),(9,10)] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,2),(8,3),(9,2),(9,3)],10)

[(1,4),(2,3),(5,8),(6,7),(9,10)] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)

[(1,8),(2,3),(4,7),(5,6),(9,10)] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,10),(2,3),(4,7),(5,6),(8,9)] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,2),(3,8),(4,7),(5,6),(9,10)] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,8),(2,7),(3,6),(4,5),(9,10)] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9)],10)

[(1,10),(2,7),(3,6),(4,5),(8,9)] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => ([(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9)],10)

[(1,2),(3,10),(4,7),(5,6),(8,9)] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,10),(2,9),(3,6),(4,5),(7,8)] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => ([(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)

[(1,2),(3,4),(5,10),(6,7),(8,9)] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,4),(2,5),(3,4),(3,5),(4,8),(4,9),(5,8),(5,9),(8,6),(8,7),(9,6),(9,7)],10)

[(1,4),(2,3),(5,10),(6,7),(8,9)] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)

[(1,10),(2,3),(4,9),(5,6),(7,8)] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => ([(2,8),(2,9),(3,8),(3,9),(4,6),(4,7),(5,6),(5,7),(6,8),(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)] => [8,7,4,3,6,5,2,1,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,6),(4,7),(5,6),(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)] => [10,9,8,5,4,7,6,3,2,1] => ([(6,8),(6,9),(7,8),(7,9)],10)

[(1,4),(2,9),(3,10),(5,7),(6,8)] => [(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => ([(0,5),(1,4),(2,7),(3,6),(4,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,10),(2,8),(3,9),(4,6),(5,7)] => [(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => ([(2,9),(3,8),(4,7),(5,6)],10)

[(1,2),(3,7),(4,8),(5,9),(6,10)] => [(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => ([(0,7),(1,6),(2,8),(2,9),(3,8),(3,9),(4,2),(5,3),(6,4),(7,5)],10)

[(1,3),(2,7),(4,8),(5,9),(6,10)] => [(1,5),(2,6),(3,7),(4,9),(8,10)] => [5,6,7,9,1,2,3,10,4,8] => ([(0,7),(1,6),(2,9),(3,8),(4,2),(4,8),(5,3),(5,9),(6,4),(7,5)],10)

[(1,4),(2,7),(3,8),(5,9),(6,10)] => [(1,5),(2,6),(3,8),(4,9),(7,10)] => [5,6,8,9,1,2,10,3,4,7] => ([(0,7),(1,6),(2,9),(3,8),(4,2),(5,3),(6,4),(6,8),(7,5),(7,9)],10)

[(1,5),(2,7),(3,8),(4,9),(6,10)] => [(1,5),(2,7),(3,8),(4,9),(6,10)] => [5,7,8,9,1,10,2,3,4,6] => ([(0,7),(0,9),(1,6),(1,8),(2,8),(3,9),(4,3),(5,2),(6,4),(7,5)],10)

[(1,6),(2,7),(3,8),(4,9),(5,10)] => [(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => ([(0,9),(1,8),(4,6),(5,7),(6,2),(7,3),(8,4),(9,5)],10)

[(1,5),(2,6),(3,8),(4,9),(7,10)] => [(1,4),(2,7),(3,8),(5,9),(6,10)] => [4,7,8,1,9,10,2,3,5,6] => ([(0,7),(0,9),(1,6),(1,8),(2,9),(3,8),(6,2),(7,3),(8,4),(9,5)],10)

[(1,4),(2,6),(3,8),(5,9),(7,10)] => [(1,4),(2,6),(3,8),(5,9),(7,10)] => [4,6,8,1,9,2,10,3,5,7] => ([(0,5),(0,9),(1,4),(1,8),(2,9),(3,8),(4,2),(4,6),(5,3),(5,7),(8,6),(9,7)],10)

[(1,3),(2,6),(4,8),(5,9),(7,10)] => [(1,4),(2,6),(3,7),(5,9),(8,10)] => [4,6,7,1,9,2,3,10,5,8] => ([(0,5),(0,9),(1,4),(1,8),(2,6),(2,9),(3,7),(3,8),(4,2),(5,3),(8,6),(9,7)],10)

[(1,2),(3,6),(4,8),(5,9),(7,10)] => [(1,4),(2,6),(3,7),(5,8),(9,10)] => [4,6,7,1,8,2,3,5,10,9] => ([(0,5),(0,9),(1,4),(1,8),(2,9),(3,8),(4,2),(5,3),(8,6),(8,7),(9,6),(9,7)],10)

[(1,2),(3,5),(4,8),(6,9),(7,10)] => [(1,4),(2,5),(3,7),(6,8),(9,10)] => [4,5,7,1,2,8,3,6,10,9] => ([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7),(6,8),(6,9),(7,8),(7,9)],10)

[(1,3),(2,5),(4,8),(6,9),(7,10)] => [(1,4),(2,5),(3,7),(6,9),(8,10)] => [4,5,7,1,2,9,3,10,6,8] => ([(0,5),(1,4),(2,7),(2,8),(3,6),(3,9),(4,2),(4,6),(5,3),(5,7),(6,8),(7,9)],10)

[(1,4),(2,5),(3,8),(6,9),(7,10)] => [(1,4),(2,5),(3,8),(6,9),(7,10)] => [4,5,8,1,2,9,10,3,6,7] => ([(0,7),(1,6),(2,9),(3,8),(6,2),(6,8),(7,3),(7,9),(8,4),(9,5)],10)

[(1,3),(2,4),(5,8),(6,9),(7,10)] => [(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => ([(0,7),(1,6),(2,8),(2,9),(3,8),(3,9),(6,2),(7,3),(8,5),(9,4)],10)

[(1,2),(3,4),(5,8),(6,9),(7,10)] => [(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3),(6,8),(6,9),(7,8),(7,9)],10)

[(1,2),(3,4),(5,7),(6,9),(8,10)] => [(1,3),(2,5),(4,6),(7,8),(9,10)] => [3,5,1,6,2,4,8,7,10,9] => ([(0,3),(0,9),(1,2),(1,8),(2,9),(3,8),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[(1,3),(2,4),(5,7),(6,9),(8,10)] => [(1,3),(2,5),(4,6),(7,9),(8,10)] => [3,5,1,6,2,4,9,10,7,8] => ([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,8),(6,9),(7,8),(7,9),(8,3),(9,2)],10)

[(1,4),(2,5),(3,7),(6,9),(8,10)] => [(1,3),(2,5),(4,8),(6,9),(7,10)] => [3,5,1,8,2,9,10,4,6,7] => ([(0,5),(0,7),(1,4),(1,6),(4,7),(4,8),(5,6),(5,9),(6,8),(7,9),(8,2),(9,3)],10)

[(1,3),(2,5),(4,7),(6,9),(8,10)] => [(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => ([(0,3),(0,9),(1,2),(1,8),(2,6),(2,9),(3,7),(3,8),(6,5),(7,4),(8,4),(8,6),(9,5),(9,7)],10)

[(1,2),(3,5),(4,7),(6,9),(8,10)] => [(1,3),(2,5),(4,7),(6,8),(9,10)] => [3,5,1,7,2,8,4,6,10,9] => ([(0,3),(0,7),(1,2),(1,6),(2,7),(2,8),(3,6),(3,9),(6,8),(7,9),(8,4),(8,5),(9,4),(9,5)],10)

[(1,2),(3,6),(4,7),(5,9),(8,10)] => [(1,3),(2,6),(4,7),(5,8),(9,10)] => [3,6,1,7,8,2,4,5,10,9] => ([(0,5),(0,9),(1,4),(1,8),(2,6),(2,7),(3,6),(3,7),(4,9),(5,8),(8,2),(9,3)],10)

[(1,3),(2,6),(4,7),(5,9),(8,10)] => [(1,3),(2,6),(4,7),(5,9),(8,10)] => [3,6,1,7,9,2,4,10,5,8] => ([(0,5),(0,9),(1,4),(1,8),(2,7),(3,6),(4,9),(5,8),(8,2),(8,6),(9,3),(9,7)],10)

[(1,4),(2,6),(3,7),(5,9),(8,10)] => [(1,3),(2,6),(4,8),(5,9),(7,10)] => [3,6,1,8,9,2,10,4,5,7] => ([(0,5),(0,9),(1,4),(1,8),(2,6),(3,7),(4,6),(4,9),(5,7),(5,8),(8,2),(9,3)],10)

[(1,5),(2,6),(3,7),(4,9),(8,10)] => [(1,3),(2,7),(4,8),(5,9),(6,10)] => [3,7,1,8,9,10,2,4,5,6] => ([(0,5),(0,9),(1,4),(1,8),(4,9),(5,8),(6,2),(7,3),(8,6),(9,7)],10)

[(1,2),(3,5),(4,6),(7,9),(8,10)] => [(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => ([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(8,3),(9,2)],10)

[(1,3),(2,5),(4,6),(7,9),(8,10)] => [(1,3),(2,4),(5,7),(6,9),(8,10)] => [3,4,1,2,7,9,5,10,6,8] => ([(0,5),(1,4),(2,7),(3,6),(4,8),(4,9),(5,8),(5,9),(8,3),(8,7),(9,2),(9,6)],10)

[(1,4),(2,5),(3,6),(7,9),(8,10)] => [(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => ([(0,5),(1,4),(4,8),(4,9),(5,8),(5,9),(6,3),(7,2),(8,6),(9,7)],10)

[(1,3),(2,4),(5,6),(7,9),(8,10)] => [(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => ([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9),(8,3),(9,2)],10)

[(1,2),(3,4),(5,6),(7,9),(8,10)] => [(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => ([(0,3),(1,2),(2,8),(2,9),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)

[(1,2),(3,4),(5,6),(7,10),(8,9)] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,6),(4,7),(5,6),(5,7),(8,4),(8,5),(9,4),(9,5)],10)

[(1,4),(2,3),(5,6),(7,10),(8,9)] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(8,4),(8,5),(8,6),(8,7),(9,4),(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)] => [4,3,2,1,10,7,6,9,8,5] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(8,4),(8,5),(9,4),(9,5)],10)

[(1,10),(2,3),(4,5),(6,9),(7,8)] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => ([(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(8,6),(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)] => [4,3,2,1,8,7,6,5,10,9] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(6,4),(6,5),(7,4),(7,5),(8,4),(8,5),(9,4),(9,5)],10)

[(1,6),(2,5),(3,4),(7,10),(8,9)] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9)],10)

[(1,10),(2,5),(3,4),(6,9),(7,8)] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => ([(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)

[(1,2),(3,10),(4,5),(6,9),(7,8)] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9)],10)

[(1,10),(2,9),(3,4),(5,8),(6,7)] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => ([(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,7),(2,10),(3,5),(4,9),(6,8)] => [(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => ([(0,7),(1,6),(2,6),(2,8),(3,7),(3,9),(4,6),(4,8),(4,9),(5,7),(5,8),(5,9)],10)

[(1,5),(2,6),(3,7),(4,10),(8,9)] => [(1,7),(2,3),(4,8),(5,9),(6,10)] => [7,3,2,8,9,10,1,4,5,6] => ([(0,9),(1,8),(2,8),(2,9),(3,8),(3,9),(4,6),(5,7),(8,4),(9,5)],10)

[(1,2),(3,4),(5,10),(6,9),(7,8)] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(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)] => [6,5,4,3,2,1,10,9,8,7] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9)],10)

[(1,10),(2,3),(4,9),(5,8),(6,7)] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => ([(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,4),(2,5),(3,10),(6,9),(7,8)] => [(1,8),(2,5),(3,4),(6,9),(7,10)] => [8,5,4,3,2,9,10,1,6,7] => ([(0,9),(1,8),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(8,6),(9,7)],10)

[(1,2),(3,10),(4,9),(5,8),(6,7)] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,3),(2,10),(4,9),(5,8),(6,7)] => [(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => ([(0,9),(1,8),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)

[(1,9),(2,10),(3,8),(4,7),(5,6)] => [(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => ([(6,9),(7,8)],10)

[(1,10),(2,9),(3,8),(4,7),(5,6)] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => ([],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)] => [12,11,10,9,8,7,6,5,4,3,2,1] => ([],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)] => [2,1,10,9,8,7,6,5,4,3,12,11] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => ([(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => ([(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(8,2),(8,3),(8,4),(8,5),(9,2),(9,3),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],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)] => [12,9,4,3,8,7,6,5,2,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => ([(0,6),(0,7),(1,6),(1,7),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],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)] => [12,3,2,11,8,7,6,5,10,9,4,1] => ([(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],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)] => [4,3,2,1,8,7,6,5,10,9,12,11] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7),(10,6),(10,7),(11,6),(11,7)],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)] => [2,1,12,11,8,7,6,5,10,9,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(6,10),(6,11),(7,10),(7,11),(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)] => [4,3,2,1,8,7,6,5,12,11,10,9] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(8,4),(8,5),(8,6),(8,7),(9,4),(9,5),(9,6),(9,7),(10,4),(10,5),(10,6),(10,7),(11,4),(11,5),(11,6),(11,7)],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)] => [12,11,10,5,4,7,6,9,8,3,2,1] => ([(6,8),(6,9),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],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)] => [2,1,10,5,4,7,6,9,8,3,12,11] => ([(0,4),(0,5),(0,8),(0,9),(1,4),(1,5),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,2),(6,3),(7,2),(7,3),(8,6),(8,7),(9,6),(9,7)],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)] => [12,3,2,5,4,7,6,9,8,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],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)] => [10,3,2,5,4,7,6,9,8,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],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)] => [2,1,12,5,4,7,6,9,8,11,10,3] => ([(0,4),(0,5),(0,10),(0,11),(1,4),(1,5),(1,10),(1,11),(6,8),(6,9),(7,8),(7,9),(8,2),(8,3),(9,2),(9,3),(10,6),(10,7),(11,6),(11,7)],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)] => [12,11,8,5,4,7,6,3,10,9,2,1] => ([(4,10),(4,11),(5,10),(5,11),(6,8),(6,9),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],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)] => [2,1,8,5,4,7,6,3,10,9,12,11] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(9,2),(9,3),(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)] => [12,9,8,5,4,7,6,3,2,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,8),(6,9),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],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)] => [10,9,8,5,4,7,6,3,2,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,8),(6,9),(7,8),(7,9),(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)] => [2,1,8,5,4,7,6,3,12,11,10,9] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,2),(6,3),(7,2),(7,3)],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)] => [12,3,2,5,4,7,6,11,10,9,8,1] => ([(2,8),(2,9),(3,8),(3,9),(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)

[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],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)] => [2,1,12,5,4,7,6,11,10,9,8,3] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(8,10),(8,11),(9,10),(9,11),(10,2),(10,3),(10,4),(10,5),(11,2),(11,3),(11,4),(11,5)],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)] => [8,3,2,5,4,7,6,1,12,11,10,9] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],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)] => [12,11,4,3,10,7,6,9,8,5,2,1] => ([(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(8,10),(8,11),(9,10),(9,11)],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)] => [2,1,4,3,10,7,6,9,8,5,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,4),(6,5),(7,4),(7,5),(8,2),(8,3),(8,6),(8,7),(9,2),(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)] => [12,5,4,3,2,7,6,9,8,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,8),(6,9),(7,8),(7,9),(10,6),(10,7),(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)] => [10,5,4,3,2,7,6,9,8,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,6),(8,7),(9,6),(9,7)],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)] => [2,1,4,3,12,7,6,9,8,11,10,5] => ([(0,10),(0,11),(1,10),(1,11),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,2),(10,3),(10,6),(10,7),(11,2),(11,3),(11,6),(11,7)],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)] => [12,3,2,11,10,7,6,9,8,5,4,1] => ([(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(10,4),(10,5),(11,4),(11,5)],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)] => [4,3,2,1,10,7,6,9,8,5,12,11] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(5,6),(5,7),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],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)] => [2,1,12,11,10,7,6,9,8,5,4,3] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(10,2),(10,3),(11,2),(11,3)],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)] => [4,3,2,1,12,7,6,9,8,11,10,5] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(5,6),(5,7),(10,4),(10,5),(11,4),(11,5)],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)] => [12,5,4,3,2,7,6,11,10,9,8,1] => ([(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(10,6),(10,7),(10,8),(10,9),(11,6),(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)] => [8,5,4,3,2,7,6,1,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(4,8),(4,9),(5,8),(5,9),(8,10),(8,11),(9,10),(9,11),(10,6),(10,7),(11,6),(11,7)],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)] => [2,1,4,3,12,7,6,11,10,9,8,5] => ([(0,10),(0,11),(1,10),(1,11),(8,4),(8,5),(8,6),(8,7),(9,4),(9,5),(9,6),(9,7),(10,2),(10,3),(10,8),(10,9),(11,2),(11,3),(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)] => [8,5,4,3,2,7,6,1,12,11,10,9] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(10,4),(10,5),(10,6),(10,7),(11,4),(11,5),(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)] => [12,11,10,9,6,5,8,7,4,3,2,1] => ([(8,10),(8,11),(9,10),(9,11)],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)] => [2,1,10,9,6,5,8,7,4,3,12,11] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(9,2),(9,3)],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)] => [12,3,2,9,6,5,8,7,4,11,10,1] => ([(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,4),(8,5),(9,4),(9,5)],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)] => [10,3,2,9,6,5,8,7,4,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,4),(8,5),(9,4),(9,5)],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)] => [2,1,12,9,6,5,8,7,4,11,10,3] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(9,2),(9,3)],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)] => [12,11,4,3,6,5,8,7,10,9,2,1] => ([(4,6),(4,7),(5,6),(5,7),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8),(11,9)],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)] => [12,9,4,3,6,5,8,7,2,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9),(8,10),(8,11),(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)] => [10,9,4,3,6,5,8,7,2,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(7,8),(7,9),(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)] => [2,1,4,3,6,5,8,7,12,11,10,9] => ([(0,8),(0,9),(1,8),(1,9),(6,10),(6,11),(7,10),(7,11),(8,6),(8,7),(9,6),(9,7),(10,2),(10,3),(10,4),(10,5),(11,2),(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)] => [12,3,2,11,6,5,8,7,10,9,4,1] => ([(2,6),(2,7),(2,10),(2,11),(3,6),(3,7),(3,10),(3,11),(8,4),(8,5),(9,4),(9,5),(10,8),(10,9),(11,8),(11,9)],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)] => [4,3,2,1,6,5,8,7,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(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)] => [2,1,12,11,6,5,8,7,10,9,4,3] => ([(0,4),(0,5),(0,6),(0,7),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,10),(1,11),(8,2),(8,3),(9,2),(9,3),(10,8),(10,9),(11,8),(11,9)],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)] => [4,3,2,1,6,5,8,7,12,11,10,9] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(8,4),(8,5),(8,6),(8,7),(9,4),(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)] => [12,11,10,7,6,5,4,9,8,3,2,1] => ([(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],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)] => [2,1,10,7,6,5,4,9,8,3,12,11] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,10),(2,11),(3,10),(3,11),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],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)] => [12,3,2,7,6,5,4,9,8,11,10,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8),(11,9)],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)] => [10,3,2,7,6,5,4,9,8,1,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,10),(4,11),(5,10),(5,11),(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)] => [2,1,12,7,6,5,4,9,8,11,10,3] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,2),(10,3),(11,2),(11,3)],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)] => [12,11,8,7,6,5,4,3,10,9,2,1] => ([(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,2),(10,3),(11,2),(11,3)],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)] => [12,9,8,7,6,5,4,3,2,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8),(11,9)],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)] => [2,1,12,7,6,5,4,11,10,9,8,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => ([(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],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)] => [2,1,4,3,6,5,10,9,8,7,12,11] => ([(0,6),(0,7),(1,6),(1,7),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,8),(6,9),(7,8),(7,9),(8,2),(8,3),(8,4),(8,5),(9,2),(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)] => [12,7,4,3,6,5,2,9,8,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,6),(4,7),(5,6),(5,7),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8),(11,9)],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)] => [10,7,4,3,6,5,2,9,8,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(4,6),(4,7),(5,6),(5,7),(6,10),(6,11),(7,10),(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)] => [2,1,4,3,6,5,12,9,8,11,10,7] => ([(0,8),(0,9),(1,8),(1,9),(6,4),(6,5),(7,4),(7,5),(8,10),(8,11),(9,10),(9,11),(10,2),(10,3),(10,6),(10,7),(11,2),(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)] => [12,3,2,11,6,5,10,9,8,7,4,1] => ([(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(10,4),(10,5),(10,6),(10,7),(11,4),(11,5),(11,6),(11,7)],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)] => [4,3,2,1,6,5,10,9,8,7,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,8),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,4),(8,5),(8,6),(8,7),(9,4),(9,5),(9,6),(9,7)],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)] => [2,1,12,11,6,5,10,9,8,7,4,3] => ([(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(10,2),(10,3),(10,4),(10,5),(11,2),(11,3),(11,4),(11,5)],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)] => [4,3,2,1,6,5,12,9,8,11,10,7] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(10,8),(10,9),(11,6),(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)] => [12,7,4,3,6,5,2,11,10,9,8,1] => ([(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],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)] => [8,7,4,3,6,5,2,1,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,6),(4,7),(5,6),(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)] => [2,1,4,3,6,5,12,11,10,9,8,7] => ([(0,8),(0,9),(1,8),(1,9),(8,10),(8,11),(9,10),(9,11),(10,2),(10,3),(10,4),(10,5),(10,6),(10,7),(11,2),(11,3),(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)] => [8,7,4,3,6,5,2,1,12,11,10,9] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(5,6),(5,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],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)] => [4,3,2,1,6,5,12,11,10,9,8,7] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(10,4),(10,5),(10,6),(10,7),(10,8),(10,9),(11,4),(11,5),(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)] => [12,11,10,5,4,9,8,7,6,3,2,1] => ([(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],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)] => [2,1,10,5,4,9,8,7,6,3,12,11] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(8,4),(8,5),(9,2),(9,3),(9,4),(9,5)],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)] => [12,3,2,5,4,9,8,7,6,11,10,1] => ([(2,8),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,4),(8,5),(8,6),(8,7),(9,4),(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)] => [10,3,2,5,4,9,8,7,6,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,4),(8,5),(8,6),(8,7),(9,4),(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)] => [2,1,12,5,4,9,8,7,6,11,10,3] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(8,2),(8,3),(8,4),(8,5),(9,2),(9,3),(9,4),(9,5)],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)] => [12,11,6,5,4,3,8,7,10,9,2,1] => ([(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(11,8),(11,9)],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)] => [2,1,6,5,4,3,8,7,10,9,12,11] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(9,2),(9,3),(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)] => [12,9,6,5,4,3,8,7,2,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,10),(8,11),(9,10),(9,11)],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)] => [10,9,6,5,4,3,8,7,2,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,8),(4,9),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(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)] => [2,1,6,5,4,3,8,7,12,11,10,9] => ([(0,6),(0,7),(0,8),(0,9),(1,6),(1,7),(1,8),(1,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11),(10,2),(10,3),(10,4),(10,5),(11,2),(11,3),(11,4),(11,5)],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)] => [12,3,2,5,4,11,8,7,10,9,6,1] => ([(2,10),(2,11),(3,10),(3,11),(8,6),(8,7),(9,6),(9,7),(10,4),(10,5),(10,8),(10,9),(11,4),(11,5),(11,8),(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)] => [6,3,2,5,4,1,8,7,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(3,6),(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)] => [2,1,12,5,4,11,8,7,10,9,6,3] => ([(0,6),(0,7),(0,10),(0,11),(1,6),(1,7),(1,10),(1,11),(8,4),(8,5),(9,4),(9,5),(10,2),(10,3),(10,8),(10,9),(11,2),(11,3),(11,8),(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)] => [6,3,2,5,4,1,8,7,12,11,10,9] => ([(0,10),(0,11),(1,10),(1,11),(2,4),(2,5),(3,4),(3,5),(4,10),(4,11),(5,10),(5,11),(10,6),(10,7),(10,8),(10,9),(11,6),(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)] => [12,11,4,3,10,9,8,7,6,5,2,1] => ([(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)],12)

[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(9,2),(9,3),(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)] => [12,5,4,3,2,9,8,7,6,11,10,1] => ([(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(3,6),(3,7),(3,8),(3,9),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => ([(0,8),(0,9),(1,8),(1,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(9,2),(9,3),(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)] => [12,3,2,11,10,9,8,7,6,5,4,1] => ([(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11)],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)] => [4,3,2,1,10,9,8,7,6,5,12,11] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(8,10),(8,11),(9,10),(9,11)],12)

[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11)],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)] => [4,3,2,1,12,9,8,7,6,11,10,5] => ([(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(8,4),(8,5),(9,4),(9,5),(10,4),(10,5),(11,4),(11,5)],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)] => [12,5,4,3,2,11,8,7,10,9,6,1] => ([(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(10,6),(10,7),(11,6),(11,7)],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)] => [6,5,4,3,2,1,8,7,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,8),(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)] => [2,1,4,3,12,11,8,7,10,9,6,5] => ([(0,10),(0,11),(1,10),(1,11),(8,6),(8,7),(9,6),(9,7),(10,2),(10,3),(10,4),(10,5),(10,8),(10,9),(11,2),(11,3),(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)] => [6,5,4,3,2,1,8,7,12,11,10,9] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(10,6),(10,7),(10,8),(10,9),(11,6),(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)] => [4,3,2,1,12,11,8,7,10,9,6,5] => ([(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(10,4),(10,5),(11,4),(11,5)],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)] => [12,11,6,5,4,3,10,9,8,7,2,1] => ([(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(8,6),(8,7),(9,6),(9,7),(10,6),(10,7),(11,6),(11,7)],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)] => [12,7,6,5,4,3,2,9,8,11,10,1] => ([(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(10,8),(10,9),(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)] => [10,7,6,5,4,3,2,9,8,1,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,8),(6,9),(7,8),(7,9),(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)] => [2,1,6,5,4,3,12,9,8,11,10,7] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(10,2),(10,3),(11,2),(11,3)],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)] => [12,3,2,5,4,11,10,9,8,7,6,1] => ([(2,10),(2,11),(3,10),(3,11),(10,4),(10,5),(10,6),(10,7),(10,8),(10,9),(11,4),(11,5),(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)] => [6,3,2,5,4,1,10,9,8,7,12,11] => ([(0,4),(0,5),(1,4),(1,5),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(8,6),(8,7),(9,6),(9,7),(10,6),(10,7),(11,6),(11,7)],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)] => [2,1,12,5,4,11,10,9,8,7,6,3] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(10,2),(10,3),(10,4),(10,5),(10,6),(10,7),(11,2),(11,3),(11,4),(11,5),(11,6),(11,7)],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)] => [6,3,2,5,4,1,12,9,8,11,10,7] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,6),(2,7),(3,6),(3,7),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11),(10,4),(10,5),(11,4),(11,5)],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)] => [12,7,6,5,4,3,2,11,10,9,8,1] => ([(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,10),(2,11),(3,10),(3,11),(4,10),(4,11),(5,10),(5,11),(6,10),(6,11),(7,10),(7,11),(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)] => [2,1,6,5,4,3,12,11,10,9,8,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)],12)

[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(6,8),(6,9),(6,10),(6,11),(7,8),(7,9),(7,10),(7,11)],12)

[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)],12)

[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => ([(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)],12)

[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(8,6),(8,7),(9,6),(9,7),(10,6),(10,7),(11,6),(11,7)],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)] => [2,1,4,3,12,11,10,9,8,7,6,5] => ([(0,10),(0,11),(1,10),(1,11),(10,2),(10,3),(10,4),(10,5),(10,6),(10,7),(10,8),(10,9),(11,2),(11,3),(11,4),(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)] => [6,5,4,3,2,1,12,9,8,11,10,7] => ([(0,8),(0,9),(0,10),(0,11),(1,8),(1,9),(1,10),(1,11),(2,8),(2,9),(2,10),(2,11),(3,8),(3,9),(3,10),(3,11),(4,8),(4,9),(4,10),(4,11),(5,8),(5,9),(5,10),(5,11),(10,6),(10,7),(11,6),(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)] => [4,3,2,1,12,11,10,9,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11)],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)] => [6,5,4,3,2,1,12,11,10,9,8,7] => ([(0,6),(0,7),(0,8),(0,9),(0,10),(0,11),(1,6),(1,7),(1,8),(1,9),(1,10),(1,11),(2,6),(2,7),(2,8),(2,9),(2,10),(2,11),(3,6),(3,7),(3,8),(3,9),(3,10),(3,11),(4,6),(4,7),(4,8),(4,9),(4,10),(4,11),(5,6),(5,7),(5,8),(5,9),(5,10),(5,11)],12)

[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => ([(0,3),(1,2),(2,10),(2,11),(3,10),(3,11),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => ([(0,6),(0,7),(1,6),(1,7),(2,10),(2,11),(3,10),(3,11),(6,3),(7,2),(8,4),(8,5),(9,4),(9,5),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => [(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => [3,5,1,6,2,4,8,7,10,9,12,11] => ([(0,3),(0,11),(1,2),(1,10),(2,11),(3,10),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => ([(0,3),(1,2),(2,4),(3,5),(4,10),(4,11),(5,10),(5,11),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(6,3),(7,2),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => ([(0,5),(1,4),(2,10),(2,11),(3,10),(3,11),(4,8),(4,9),(5,8),(5,9),(8,3),(9,2),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => [(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => [2,1,5,7,3,8,4,6,10,9,12,11] => ([(0,6),(0,7),(1,6),(1,7),(2,11),(3,10),(6,3),(6,11),(7,2),(7,10),(8,4),(8,5),(9,4),(9,5),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => [(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => [3,5,1,7,2,8,4,6,10,9,12,11] => ([(0,3),(0,7),(1,2),(1,6),(2,7),(2,10),(3,6),(3,11),(6,10),(7,11),(8,4),(8,5),(9,4),(9,5),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => [(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => [4,5,7,1,2,8,3,6,10,9,12,11] => ([(0,5),(1,4),(2,11),(3,10),(4,2),(4,10),(5,3),(5,11),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,5),(3,4),(4,10),(4,11),(5,10),(5,11),(8,3),(9,2),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => [(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => [3,6,1,7,8,2,4,5,10,9,12,11] => ([(0,3),(0,9),(1,2),(1,8),(2,9),(3,8),(4,10),(4,11),(5,10),(5,11),(8,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => [(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => [4,6,7,1,8,2,3,5,10,9,12,11] => ([(0,3),(0,11),(1,2),(1,10),(2,4),(3,5),(4,11),(5,10),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => ([(0,7),(1,6),(2,8),(2,9),(3,8),(3,9),(4,2),(5,3),(6,4),(7,5),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(8,4),(8,5),(9,4),(9,5),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => ([(0,5),(1,4),(2,8),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,3),(7,2),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,6),(2,7),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(8,3),(9,2),(10,5),(11,4)],12)

[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => [(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => [3,5,1,6,2,4,9,10,7,8,12,11] => ([(0,3),(0,11),(1,2),(1,10),(2,11),(3,10),(4,8),(4,9),(5,8),(5,9),(6,5),(7,4),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => ([(0,7),(1,6),(2,10),(2,11),(3,10),(3,11),(4,8),(4,9),(5,8),(5,9),(6,2),(7,3),(10,5),(11,4)],12)

[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => [(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => [2,1,4,3,7,9,5,10,6,8,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,9),(3,8),(6,3),(6,9),(7,2),(7,8),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => [(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => [3,4,1,2,7,9,5,10,6,8,12,11] => ([(0,5),(1,4),(2,11),(3,10),(4,8),(4,9),(5,8),(5,9),(8,3),(8,11),(9,2),(9,10),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => [(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => [2,1,5,7,3,9,4,10,6,8,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,7),(2,11),(3,6),(3,10),(6,11),(7,10),(8,3),(8,7),(9,2),(9,6),(10,4),(10,5),(11,4),(11,5)],12)

[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => [3,5,1,7,2,9,4,10,6,8,12,11] => ([(0,3),(0,11),(1,2),(1,10),(2,6),(2,11),(3,7),(3,10),(6,9),(7,8),(8,4),(8,5),(9,4),(9,5),(10,6),(10,8),(11,7),(11,9)],12)

[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => [(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => [4,5,7,1,2,9,3,10,6,8,12,11] => ([(0,3),(1,2),(2,4),(2,8),(3,5),(3,9),(4,9),(4,10),(5,8),(5,11),(8,10),(9,11),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => [(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => [2,1,6,7,9,3,4,10,5,8,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,5),(2,11),(3,4),(3,10),(4,11),(5,10),(8,3),(9,2),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => [(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => [3,6,1,7,9,2,4,10,5,8,12,11] => ([(0,5),(0,9),(1,4),(1,8),(2,11),(3,10),(4,9),(5,8),(8,2),(8,10),(9,3),(9,11),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => [(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => [4,6,7,1,9,2,3,10,5,8,12,11] => ([(0,3),(0,9),(1,2),(1,8),(2,4),(3,5),(4,9),(4,10),(5,8),(5,11),(8,10),(9,11),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => [(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => [5,6,7,9,1,2,3,10,4,8,12,11] => ([(0,7),(1,6),(2,9),(3,8),(4,2),(4,8),(5,3),(5,9),(6,4),(7,5),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(3,4),(4,6),(4,7),(5,6),(5,7),(8,3),(9,2),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => ([(0,5),(1,4),(2,8),(2,9),(3,8),(3,9),(4,10),(4,11),(5,10),(5,11),(6,3),(7,2),(10,6),(11,7)],12)

[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => [(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => [2,1,5,8,3,9,10,4,6,7,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,9),(3,8),(4,6),(4,7),(5,6),(5,7),(8,4),(9,5),(10,3),(10,9),(11,2),(11,8)],12)

[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => [(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => [3,5,1,8,2,9,10,4,6,7,12,11] => ([(0,5),(0,11),(1,4),(1,10),(2,8),(2,9),(3,8),(3,9),(4,6),(4,11),(5,7),(5,10),(6,2),(7,3),(10,6),(11,7)],12)

[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => [(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => [4,5,8,1,2,9,10,3,6,7,12,11] => ([(0,7),(1,6),(2,11),(3,10),(4,8),(4,9),(5,8),(5,9),(6,2),(6,10),(7,3),(7,11),(10,4),(11,5)],12)

[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => [(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => [2,1,6,8,9,3,10,4,5,7,12,11] => ([(0,8),(0,9),(1,8),(1,9),(2,5),(3,4),(4,10),(5,11),(8,3),(8,11),(9,2),(9,10),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => [(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => [3,6,1,8,9,2,10,4,5,7,12,11] => ([(0,5),(0,9),(1,4),(1,8),(2,10),(3,11),(4,9),(4,10),(5,8),(5,11),(8,2),(9,3),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => [(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => [4,6,8,1,9,2,10,3,5,7,12,11] => ([(0,5),(0,9),(1,4),(1,8),(2,9),(3,8),(4,2),(4,10),(5,3),(5,11),(8,10),(9,11),(10,6),(10,7),(11,6),(11,7)],12)

[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => [(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => [5,6,8,9,1,2,10,3,4,7,12,11] => ([(0,7),(1,6),(2,9),(3,8),(4,2),(5,3),(6,4),(6,8),(7,5),(7,9),(8,10),(8,11),(9,10),(9,11)],12)

[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => ([(0,10),(0,11),(1,10),(1,11),(2,8),(2,9),(3,8),(3,9),(4,6),(5,7),(6,3),(7,2),(10,4),(11,5)],12)

[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => [(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => [3,7,1,8,9,10,2,4,5,6,12,11] => ([(0,5),(0,11),(1,4),(1,10),(2,8),(2,9),(3,8),(3,9),(4,11),(5,10),(6,2),(7,3),(10,6),(11,7)],12)

[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => [(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => [4,7,8,1,9,10,2,3,5,6,12,11] => ([(0,7),(0,11),(1,6),(1,10),(2,11),(3,10),(4,8),(4,9),(5,8),(5,9),(6,2),(7,3),(10,4),(11,5)],12)

[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => [(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => [5,7,8,9,1,10,2,3,4,6,12,11] => ([(0,7),(0,11),(1,6),(1,10),(2,10),(3,11),(4,3),(5,2),(6,4),(7,5),(10,8),(10,9),(11,8),(11,9)],12)

[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => ([(0,9),(1,8),(2,10),(2,11),(3,10),(3,11),(4,6),(5,7),(6,2),(7,3),(8,4),(9,5)],12)

[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => ([(0,10),(0,11),(1,10),(1,11),(4,3),(5,2),(6,8),(6,9),(7,8),(7,9),(8,4),(8,5),(9,4),(9,5),(10,6),(10,7),(11,6),(11,7)],12)

[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => ([(0,5),(1,4),(4,10),(4,11),(5,10),(5,11),(6,3),(7,2),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => ([(0,8),(0,9),(1,8),(1,9),(4,10),(4,11),(5,10),(5,11),(6,3),(7,2),(8,5),(9,4),(10,6),(10,7),(11,6),(11,7)],12)

[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => [(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => [3,5,1,6,2,4,8,7,11,12,9,10] => ([(0,5),(0,11),(1,4),(1,10),(4,11),(5,10),(6,3),(7,2),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => ([(0,7),(1,6),(4,8),(4,9),(5,8),(5,9),(6,4),(7,5),(8,10),(8,11),(9,10),(9,11),(10,3),(11,2)],12)

[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => ([(0,10),(0,11),(1,10),(1,11),(4,8),(4,9),(5,8),(5,9),(6,5),(7,4),(8,3),(9,2),(10,6),(10,7),(11,6),(11,7)],12)

[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => ([(0,7),(1,6),(4,8),(4,9),(5,8),(5,9),(6,10),(6,11),(7,10),(7,11),(8,3),(9,2),(10,5),(11,4)],12)

[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => [(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => [2,1,5,7,3,8,4,6,11,12,9,10] => ([(0,8),(0,9),(1,8),(1,9),(4,11),(5,10),(6,3),(7,2),(8,5),(8,11),(9,4),(9,10),(10,6),(10,7),(11,6),(11,7)],12)

[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => [(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => [3,5,1,7,2,8,4,6,11,12,9,10] => ([(0,5),(0,9),(1,4),(1,8),(4,9),(4,10),(5,8),(5,11),(6,3),(7,2),(8,10),(9,11),(10,6),(10,7),(11,6),(11,7)],12)

[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => [(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => [4,5,7,1,2,8,3,6,11,12,9,10] => ([(0,7),(1,6),(4,9),(5,8),(6,4),(6,8),(7,5),(7,9),(8,10),(8,11),(9,10),(9,11),(10,3),(11,2)],12)

[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => ([(0,8),(0,9),(1,8),(1,9),(4,10),(4,11),(5,10),(5,11),(6,5),(7,4),(8,6),(9,7),(10,3),(11,2)],12)

[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => [(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => [3,6,1,7,8,2,4,5,11,12,9,10] => ([(0,7),(0,11),(1,6),(1,10),(2,8),(2,9),(3,8),(3,9),(6,11),(7,10),(8,5),(9,4),(10,2),(11,3)],12)

[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => [(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => [4,6,7,1,8,2,3,5,11,12,9,10] => ([(0,7),(0,9),(1,6),(1,8),(4,9),(5,8),(6,4),(7,5),(8,10),(8,11),(9,10),(9,11),(10,3),(11,2)],12)

[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => ([(0,9),(1,8),(2,10),(2,11),(3,10),(3,11),(6,2),(7,3),(8,6),(9,7),(10,5),(11,4)],12)

[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => [(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => [2,1,4,3,6,5,9,11,7,12,8,10] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => [(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => [3,4,1,2,6,5,9,11,7,12,8,10] => ([(0,5),(1,4),(2,7),(3,6),(4,10),(4,11),(5,10),(5,11),(8,3),(8,7),(9,2),(9,6),(10,8),(10,9),(11,8),(11,9)],12)

[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => [(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => [2,1,5,6,3,4,9,11,7,12,8,10] => ([(0,8),(0,9),(1,8),(1,9),(2,7),(3,6),(4,10),(4,11),(5,10),(5,11),(8,5),(9,4),(10,3),(10,7),(11,2),(11,6)],12)

[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => [(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => [3,5,1,6,2,4,9,11,7,12,8,10] => ([(0,5),(0,11),(1,4),(1,10),(2,7),(3,6),(4,11),(5,10),(8,3),(8,7),(9,2),(9,6),(10,8),(10,9),(11,8),(11,9)],12)

[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => [(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => [4,5,6,1,2,3,9,11,7,12,8,10] => ([(0,7),(1,6),(2,10),(2,11),(3,10),(3,11),(4,9),(5,8),(6,2),(7,3),(10,5),(10,9),(11,4),(11,8)],12)

[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => [(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => [2,1,4,3,7,9,5,11,6,12,8,10] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(2,9),(3,4),(3,8),(6,3),(6,9),(7,2),(7,8),(8,5),(9,4),(10,6),(10,7),(11,6),(11,7)],12)

[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => [(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => [3,4,1,2,7,9,5,11,6,12,8,10] => ([(0,5),(1,4),(2,7),(2,11),(3,6),(3,10),(4,8),(4,9),(5,8),(5,9),(8,3),(8,11),(9,2),(9,10),(10,7),(11,6)],12)

[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => [(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10] => ([(0,8),(0,9),(1,8),(1,9),(2,7),(2,11),(3,6),(3,10),(6,4),(7,5),(8,3),(8,11),(9,2),(9,10),(10,4),(10,7),(11,5),(11,6)],12)

[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [3,5,1,7,2,9,4,11,6,12,8,10] => ([(0,3),(0,11),(1,2),(1,10),(2,8),(2,11),(3,9),(3,10),(6,4),(7,5),(8,4),(8,7),(9,5),(9,6),(10,6),(10,8),(11,7),(11,9)],12)

[(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => [(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => [4,5,7,1,2,9,3,11,6,12,8,10] => ([(0,3),(1,2),(2,4),(2,10),(3,5),(3,11),(4,8),(4,11),(5,9),(5,10),(8,7),(9,6),(10,6),(10,8),(11,7),(11,9)],12)

[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => [(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => [2,1,6,7,9,3,4,11,5,12,8,10] => ([(0,8),(0,9),(1,8),(1,9),(2,5),(2,11),(3,4),(3,10),(4,6),(4,11),(5,7),(5,10),(8,3),(9,2),(10,6),(11,7)],12)

[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => [(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => [3,6,1,7,9,2,4,11,5,12,8,10] => ([(0,3),(0,11),(1,2),(1,10),(2,11),(3,10),(4,6),(4,9),(5,7),(5,8),(8,6),(9,7),(10,4),(10,8),(11,5),(11,9)],12)

[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => [(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => [4,6,7,1,9,2,3,11,5,12,8,10] => ([(0,3),(0,11),(1,2),(1,10),(2,4),(3,5),(4,8),(4,11),(5,9),(5,10),(8,7),(9,6),(10,6),(10,8),(11,7),(11,9)],12)

[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => [(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => [5,6,7,9,1,2,3,11,4,12,8,10] => ([(0,7),(1,6),(2,9),(2,10),(3,8),(3,11),(4,2),(4,8),(5,3),(5,9),(6,4),(7,5),(8,10),(9,11)],12)

[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => [(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => [2,1,4,3,8,9,11,5,6,12,7,10] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(2,9),(3,4),(3,8),(4,9),(5,8),(6,3),(7,2),(10,6),(10,7),(11,6),(11,7)],12)

[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => [(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => [3,4,1,2,8,9,11,5,6,12,7,10] => ([(0,5),(1,4),(2,11),(3,10),(4,8),(4,9),(5,8),(5,9),(6,3),(6,11),(7,2),(7,10),(8,6),(9,7)],12)

[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => [(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => [2,1,5,8,3,9,11,4,6,12,7,10] => ([(0,10),(0,11),(1,10),(1,11),(2,9),(3,8),(4,7),(5,6),(8,4),(8,6),(9,5),(9,7),(10,3),(10,9),(11,2),(11,8)],12)

[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => [(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => [3,5,1,8,2,9,11,4,6,12,7,10] => ([(0,5),(0,11),(1,4),(1,10),(2,7),(3,6),(4,8),(4,11),(5,9),(5,10),(8,2),(8,6),(9,3),(9,7),(10,8),(11,9)],12)

[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => [(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => [4,5,8,1,2,9,11,3,6,12,7,10] => ([(0,7),(1,6),(2,11),(3,10),(4,9),(5,8),(6,2),(6,10),(7,3),(7,11),(10,4),(10,8),(11,5),(11,9)],12)

[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => [(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => [2,1,6,8,9,3,11,4,5,12,7,10] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(3,4),(4,6),(4,8),(5,7),(5,9),(8,7),(9,6),(10,3),(10,9),(11,2),(11,8)],12)

[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => [(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => [3,6,1,8,9,2,11,4,5,12,7,10] => ([(0,5),(0,9),(1,4),(1,8),(2,7),(2,10),(3,6),(3,11),(4,9),(4,10),(5,8),(5,11),(8,2),(9,3),(10,6),(11,7)],12)

[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => [(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => [4,6,8,1,9,2,11,3,5,12,7,10] => ([(0,5),(0,11),(1,4),(1,10),(2,11),(3,10),(4,2),(4,8),(5,3),(5,9),(8,7),(9,6),(10,6),(10,8),(11,7),(11,9)],12)

[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => [(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => [5,6,8,9,1,2,11,3,4,12,7,10] => ([(0,7),(1,6),(2,9),(2,10),(3,8),(3,11),(4,2),(5,3),(6,4),(6,8),(7,5),(7,9),(8,10),(9,11)],12)

[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => [(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => [2,1,7,8,9,11,3,4,5,12,6,10] => ([(0,10),(0,11),(1,10),(1,11),(2,9),(3,8),(4,6),(5,7),(6,3),(6,9),(7,2),(7,8),(10,4),(11,5)],12)

[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => [(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => [3,7,1,8,9,11,2,4,5,12,6,10] => ([(0,5),(0,11),(1,4),(1,10),(2,9),(3,8),(4,11),(5,10),(6,2),(6,8),(7,3),(7,9),(10,6),(11,7)],12)

[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => [(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => [4,7,8,1,9,11,2,3,5,12,6,10] => ([(0,7),(0,11),(1,6),(1,10),(2,11),(3,10),(4,9),(5,8),(6,2),(7,3),(10,4),(10,8),(11,5),(11,9)],12)

[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => [(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => [5,7,8,9,1,11,2,3,4,12,6,10] => ([(0,7),(0,11),(1,6),(1,10),(2,9),(2,10),(3,8),(3,11),(4,3),(5,2),(6,4),(7,5),(10,8),(11,9)],12)

[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => [(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => [6,7,8,9,11,1,2,3,4,12,5,10] => ([(0,9),(1,8),(2,11),(3,10),(4,6),(5,7),(6,2),(6,10),(7,3),(7,11),(8,4),(9,5)],12)

[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(3,4),(6,3),(7,2),(8,6),(8,7),(9,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => ([(0,5),(1,4),(4,8),(4,9),(5,8),(5,9),(6,3),(7,2),(8,10),(8,11),(9,10),(9,11),(10,6),(11,7)],12)

[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => ([(0,10),(0,11),(1,10),(1,11),(4,8),(4,9),(5,8),(5,9),(6,3),(7,2),(8,6),(9,7),(10,5),(11,4)],12)

[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => [(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => [3,5,1,6,2,4,10,11,12,7,8,9] => ([(0,5),(0,11),(1,4),(1,10),(4,11),(5,10),(6,3),(7,2),(8,6),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => ([(0,9),(1,8),(4,10),(4,11),(5,10),(5,11),(6,3),(7,2),(8,4),(9,5),(10,6),(11,7)],12)

[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => [(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => [2,1,4,3,7,10,5,11,12,6,8,9] => ([(0,10),(0,11),(1,10),(1,11),(4,6),(5,7),(6,3),(7,2),(8,5),(8,6),(9,4),(9,7),(10,8),(10,9),(11,8),(11,9)],12)

[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => [(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => [3,4,1,2,7,10,5,11,12,6,8,9] => ([(0,7),(1,6),(2,11),(3,10),(6,8),(6,9),(7,8),(7,9),(8,3),(8,11),(9,2),(9,10),(10,4),(11,5)],12)

[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => [(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => [2,1,5,7,3,10,4,11,12,6,8,9] => ([(0,10),(0,11),(1,10),(1,11),(4,6),(4,9),(5,7),(5,8),(6,3),(7,2),(8,6),(9,7),(10,4),(10,8),(11,5),(11,9)],12)

[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => [(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => [3,5,1,7,2,10,4,11,12,6,8,9] => ([(0,5),(0,11),(1,4),(1,10),(4,8),(4,11),(5,9),(5,10),(6,2),(7,3),(8,7),(9,6),(10,6),(10,8),(11,7),(11,9)],12)

[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => [(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => [4,5,7,1,2,10,3,11,12,6,8,9] => ([(0,7),(1,6),(4,9),(4,10),(5,8),(5,11),(6,4),(6,8),(7,5),(7,9),(8,10),(9,11),(10,2),(11,3)],12)

[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => [(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => [2,1,6,7,10,3,4,11,12,5,8,9] => ([(0,8),(0,9),(1,8),(1,9),(4,10),(5,11),(6,5),(6,10),(7,4),(7,11),(8,6),(9,7),(10,3),(11,2)],12)

[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => [(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => [3,6,1,7,10,2,4,11,12,5,8,9] => ([(0,7),(0,11),(1,6),(1,10),(2,9),(3,8),(6,11),(7,10),(8,4),(9,5),(10,2),(10,8),(11,3),(11,9)],12)

[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => [(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => [4,6,7,1,10,2,3,11,12,5,8,9] => ([(0,7),(0,9),(1,6),(1,8),(4,9),(4,10),(5,8),(5,11),(6,4),(7,5),(8,10),(9,11),(10,2),(11,3)],12)

[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => [(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => [5,6,7,10,1,2,3,11,12,4,8,9] => ([(0,9),(1,8),(2,11),(3,10),(6,2),(6,10),(7,3),(7,11),(8,6),(9,7),(10,4),(11,5)],12)

[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => [(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => [2,1,4,3,8,10,11,5,12,6,7,9] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(3,4),(4,6),(5,7),(8,3),(8,7),(9,2),(9,6),(10,8),(10,9),(11,8),(11,9)],12)

[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => [(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => [3,4,1,2,8,10,11,5,12,6,7,9] => ([(0,5),(1,4),(2,11),(3,10),(4,8),(4,9),(5,8),(5,9),(6,3),(7,2),(8,7),(8,10),(9,6),(9,11)],12)

[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => [(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => [2,1,5,8,3,10,11,4,12,6,7,9] => ([(0,10),(0,11),(1,10),(1,11),(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,3),(7,2),(10,4),(10,6),(11,5),(11,7)],12)

[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => [(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => [3,5,1,8,2,10,11,4,12,6,7,9] => ([(0,5),(0,11),(1,4),(1,10),(2,9),(3,8),(4,6),(4,11),(5,7),(5,10),(6,2),(7,3),(10,6),(10,8),(11,7),(11,9)],12)

[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => [(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => [4,5,8,1,2,10,11,3,12,6,7,9] => ([(0,7),(1,6),(2,8),(3,9),(4,8),(4,11),(5,9),(5,10),(6,4),(6,10),(7,5),(7,11),(10,2),(11,3)],12)

[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => [(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => [2,1,6,8,10,3,11,4,12,5,7,9] => ([(0,10),(0,11),(1,10),(1,11),(2,5),(2,7),(3,4),(3,6),(4,8),(5,9),(8,7),(9,6),(10,3),(10,9),(11,2),(11,8)],12)

[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => [(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => [3,6,1,8,10,2,11,4,12,5,7,9] => ([(0,5),(0,11),(1,4),(1,10),(2,8),(3,9),(4,8),(4,11),(5,9),(5,10),(8,7),(9,6),(10,2),(10,6),(11,3),(11,7)],12)

[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => [(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => [4,6,8,1,10,2,11,3,12,5,7,9] => ([(0,3),(0,11),(1,2),(1,10),(2,4),(2,8),(3,5),(3,9),(4,6),(4,11),(5,7),(5,10),(8,6),(9,7),(10,8),(11,9)],12)

[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => [(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => [5,6,8,10,1,2,11,3,12,4,7,9] => ([(0,7),(1,6),(2,9),(3,8),(4,2),(4,10),(5,3),(5,11),(6,4),(6,8),(7,5),(7,9),(8,10),(9,11)],12)

[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => [(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => [2,1,7,8,10,11,3,4,12,5,6,9] => ([(0,10),(0,11),(1,10),(1,11),(2,9),(3,8),(4,3),(5,2),(6,5),(6,8),(7,4),(7,9),(10,6),(11,7)],12)

[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => [(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => [3,7,1,8,10,11,2,4,12,5,6,9] => ([(0,5),(0,11),(1,4),(1,10),(2,9),(3,8),(4,11),(5,10),(6,2),(7,3),(10,6),(10,8),(11,7),(11,9)],12)

[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => [(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => [4,7,8,1,10,11,2,3,12,5,6,9] => ([(0,7),(0,11),(1,6),(1,10),(2,8),(3,9),(4,8),(4,11),(5,9),(5,10),(6,4),(7,5),(10,2),(11,3)],12)

[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => [(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => [5,7,8,10,1,11,2,3,12,4,6,9] => ([(0,7),(0,11),(1,6),(1,10),(2,10),(3,11),(4,3),(4,8),(5,2),(5,9),(6,4),(7,5),(10,8),(11,9)],12)

[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => [(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => [6,7,8,10,11,1,2,3,12,4,5,9] => ([(0,9),(1,8),(2,11),(3,10),(4,2),(5,3),(6,4),(6,10),(7,5),(7,11),(8,6),(9,7)],12)

[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => ([(0,8),(0,9),(1,8),(1,9),(4,6),(5,7),(6,3),(7,2),(8,10),(8,11),(9,10),(9,11),(10,4),(11,5)],12)

[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => ([(0,5),(1,4),(4,10),(4,11),(5,10),(5,11),(6,3),(7,2),(8,6),(9,7),(10,8),(11,9)],12)

[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => [(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => [2,1,5,9,3,10,11,12,4,6,7,8] => ([(0,10),(0,11),(1,10),(1,11),(4,8),(5,9),(6,3),(7,2),(8,6),(9,7),(10,5),(10,8),(11,4),(11,9)],12)

[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => [(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => [3,5,1,9,2,10,11,12,4,6,7,8] => ([(0,5),(0,11),(1,4),(1,10),(4,8),(4,11),(5,9),(5,10),(6,2),(7,3),(8,6),(9,7),(10,8),(11,9)],12)

[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => [(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => [4,5,9,1,2,10,11,12,3,6,7,8] => ([(0,9),(1,8),(4,11),(5,10),(6,2),(7,3),(8,4),(8,10),(9,5),(9,11),(10,6),(11,7)],12)

[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => [(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => [2,1,6,9,10,3,11,12,4,5,7,8] => ([(0,8),(0,9),(1,8),(1,9),(4,10),(5,11),(6,4),(7,5),(8,7),(8,10),(9,6),(9,11),(10,3),(11,2)],12)

[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => [(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => [3,6,1,9,10,2,11,12,4,5,7,8] => ([(0,7),(0,11),(1,6),(1,10),(2,8),(3,9),(6,8),(6,11),(7,9),(7,10),(8,4),(9,5),(10,2),(11,3)],12)

[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => [(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => [4,6,9,1,10,2,11,12,3,5,7,8] => ([(0,7),(0,9),(1,6),(1,8),(4,9),(5,8),(6,4),(6,10),(7,5),(7,11),(8,10),(9,11),(10,2),(11,3)],12)

[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => [(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => [5,6,9,10,1,2,11,12,3,4,7,8] => ([(0,9),(1,8),(2,11),(3,10),(6,2),(7,3),(8,6),(8,10),(9,7),(9,11),(10,4),(11,5)],12)

[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => [(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => [2,1,7,9,10,11,3,12,4,5,6,8] => ([(0,10),(0,11),(1,10),(1,11),(2,9),(3,8),(4,6),(5,7),(6,3),(7,2),(10,5),(10,8),(11,4),(11,9)],12)

[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => [(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => [3,7,1,9,10,11,2,12,4,5,6,8] => ([(0,5),(0,11),(1,4),(1,10),(2,8),(3,9),(4,8),(4,11),(5,9),(5,10),(6,2),(7,3),(10,6),(11,7)],12)

[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => [(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => [4,7,9,1,10,11,2,12,3,5,6,8] => ([(0,7),(0,11),(1,6),(1,10),(2,11),(3,10),(4,8),(5,9),(6,2),(6,8),(7,3),(7,9),(10,4),(11,5)],12)

[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => [(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => [5,7,9,10,1,11,2,12,3,4,6,8] => ([(0,7),(0,11),(1,6),(1,10),(2,10),(3,11),(4,3),(5,2),(6,4),(6,8),(7,5),(7,9),(10,8),(11,9)],12)

[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => [(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => [6,7,9,10,11,1,2,12,3,4,5,8] => ([(0,9),(1,8),(2,10),(3,11),(4,6),(5,7),(6,3),(7,2),(8,4),(8,10),(9,5),(9,11)],12)

[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => ([(0,10),(0,11),(1,10),(1,11),(4,6),(5,7),(6,3),(7,2),(8,4),(9,5),(10,8),(11,9)],12)

[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => [(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => [3,8,1,9,10,11,12,2,4,5,6,7] => ([(0,5),(0,11),(1,4),(1,10),(4,11),(5,10),(6,2),(7,3),(8,6),(9,7),(10,8),(11,9)],12)

[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => [(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => [4,8,9,1,10,11,12,2,3,5,6,7] => ([(0,9),(0,11),(1,8),(1,10),(4,11),(5,10),(6,2),(7,3),(8,4),(9,5),(10,6),(11,7)],12)

[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => [(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => [5,8,9,10,1,11,12,2,3,4,6,7] => ([(0,9),(0,11),(1,8),(1,10),(2,10),(3,11),(6,3),(7,2),(8,6),(9,7),(10,4),(11,5)],12)

[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => [(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => [6,8,9,10,11,1,12,2,3,4,5,7] => ([(0,9),(0,11),(1,8),(1,10),(2,10),(3,11),(4,6),(5,7),(6,3),(7,2),(8,4),(9,5)],12)

[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => ([(0,11),(1,10),(4,8),(5,9),(6,4),(7,5),(8,2),(9,3),(10,6),(11,7)],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

to permutation

Description

Returns the fixed point free involution whose transpositions are the pairs in the 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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$