Identifier
Values
=>
Cc0012;cc-rep
[(1,2)]=>2
[(1,2),(3,4)]=>2
[(1,3),(2,4)]=>2
[(1,4),(2,3)]=>2
[(1,2),(3,4),(5,6)]=>8
[(1,3),(2,4),(5,6)]=>8
[(1,4),(2,3),(5,6)]=>8
[(1,5),(2,3),(4,6)]=>2
[(1,6),(2,3),(4,5)]=>2
[(1,6),(2,4),(3,5)]=>2
[(1,5),(2,4),(3,6)]=>2
[(1,4),(2,5),(3,6)]=>2
[(1,3),(2,5),(4,6)]=>2
[(1,2),(3,5),(4,6)]=>2
[(1,2),(3,6),(4,5)]=>2
[(1,3),(2,6),(4,5)]=>2
[(1,4),(2,6),(3,5)]=>2
[(1,5),(2,6),(3,4)]=>2
[(1,6),(2,5),(3,4)]=>2
[(1,2),(3,4),(5,6),(7,8)]=>4
[(1,3),(2,4),(5,6),(7,8)]=>4
[(1,4),(2,3),(5,6),(7,8)]=>4
[(1,5),(2,3),(4,6),(7,8)]=>4
[(1,6),(2,3),(4,5),(7,8)]=>4
[(1,7),(2,3),(4,5),(6,8)]=>4
[(1,8),(2,3),(4,5),(6,7)]=>8
[(1,8),(2,4),(3,5),(6,7)]=>8
[(1,7),(2,4),(3,5),(6,8)]=>4
[(1,6),(2,4),(3,5),(7,8)]=>4
[(1,5),(2,4),(3,6),(7,8)]=>4
[(1,4),(2,5),(3,6),(7,8)]=>4
[(1,3),(2,5),(4,6),(7,8)]=>4
[(1,2),(3,5),(4,6),(7,8)]=>4
[(1,2),(3,6),(4,5),(7,8)]=>4
[(1,3),(2,6),(4,5),(7,8)]=>4
[(1,4),(2,6),(3,5),(7,8)]=>4
[(1,5),(2,6),(3,4),(7,8)]=>4
[(1,6),(2,5),(3,4),(7,8)]=>4
[(1,7),(2,5),(3,4),(6,8)]=>4
[(1,8),(2,5),(3,4),(6,7)]=>8
[(1,8),(2,6),(3,4),(5,7)]=>2
[(1,7),(2,6),(3,4),(5,8)]=>2
[(1,6),(2,7),(3,4),(5,8)]=>2
[(1,5),(2,7),(3,4),(6,8)]=>4
[(1,4),(2,7),(3,5),(6,8)]=>4
[(1,3),(2,7),(4,5),(6,8)]=>4
[(1,2),(3,7),(4,5),(6,8)]=>4
[(1,2),(3,8),(4,5),(6,7)]=>8
[(1,3),(2,8),(4,5),(6,7)]=>8
[(1,4),(2,8),(3,5),(6,7)]=>8
[(1,5),(2,8),(3,4),(6,7)]=>8
[(1,6),(2,8),(3,4),(5,7)]=>2
[(1,7),(2,8),(3,4),(5,6)]=>2
[(1,8),(2,7),(3,4),(5,6)]=>2
[(1,8),(2,7),(3,5),(4,6)]=>2
[(1,7),(2,8),(3,5),(4,6)]=>2
[(1,6),(2,8),(3,5),(4,7)]=>2
[(1,5),(2,8),(3,6),(4,7)]=>2
[(1,4),(2,8),(3,6),(5,7)]=>2
[(1,3),(2,8),(4,6),(5,7)]=>2
[(1,2),(3,8),(4,6),(5,7)]=>2
[(1,2),(3,7),(4,6),(5,8)]=>2
[(1,3),(2,7),(4,6),(5,8)]=>2
[(1,4),(2,7),(3,6),(5,8)]=>2
[(1,5),(2,7),(3,6),(4,8)]=>2
[(1,6),(2,7),(3,5),(4,8)]=>2
[(1,7),(2,6),(3,5),(4,8)]=>2
[(1,8),(2,6),(3,5),(4,7)]=>2
[(1,8),(2,5),(3,6),(4,7)]=>2
[(1,7),(2,5),(3,6),(4,8)]=>2
[(1,6),(2,5),(3,7),(4,8)]=>2
[(1,5),(2,6),(3,7),(4,8)]=>2
[(1,4),(2,6),(3,7),(5,8)]=>2
[(1,3),(2,6),(4,7),(5,8)]=>2
[(1,2),(3,6),(4,7),(5,8)]=>2
[(1,2),(3,5),(4,7),(6,8)]=>4
[(1,3),(2,5),(4,7),(6,8)]=>4
[(1,4),(2,5),(3,7),(6,8)]=>4
[(1,5),(2,4),(3,7),(6,8)]=>4
[(1,6),(2,4),(3,7),(5,8)]=>2
[(1,7),(2,4),(3,6),(5,8)]=>2
[(1,8),(2,4),(3,6),(5,7)]=>2
[(1,8),(2,3),(4,6),(5,7)]=>2
[(1,7),(2,3),(4,6),(5,8)]=>2
[(1,6),(2,3),(4,7),(5,8)]=>2
[(1,5),(2,3),(4,7),(6,8)]=>4
[(1,4),(2,3),(5,7),(6,8)]=>4
[(1,3),(2,4),(5,7),(6,8)]=>4
[(1,2),(3,4),(5,7),(6,8)]=>4
[(1,2),(3,4),(5,8),(6,7)]=>8
[(1,3),(2,4),(5,8),(6,7)]=>8
[(1,4),(2,3),(5,8),(6,7)]=>8
[(1,5),(2,3),(4,8),(6,7)]=>8
[(1,6),(2,3),(4,8),(5,7)]=>2
[(1,7),(2,3),(4,8),(5,6)]=>2
[(1,8),(2,3),(4,7),(5,6)]=>2
[(1,8),(2,4),(3,7),(5,6)]=>2
[(1,7),(2,4),(3,8),(5,6)]=>2
[(1,6),(2,4),(3,8),(5,7)]=>2
[(1,5),(2,4),(3,8),(6,7)]=>8
[(1,4),(2,5),(3,8),(6,7)]=>8
[(1,3),(2,5),(4,8),(6,7)]=>8
[(1,2),(3,5),(4,8),(6,7)]=>8
[(1,2),(3,6),(4,8),(5,7)]=>2
[(1,3),(2,6),(4,8),(5,7)]=>2
[(1,4),(2,6),(3,8),(5,7)]=>2
[(1,5),(2,6),(3,8),(4,7)]=>2
[(1,6),(2,5),(3,8),(4,7)]=>2
[(1,7),(2,5),(3,8),(4,6)]=>2
[(1,8),(2,5),(3,7),(4,6)]=>2
[(1,8),(2,6),(3,7),(4,5)]=>2
[(1,7),(2,6),(3,8),(4,5)]=>2
[(1,6),(2,7),(3,8),(4,5)]=>2
[(1,5),(2,7),(3,8),(4,6)]=>2
[(1,4),(2,7),(3,8),(5,6)]=>2
[(1,3),(2,7),(4,8),(5,6)]=>2
[(1,2),(3,7),(4,8),(5,6)]=>2
[(1,2),(3,8),(4,7),(5,6)]=>2
[(1,3),(2,8),(4,7),(5,6)]=>2
[(1,4),(2,8),(3,7),(5,6)]=>2
[(1,5),(2,8),(3,7),(4,6)]=>2
[(1,6),(2,8),(3,7),(4,5)]=>2
[(1,7),(2,8),(3,6),(4,5)]=>2
[(1,8),(2,7),(3,6),(4,5)]=>2
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>16
[(1,3),(2,4),(5,6),(7,8),(9,10)]=>16
[(1,4),(2,3),(5,6),(7,8),(9,10)]=>16
[(1,5),(2,3),(4,6),(7,8),(9,10)]=>16
[(1,6),(2,3),(4,5),(7,8),(9,10)]=>16
[(1,7),(2,3),(4,5),(6,8),(9,10)]=>4
[(1,8),(2,3),(4,5),(6,7),(9,10)]=>8
[(1,9),(2,3),(4,5),(6,7),(8,10)]=>4
[(1,10),(2,3),(4,5),(6,7),(8,9)]=>4
[(1,10),(2,4),(3,5),(6,7),(8,9)]=>4
[(1,9),(2,4),(3,5),(6,7),(8,10)]=>4
[(1,8),(2,4),(3,5),(6,7),(9,10)]=>8
[(1,7),(2,4),(3,5),(6,8),(9,10)]=>4
[(1,6),(2,4),(3,5),(7,8),(9,10)]=>16
[(1,5),(2,4),(3,6),(7,8),(9,10)]=>16
[(1,4),(2,5),(3,6),(7,8),(9,10)]=>16
[(1,3),(2,5),(4,6),(7,8),(9,10)]=>16
[(1,2),(3,5),(4,6),(7,8),(9,10)]=>16
[(1,2),(3,6),(4,5),(7,8),(9,10)]=>16
[(1,3),(2,6),(4,5),(7,8),(9,10)]=>16
[(1,4),(2,6),(3,5),(7,8),(9,10)]=>16
[(1,5),(2,6),(3,4),(7,8),(9,10)]=>16
[(1,6),(2,5),(3,4),(7,8),(9,10)]=>16
[(1,7),(2,5),(3,4),(6,8),(9,10)]=>4
[(1,8),(2,5),(3,4),(6,7),(9,10)]=>8
[(1,9),(2,5),(3,4),(6,7),(8,10)]=>4
[(1,10),(2,5),(3,4),(6,7),(8,9)]=>4
[(1,10),(2,6),(3,4),(5,7),(8,9)]=>4
[(1,9),(2,6),(3,4),(5,7),(8,10)]=>4
[(1,8),(2,6),(3,4),(5,7),(9,10)]=>8
[(1,7),(2,6),(3,4),(5,8),(9,10)]=>4
[(1,6),(2,7),(3,4),(5,8),(9,10)]=>4
[(1,5),(2,7),(3,4),(6,8),(9,10)]=>4
[(1,4),(2,7),(3,5),(6,8),(9,10)]=>4
[(1,3),(2,7),(4,5),(6,8),(9,10)]=>4
[(1,2),(3,7),(4,5),(6,8),(9,10)]=>4
[(1,2),(3,8),(4,5),(6,7),(9,10)]=>8
[(1,3),(2,8),(4,5),(6,7),(9,10)]=>8
[(1,4),(2,8),(3,5),(6,7),(9,10)]=>8
[(1,5),(2,8),(3,4),(6,7),(9,10)]=>8
[(1,6),(2,8),(3,4),(5,7),(9,10)]=>8
[(1,7),(2,8),(3,4),(5,6),(9,10)]=>4
[(1,8),(2,7),(3,4),(5,6),(9,10)]=>4
[(1,9),(2,7),(3,4),(5,6),(8,10)]=>8
[(1,10),(2,7),(3,4),(5,6),(8,9)]=>4
[(1,10),(2,8),(3,4),(5,6),(7,9)]=>4
[(1,9),(2,8),(3,4),(5,6),(7,10)]=>4
[(1,8),(2,9),(3,4),(5,6),(7,10)]=>4
[(1,7),(2,9),(3,4),(5,6),(8,10)]=>8
[(1,6),(2,9),(3,4),(5,7),(8,10)]=>4
[(1,5),(2,9),(3,4),(6,7),(8,10)]=>4
[(1,4),(2,9),(3,5),(6,7),(8,10)]=>4
[(1,3),(2,9),(4,5),(6,7),(8,10)]=>4
[(1,2),(3,9),(4,5),(6,7),(8,10)]=>4
[(1,2),(3,10),(4,5),(6,7),(8,9)]=>4
[(1,3),(2,10),(4,5),(6,7),(8,9)]=>4
[(1,4),(2,10),(3,5),(6,7),(8,9)]=>4
[(1,5),(2,10),(3,4),(6,7),(8,9)]=>4
[(1,6),(2,10),(3,4),(5,7),(8,9)]=>4
[(1,7),(2,10),(3,4),(5,6),(8,9)]=>4
[(1,8),(2,10),(3,4),(5,6),(7,9)]=>4
[(1,9),(2,10),(3,4),(5,6),(7,8)]=>8
[(1,10),(2,9),(3,4),(5,6),(7,8)]=>8
[(1,10),(2,9),(3,5),(4,6),(7,8)]=>8
[(1,9),(2,10),(3,5),(4,6),(7,8)]=>8
[(1,8),(2,10),(3,5),(4,6),(7,9)]=>4
[(1,7),(2,10),(3,5),(4,6),(8,9)]=>4
[(1,6),(2,10),(3,5),(4,7),(8,9)]=>4
[(1,5),(2,10),(3,6),(4,7),(8,9)]=>4
[(1,4),(2,10),(3,6),(5,7),(8,9)]=>4
[(1,3),(2,10),(4,6),(5,7),(8,9)]=>4
[(1,2),(3,10),(4,6),(5,7),(8,9)]=>4
[(1,2),(3,9),(4,6),(5,7),(8,10)]=>4
[(1,3),(2,9),(4,6),(5,7),(8,10)]=>4
[(1,4),(2,9),(3,6),(5,7),(8,10)]=>4
[(1,5),(2,9),(3,6),(4,7),(8,10)]=>4
[(1,6),(2,9),(3,5),(4,7),(8,10)]=>4
[(1,7),(2,9),(3,5),(4,6),(8,10)]=>8
[(1,8),(2,9),(3,5),(4,6),(7,10)]=>4
[(1,9),(2,8),(3,5),(4,6),(7,10)]=>4
[(1,10),(2,8),(3,5),(4,6),(7,9)]=>4
[(1,10),(2,7),(3,5),(4,6),(8,9)]=>4
[(1,9),(2,7),(3,5),(4,6),(8,10)]=>8
[(1,8),(2,7),(3,5),(4,6),(9,10)]=>4
[(1,7),(2,8),(3,5),(4,6),(9,10)]=>4
[(1,6),(2,8),(3,5),(4,7),(9,10)]=>8
[(1,5),(2,8),(3,6),(4,7),(9,10)]=>8
[(1,4),(2,8),(3,6),(5,7),(9,10)]=>8
[(1,3),(2,8),(4,6),(5,7),(9,10)]=>8
[(1,2),(3,8),(4,6),(5,7),(9,10)]=>8
[(1,2),(3,7),(4,6),(5,8),(9,10)]=>4
[(1,3),(2,7),(4,6),(5,8),(9,10)]=>4
[(1,4),(2,7),(3,6),(5,8),(9,10)]=>4
[(1,5),(2,7),(3,6),(4,8),(9,10)]=>4
[(1,6),(2,7),(3,5),(4,8),(9,10)]=>4
[(1,7),(2,6),(3,5),(4,8),(9,10)]=>4
[(1,8),(2,6),(3,5),(4,7),(9,10)]=>8
[(1,9),(2,6),(3,5),(4,7),(8,10)]=>4
[(1,10),(2,6),(3,5),(4,7),(8,9)]=>4
[(1,10),(2,5),(3,6),(4,7),(8,9)]=>4
[(1,9),(2,5),(3,6),(4,7),(8,10)]=>4
[(1,8),(2,5),(3,6),(4,7),(9,10)]=>8
[(1,7),(2,5),(3,6),(4,8),(9,10)]=>4
[(1,6),(2,5),(3,7),(4,8),(9,10)]=>8
[(1,5),(2,6),(3,7),(4,8),(9,10)]=>8
[(1,4),(2,6),(3,7),(5,8),(9,10)]=>8
[(1,3),(2,6),(4,7),(5,8),(9,10)]=>8
[(1,2),(3,6),(4,7),(5,8),(9,10)]=>8
[(1,2),(3,5),(4,7),(6,8),(9,10)]=>8
[(1,3),(2,5),(4,7),(6,8),(9,10)]=>8
[(1,4),(2,5),(3,7),(6,8),(9,10)]=>8
[(1,5),(2,4),(3,7),(6,8),(9,10)]=>8
[(1,6),(2,4),(3,7),(5,8),(9,10)]=>8
[(1,7),(2,4),(3,6),(5,8),(9,10)]=>4
[(1,8),(2,4),(3,6),(5,7),(9,10)]=>8
[(1,9),(2,4),(3,6),(5,7),(8,10)]=>4
[(1,10),(2,4),(3,6),(5,7),(8,9)]=>4
[(1,10),(2,3),(4,6),(5,7),(8,9)]=>4
[(1,9),(2,3),(4,6),(5,7),(8,10)]=>4
[(1,8),(2,3),(4,6),(5,7),(9,10)]=>8
[(1,7),(2,3),(4,6),(5,8),(9,10)]=>4
[(1,6),(2,3),(4,7),(5,8),(9,10)]=>8
[(1,5),(2,3),(4,7),(6,8),(9,10)]=>8
[(1,4),(2,3),(5,7),(6,8),(9,10)]=>8
[(1,3),(2,4),(5,7),(6,8),(9,10)]=>8
[(1,2),(3,4),(5,7),(6,8),(9,10)]=>8
[(1,2),(3,4),(5,8),(6,7),(9,10)]=>8
[(1,3),(2,4),(5,8),(6,7),(9,10)]=>8
[(1,4),(2,3),(5,8),(6,7),(9,10)]=>8
[(1,5),(2,3),(4,8),(6,7),(9,10)]=>8
[(1,6),(2,3),(4,8),(5,7),(9,10)]=>8
[(1,7),(2,3),(4,8),(5,6),(9,10)]=>4
[(1,8),(2,3),(4,7),(5,6),(9,10)]=>4
[(1,9),(2,3),(4,7),(5,6),(8,10)]=>8
[(1,10),(2,3),(4,7),(5,6),(8,9)]=>4
[(1,10),(2,4),(3,7),(5,6),(8,9)]=>4
[(1,9),(2,4),(3,7),(5,6),(8,10)]=>8
[(1,8),(2,4),(3,7),(5,6),(9,10)]=>4
[(1,7),(2,4),(3,8),(5,6),(9,10)]=>4
[(1,6),(2,4),(3,8),(5,7),(9,10)]=>8
[(1,5),(2,4),(3,8),(6,7),(9,10)]=>8
[(1,4),(2,5),(3,8),(6,7),(9,10)]=>8
[(1,3),(2,5),(4,8),(6,7),(9,10)]=>8
[(1,2),(3,5),(4,8),(6,7),(9,10)]=>8
[(1,2),(3,6),(4,8),(5,7),(9,10)]=>8
[(1,3),(2,6),(4,8),(5,7),(9,10)]=>8
[(1,4),(2,6),(3,8),(5,7),(9,10)]=>8
[(1,5),(2,6),(3,8),(4,7),(9,10)]=>8
[(1,6),(2,5),(3,8),(4,7),(9,10)]=>8
[(1,7),(2,5),(3,8),(4,6),(9,10)]=>4
[(1,8),(2,5),(3,7),(4,6),(9,10)]=>4
[(1,9),(2,5),(3,7),(4,6),(8,10)]=>8
[(1,10),(2,5),(3,7),(4,6),(8,9)]=>4
[(1,10),(2,6),(3,7),(4,5),(8,9)]=>4
[(1,9),(2,6),(3,7),(4,5),(8,10)]=>8
[(1,8),(2,6),(3,7),(4,5),(9,10)]=>4
[(1,7),(2,6),(3,8),(4,5),(9,10)]=>4
[(1,6),(2,7),(3,8),(4,5),(9,10)]=>4
[(1,5),(2,7),(3,8),(4,6),(9,10)]=>4
[(1,4),(2,7),(3,8),(5,6),(9,10)]=>4
[(1,3),(2,7),(4,8),(5,6),(9,10)]=>4
[(1,2),(3,7),(4,8),(5,6),(9,10)]=>4
[(1,2),(3,8),(4,7),(5,6),(9,10)]=>4
[(1,3),(2,8),(4,7),(5,6),(9,10)]=>4
[(1,4),(2,8),(3,7),(5,6),(9,10)]=>4
[(1,5),(2,8),(3,7),(4,6),(9,10)]=>4
[(1,6),(2,8),(3,7),(4,5),(9,10)]=>4
[(1,7),(2,8),(3,6),(4,5),(9,10)]=>4
[(1,8),(2,7),(3,6),(4,5),(9,10)]=>4
[(1,9),(2,7),(3,6),(4,5),(8,10)]=>8
[(1,10),(2,7),(3,6),(4,5),(8,9)]=>4
[(1,10),(2,8),(3,6),(4,5),(7,9)]=>4
[(1,9),(2,8),(3,6),(4,5),(7,10)]=>4
[(1,8),(2,9),(3,6),(4,5),(7,10)]=>4
[(1,7),(2,9),(3,6),(4,5),(8,10)]=>8
[(1,6),(2,9),(3,7),(4,5),(8,10)]=>8
[(1,5),(2,9),(3,7),(4,6),(8,10)]=>8
[(1,4),(2,9),(3,7),(5,6),(8,10)]=>8
[(1,3),(2,9),(4,7),(5,6),(8,10)]=>8
[(1,2),(3,9),(4,7),(5,6),(8,10)]=>8
[(1,2),(3,10),(4,7),(5,6),(8,9)]=>4
[(1,3),(2,10),(4,7),(5,6),(8,9)]=>4
[(1,4),(2,10),(3,7),(5,6),(8,9)]=>4
[(1,5),(2,10),(3,7),(4,6),(8,9)]=>4
[(1,6),(2,10),(3,7),(4,5),(8,9)]=>4
[(1,7),(2,10),(3,6),(4,5),(8,9)]=>4
[(1,8),(2,10),(3,6),(4,5),(7,9)]=>4
[(1,9),(2,10),(3,6),(4,5),(7,8)]=>8
[(1,10),(2,9),(3,6),(4,5),(7,8)]=>8
[(1,10),(2,9),(3,7),(4,5),(6,8)]=>2
[(1,9),(2,10),(3,7),(4,5),(6,8)]=>2
[(1,8),(2,10),(3,7),(4,5),(6,9)]=>2
[(1,7),(2,10),(3,8),(4,5),(6,9)]=>2
[(1,6),(2,10),(3,8),(4,5),(7,9)]=>4
[(1,5),(2,10),(3,8),(4,6),(7,9)]=>4
[(1,4),(2,10),(3,8),(5,6),(7,9)]=>4
[(1,3),(2,10),(4,8),(5,6),(7,9)]=>4
[(1,2),(3,10),(4,8),(5,6),(7,9)]=>4
[(1,2),(3,9),(4,8),(5,6),(7,10)]=>4
[(1,3),(2,9),(4,8),(5,6),(7,10)]=>4
[(1,4),(2,9),(3,8),(5,6),(7,10)]=>4
[(1,5),(2,9),(3,8),(4,6),(7,10)]=>4
[(1,6),(2,9),(3,8),(4,5),(7,10)]=>4
[(1,7),(2,9),(3,8),(4,5),(6,10)]=>2
[(1,8),(2,9),(3,7),(4,5),(6,10)]=>2
[(1,9),(2,8),(3,7),(4,5),(6,10)]=>2
[(1,10),(2,8),(3,7),(4,5),(6,9)]=>2
[(1,10),(2,7),(3,8),(4,5),(6,9)]=>2
[(1,9),(2,7),(3,8),(4,5),(6,10)]=>2
[(1,8),(2,7),(3,9),(4,5),(6,10)]=>2
[(1,7),(2,8),(3,9),(4,5),(6,10)]=>2
[(1,6),(2,8),(3,9),(4,5),(7,10)]=>4
[(1,5),(2,8),(3,9),(4,6),(7,10)]=>4
[(1,4),(2,8),(3,9),(5,6),(7,10)]=>4
[(1,3),(2,8),(4,9),(5,6),(7,10)]=>4
[(1,2),(3,8),(4,9),(5,6),(7,10)]=>4
[(1,2),(3,7),(4,9),(5,6),(8,10)]=>8
[(1,3),(2,7),(4,9),(5,6),(8,10)]=>8
[(1,4),(2,7),(3,9),(5,6),(8,10)]=>8
[(1,5),(2,7),(3,9),(4,6),(8,10)]=>8
[(1,6),(2,7),(3,9),(4,5),(8,10)]=>8
[(1,7),(2,6),(3,9),(4,5),(8,10)]=>8
[(1,8),(2,6),(3,9),(4,5),(7,10)]=>4
[(1,9),(2,6),(3,8),(4,5),(7,10)]=>4
[(1,10),(2,6),(3,8),(4,5),(7,9)]=>4
[(1,10),(2,5),(3,8),(4,6),(7,9)]=>4
[(1,9),(2,5),(3,8),(4,6),(7,10)]=>4
[(1,8),(2,5),(3,9),(4,6),(7,10)]=>4
[(1,7),(2,5),(3,9),(4,6),(8,10)]=>8
[(1,6),(2,5),(3,9),(4,7),(8,10)]=>4
[(1,5),(2,6),(3,9),(4,7),(8,10)]=>4
[(1,4),(2,6),(3,9),(5,7),(8,10)]=>4
[(1,3),(2,6),(4,9),(5,7),(8,10)]=>4
[(1,2),(3,6),(4,9),(5,7),(8,10)]=>4
[(1,2),(3,5),(4,9),(6,7),(8,10)]=>4
[(1,3),(2,5),(4,9),(6,7),(8,10)]=>4
[(1,4),(2,5),(3,9),(6,7),(8,10)]=>4
[(1,5),(2,4),(3,9),(6,7),(8,10)]=>4
[(1,6),(2,4),(3,9),(5,7),(8,10)]=>4
[(1,7),(2,4),(3,9),(5,6),(8,10)]=>8
[(1,8),(2,4),(3,9),(5,6),(7,10)]=>4
[(1,9),(2,4),(3,8),(5,6),(7,10)]=>4
[(1,10),(2,4),(3,8),(5,6),(7,9)]=>4
[(1,10),(2,3),(4,8),(5,6),(7,9)]=>4
[(1,9),(2,3),(4,8),(5,6),(7,10)]=>4
[(1,8),(2,3),(4,9),(5,6),(7,10)]=>4
[(1,7),(2,3),(4,9),(5,6),(8,10)]=>8
[(1,6),(2,3),(4,9),(5,7),(8,10)]=>4
[(1,5),(2,3),(4,9),(6,7),(8,10)]=>4
[(1,4),(2,3),(5,9),(6,7),(8,10)]=>4
[(1,3),(2,4),(5,9),(6,7),(8,10)]=>4
[(1,2),(3,4),(5,9),(6,7),(8,10)]=>4
[(1,2),(3,4),(5,10),(6,7),(8,9)]=>4
[(1,3),(2,4),(5,10),(6,7),(8,9)]=>4
[(1,4),(2,3),(5,10),(6,7),(8,9)]=>4
[(1,5),(2,3),(4,10),(6,7),(8,9)]=>4
[(1,6),(2,3),(4,10),(5,7),(8,9)]=>4
[(1,7),(2,3),(4,10),(5,6),(8,9)]=>4
[(1,8),(2,3),(4,10),(5,6),(7,9)]=>4
[(1,9),(2,3),(4,10),(5,6),(7,8)]=>8
[(1,10),(2,3),(4,9),(5,6),(7,8)]=>8
[(1,10),(2,4),(3,9),(5,6),(7,8)]=>8
[(1,9),(2,4),(3,10),(5,6),(7,8)]=>8
[(1,8),(2,4),(3,10),(5,6),(7,9)]=>4
[(1,7),(2,4),(3,10),(5,6),(8,9)]=>4
[(1,6),(2,4),(3,10),(5,7),(8,9)]=>4
[(1,5),(2,4),(3,10),(6,7),(8,9)]=>4
[(1,4),(2,5),(3,10),(6,7),(8,9)]=>4
[(1,3),(2,5),(4,10),(6,7),(8,9)]=>4
[(1,2),(3,5),(4,10),(6,7),(8,9)]=>4
[(1,2),(3,6),(4,10),(5,7),(8,9)]=>4
[(1,3),(2,6),(4,10),(5,7),(8,9)]=>4
[(1,4),(2,6),(3,10),(5,7),(8,9)]=>4
[(1,5),(2,6),(3,10),(4,7),(8,9)]=>4
[(1,6),(2,5),(3,10),(4,7),(8,9)]=>4
[(1,7),(2,5),(3,10),(4,6),(8,9)]=>4
[(1,8),(2,5),(3,10),(4,6),(7,9)]=>4
[(1,9),(2,5),(3,10),(4,6),(7,8)]=>8
[(1,10),(2,5),(3,9),(4,6),(7,8)]=>8
[(1,10),(2,6),(3,9),(4,5),(7,8)]=>8
[(1,9),(2,6),(3,10),(4,5),(7,8)]=>8
[(1,8),(2,6),(3,10),(4,5),(7,9)]=>4
[(1,7),(2,6),(3,10),(4,5),(8,9)]=>4
[(1,6),(2,7),(3,10),(4,5),(8,9)]=>4
[(1,5),(2,7),(3,10),(4,6),(8,9)]=>4
[(1,4),(2,7),(3,10),(5,6),(8,9)]=>4
[(1,3),(2,7),(4,10),(5,6),(8,9)]=>4
[(1,2),(3,7),(4,10),(5,6),(8,9)]=>4
[(1,2),(3,8),(4,10),(5,6),(7,9)]=>4
[(1,3),(2,8),(4,10),(5,6),(7,9)]=>4
[(1,4),(2,8),(3,10),(5,6),(7,9)]=>4
[(1,5),(2,8),(3,10),(4,6),(7,9)]=>4
[(1,6),(2,8),(3,10),(4,5),(7,9)]=>4
[(1,7),(2,8),(3,10),(4,5),(6,9)]=>2
[(1,8),(2,7),(3,10),(4,5),(6,9)]=>2
[(1,9),(2,7),(3,10),(4,5),(6,8)]=>2
[(1,10),(2,7),(3,9),(4,5),(6,8)]=>2
[(1,10),(2,8),(3,9),(4,5),(6,7)]=>2
[(1,9),(2,8),(3,10),(4,5),(6,7)]=>2
[(1,8),(2,9),(3,10),(4,5),(6,7)]=>2
[(1,7),(2,9),(3,10),(4,5),(6,8)]=>2
[(1,6),(2,9),(3,10),(4,5),(7,8)]=>8
[(1,5),(2,9),(3,10),(4,6),(7,8)]=>8
[(1,4),(2,9),(3,10),(5,6),(7,8)]=>8
[(1,3),(2,9),(4,10),(5,6),(7,8)]=>8
[(1,2),(3,9),(4,10),(5,6),(7,8)]=>8
[(1,2),(3,10),(4,9),(5,6),(7,8)]=>8
[(1,3),(2,10),(4,9),(5,6),(7,8)]=>8
[(1,4),(2,10),(3,9),(5,6),(7,8)]=>8
[(1,5),(2,10),(3,9),(4,6),(7,8)]=>8
[(1,6),(2,10),(3,9),(4,5),(7,8)]=>8
[(1,7),(2,10),(3,9),(4,5),(6,8)]=>2
[(1,8),(2,10),(3,9),(4,5),(6,7)]=>2
[(1,9),(2,10),(3,8),(4,5),(6,7)]=>2
[(1,10),(2,9),(3,8),(4,5),(6,7)]=>2
[(1,10),(2,9),(3,8),(4,6),(5,7)]=>2
[(1,9),(2,10),(3,8),(4,6),(5,7)]=>2
[(1,8),(2,10),(3,9),(4,6),(5,7)]=>2
[(1,7),(2,10),(3,9),(4,6),(5,8)]=>2
[(1,6),(2,10),(3,9),(4,7),(5,8)]=>2
[(1,5),(2,10),(3,9),(4,7),(6,8)]=>2
[(1,4),(2,10),(3,9),(5,7),(6,8)]=>2
[(1,3),(2,10),(4,9),(5,7),(6,8)]=>2
[(1,2),(3,10),(4,9),(5,7),(6,8)]=>2
[(1,2),(3,9),(4,10),(5,7),(6,8)]=>2
[(1,3),(2,9),(4,10),(5,7),(6,8)]=>2
[(1,4),(2,9),(3,10),(5,7),(6,8)]=>2
[(1,5),(2,9),(3,10),(4,7),(6,8)]=>2
[(1,6),(2,9),(3,10),(4,7),(5,8)]=>2
[(1,7),(2,9),(3,10),(4,6),(5,8)]=>2
[(1,8),(2,9),(3,10),(4,6),(5,7)]=>2
[(1,9),(2,8),(3,10),(4,6),(5,7)]=>2
[(1,10),(2,8),(3,9),(4,6),(5,7)]=>2
[(1,10),(2,7),(3,9),(4,6),(5,8)]=>2
[(1,9),(2,7),(3,10),(4,6),(5,8)]=>2
[(1,8),(2,7),(3,10),(4,6),(5,9)]=>2
[(1,7),(2,8),(3,10),(4,6),(5,9)]=>2
[(1,6),(2,8),(3,10),(4,7),(5,9)]=>2
[(1,5),(2,8),(3,10),(4,7),(6,9)]=>2
[(1,4),(2,8),(3,10),(5,7),(6,9)]=>2
[(1,3),(2,8),(4,10),(5,7),(6,9)]=>2
[(1,2),(3,8),(4,10),(5,7),(6,9)]=>2
[(1,2),(3,7),(4,10),(5,8),(6,9)]=>2
[(1,3),(2,7),(4,10),(5,8),(6,9)]=>2
[(1,4),(2,7),(3,10),(5,8),(6,9)]=>2
[(1,5),(2,7),(3,10),(4,8),(6,9)]=>2
[(1,6),(2,7),(3,10),(4,8),(5,9)]=>2
[(1,7),(2,6),(3,10),(4,8),(5,9)]=>2
[(1,8),(2,6),(3,10),(4,7),(5,9)]=>2
[(1,9),(2,6),(3,10),(4,7),(5,8)]=>2
[(1,10),(2,6),(3,9),(4,7),(5,8)]=>2
[(1,10),(2,5),(3,9),(4,7),(6,8)]=>2
[(1,9),(2,5),(3,10),(4,7),(6,8)]=>2
[(1,8),(2,5),(3,10),(4,7),(6,9)]=>2
[(1,7),(2,5),(3,10),(4,8),(6,9)]=>2
[(1,6),(2,5),(3,10),(4,8),(7,9)]=>4
[(1,5),(2,6),(3,10),(4,8),(7,9)]=>4
[(1,4),(2,6),(3,10),(5,8),(7,9)]=>4
[(1,3),(2,6),(4,10),(5,8),(7,9)]=>4
[(1,2),(3,6),(4,10),(5,8),(7,9)]=>4
[(1,2),(3,5),(4,10),(6,8),(7,9)]=>4
[(1,3),(2,5),(4,10),(6,8),(7,9)]=>4
[(1,4),(2,5),(3,10),(6,8),(7,9)]=>4
[(1,5),(2,4),(3,10),(6,8),(7,9)]=>4
[(1,6),(2,4),(3,10),(5,8),(7,9)]=>4
[(1,7),(2,4),(3,10),(5,8),(6,9)]=>2
[(1,8),(2,4),(3,10),(5,7),(6,9)]=>2
[(1,9),(2,4),(3,10),(5,7),(6,8)]=>2
[(1,10),(2,4),(3,9),(5,7),(6,8)]=>2
[(1,10),(2,3),(4,9),(5,7),(6,8)]=>2
[(1,9),(2,3),(4,10),(5,7),(6,8)]=>2
[(1,8),(2,3),(4,10),(5,7),(6,9)]=>2
[(1,7),(2,3),(4,10),(5,8),(6,9)]=>2
[(1,6),(2,3),(4,10),(5,8),(7,9)]=>4
[(1,5),(2,3),(4,10),(6,8),(7,9)]=>4
[(1,4),(2,3),(5,10),(6,8),(7,9)]=>4
[(1,3),(2,4),(5,10),(6,8),(7,9)]=>4
[(1,2),(3,4),(5,10),(6,8),(7,9)]=>4
[(1,2),(3,4),(5,9),(6,8),(7,10)]=>4
[(1,3),(2,4),(5,9),(6,8),(7,10)]=>4
[(1,4),(2,3),(5,9),(6,8),(7,10)]=>4
[(1,5),(2,3),(4,9),(6,8),(7,10)]=>4
[(1,6),(2,3),(4,9),(5,8),(7,10)]=>4
[(1,7),(2,3),(4,9),(5,8),(6,10)]=>2
[(1,8),(2,3),(4,9),(5,7),(6,10)]=>2
[(1,9),(2,3),(4,8),(5,7),(6,10)]=>2
[(1,10),(2,3),(4,8),(5,7),(6,9)]=>2
[(1,10),(2,4),(3,8),(5,7),(6,9)]=>2
[(1,9),(2,4),(3,8),(5,7),(6,10)]=>2
[(1,8),(2,4),(3,9),(5,7),(6,10)]=>2
[(1,7),(2,4),(3,9),(5,8),(6,10)]=>2
[(1,6),(2,4),(3,9),(5,8),(7,10)]=>4
[(1,5),(2,4),(3,9),(6,8),(7,10)]=>4
[(1,4),(2,5),(3,9),(6,8),(7,10)]=>4
[(1,3),(2,5),(4,9),(6,8),(7,10)]=>4
[(1,2),(3,5),(4,9),(6,8),(7,10)]=>4
[(1,2),(3,6),(4,9),(5,8),(7,10)]=>4
[(1,3),(2,6),(4,9),(5,8),(7,10)]=>4
[(1,4),(2,6),(3,9),(5,8),(7,10)]=>4
[(1,5),(2,6),(3,9),(4,8),(7,10)]=>4
[(1,6),(2,5),(3,9),(4,8),(7,10)]=>4
[(1,7),(2,5),(3,9),(4,8),(6,10)]=>2
[(1,8),(2,5),(3,9),(4,7),(6,10)]=>2
[(1,9),(2,5),(3,8),(4,7),(6,10)]=>2
[(1,10),(2,5),(3,8),(4,7),(6,9)]=>2
[(1,10),(2,6),(3,8),(4,7),(5,9)]=>2
[(1,9),(2,6),(3,8),(4,7),(5,10)]=>2
[(1,8),(2,6),(3,9),(4,7),(5,10)]=>2
[(1,7),(2,6),(3,9),(4,8),(5,10)]=>2
[(1,6),(2,7),(3,9),(4,8),(5,10)]=>2
[(1,5),(2,7),(3,9),(4,8),(6,10)]=>2
[(1,4),(2,7),(3,9),(5,8),(6,10)]=>2
[(1,3),(2,7),(4,9),(5,8),(6,10)]=>2
[(1,2),(3,7),(4,9),(5,8),(6,10)]=>2
[(1,2),(3,8),(4,9),(5,7),(6,10)]=>2
[(1,3),(2,8),(4,9),(5,7),(6,10)]=>2
[(1,4),(2,8),(3,9),(5,7),(6,10)]=>2
[(1,5),(2,8),(3,9),(4,7),(6,10)]=>2
[(1,6),(2,8),(3,9),(4,7),(5,10)]=>2
[(1,7),(2,8),(3,9),(4,6),(5,10)]=>2
[(1,8),(2,7),(3,9),(4,6),(5,10)]=>2
[(1,9),(2,7),(3,8),(4,6),(5,10)]=>2
[(1,10),(2,7),(3,8),(4,6),(5,9)]=>2
[(1,10),(2,8),(3,7),(4,6),(5,9)]=>2
[(1,9),(2,8),(3,7),(4,6),(5,10)]=>2
[(1,8),(2,9),(3,7),(4,6),(5,10)]=>2
[(1,7),(2,9),(3,8),(4,6),(5,10)]=>2
[(1,6),(2,9),(3,8),(4,7),(5,10)]=>2
[(1,5),(2,9),(3,8),(4,7),(6,10)]=>2
[(1,4),(2,9),(3,8),(5,7),(6,10)]=>2
[(1,3),(2,9),(4,8),(5,7),(6,10)]=>2
[(1,2),(3,9),(4,8),(5,7),(6,10)]=>2
[(1,2),(3,10),(4,8),(5,7),(6,9)]=>2
[(1,3),(2,10),(4,8),(5,7),(6,9)]=>2
[(1,4),(2,10),(3,8),(5,7),(6,9)]=>2
[(1,5),(2,10),(3,8),(4,7),(6,9)]=>2
[(1,6),(2,10),(3,8),(4,7),(5,9)]=>2
[(1,7),(2,10),(3,8),(4,6),(5,9)]=>2
[(1,8),(2,10),(3,7),(4,6),(5,9)]=>2
[(1,9),(2,10),(3,7),(4,6),(5,8)]=>2
[(1,10),(2,9),(3,7),(4,6),(5,8)]=>2
[(1,10),(2,9),(3,6),(4,7),(5,8)]=>2
[(1,9),(2,10),(3,6),(4,7),(5,8)]=>2
[(1,8),(2,10),(3,6),(4,7),(5,9)]=>2
[(1,7),(2,10),(3,6),(4,8),(5,9)]=>2
[(1,6),(2,10),(3,7),(4,8),(5,9)]=>2
[(1,5),(2,10),(3,7),(4,8),(6,9)]=>2
[(1,4),(2,10),(3,7),(5,8),(6,9)]=>2
[(1,3),(2,10),(4,7),(5,8),(6,9)]=>2
[(1,2),(3,10),(4,7),(5,8),(6,9)]=>2
[(1,2),(3,9),(4,7),(5,8),(6,10)]=>2
[(1,3),(2,9),(4,7),(5,8),(6,10)]=>2
[(1,4),(2,9),(3,7),(5,8),(6,10)]=>2
[(1,5),(2,9),(3,7),(4,8),(6,10)]=>2
[(1,6),(2,9),(3,7),(4,8),(5,10)]=>2
[(1,7),(2,9),(3,6),(4,8),(5,10)]=>2
[(1,8),(2,9),(3,6),(4,7),(5,10)]=>2
[(1,9),(2,8),(3,6),(4,7),(5,10)]=>2
[(1,10),(2,8),(3,6),(4,7),(5,9)]=>2
[(1,10),(2,7),(3,6),(4,8),(5,9)]=>2
[(1,9),(2,7),(3,6),(4,8),(5,10)]=>2
[(1,8),(2,7),(3,6),(4,9),(5,10)]=>2
[(1,7),(2,8),(3,6),(4,9),(5,10)]=>2
[(1,6),(2,8),(3,7),(4,9),(5,10)]=>2
[(1,5),(2,8),(3,7),(4,9),(6,10)]=>2
[(1,4),(2,8),(3,7),(5,9),(6,10)]=>2
[(1,3),(2,8),(4,7),(5,9),(6,10)]=>2
[(1,2),(3,8),(4,7),(5,9),(6,10)]=>2
[(1,2),(3,7),(4,8),(5,9),(6,10)]=>2
[(1,3),(2,7),(4,8),(5,9),(6,10)]=>2
[(1,4),(2,7),(3,8),(5,9),(6,10)]=>2
[(1,5),(2,7),(3,8),(4,9),(6,10)]=>2
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>2
[(1,7),(2,6),(3,8),(4,9),(5,10)]=>2
[(1,8),(2,6),(3,7),(4,9),(5,10)]=>2
[(1,9),(2,6),(3,7),(4,8),(5,10)]=>2
[(1,10),(2,6),(3,7),(4,8),(5,9)]=>2
[(1,10),(2,5),(3,7),(4,8),(6,9)]=>2
[(1,9),(2,5),(3,7),(4,8),(6,10)]=>2
[(1,8),(2,5),(3,7),(4,9),(6,10)]=>2
[(1,7),(2,5),(3,8),(4,9),(6,10)]=>2
[(1,6),(2,5),(3,8),(4,9),(7,10)]=>4
[(1,5),(2,6),(3,8),(4,9),(7,10)]=>4
[(1,4),(2,6),(3,8),(5,9),(7,10)]=>4
[(1,3),(2,6),(4,8),(5,9),(7,10)]=>4
[(1,2),(3,6),(4,8),(5,9),(7,10)]=>4
[(1,2),(3,5),(4,8),(6,9),(7,10)]=>4
[(1,3),(2,5),(4,8),(6,9),(7,10)]=>4
[(1,4),(2,5),(3,8),(6,9),(7,10)]=>4
[(1,5),(2,4),(3,8),(6,9),(7,10)]=>4
[(1,6),(2,4),(3,8),(5,9),(7,10)]=>4
[(1,7),(2,4),(3,8),(5,9),(6,10)]=>2
[(1,8),(2,4),(3,7),(5,9),(6,10)]=>2
[(1,9),(2,4),(3,7),(5,8),(6,10)]=>2
[(1,10),(2,4),(3,7),(5,8),(6,9)]=>2
[(1,10),(2,3),(4,7),(5,8),(6,9)]=>2
[(1,9),(2,3),(4,7),(5,8),(6,10)]=>2
[(1,8),(2,3),(4,7),(5,9),(6,10)]=>2
[(1,7),(2,3),(4,8),(5,9),(6,10)]=>2
[(1,6),(2,3),(4,8),(5,9),(7,10)]=>4
[(1,5),(2,3),(4,8),(6,9),(7,10)]=>4
[(1,4),(2,3),(5,8),(6,9),(7,10)]=>4
[(1,3),(2,4),(5,8),(6,9),(7,10)]=>4
[(1,2),(3,4),(5,8),(6,9),(7,10)]=>4
[(1,2),(3,4),(5,7),(6,9),(8,10)]=>4
[(1,3),(2,4),(5,7),(6,9),(8,10)]=>4
[(1,4),(2,3),(5,7),(6,9),(8,10)]=>4
[(1,5),(2,3),(4,7),(6,9),(8,10)]=>4
[(1,6),(2,3),(4,7),(5,9),(8,10)]=>4
[(1,7),(2,3),(4,6),(5,9),(8,10)]=>8
[(1,8),(2,3),(4,6),(5,9),(7,10)]=>4
[(1,9),(2,3),(4,6),(5,8),(7,10)]=>4
[(1,10),(2,3),(4,6),(5,8),(7,9)]=>4
[(1,10),(2,4),(3,6),(5,8),(7,9)]=>4
[(1,9),(2,4),(3,6),(5,8),(7,10)]=>4
[(1,8),(2,4),(3,6),(5,9),(7,10)]=>4
[(1,7),(2,4),(3,6),(5,9),(8,10)]=>8
[(1,6),(2,4),(3,7),(5,9),(8,10)]=>4
[(1,5),(2,4),(3,7),(6,9),(8,10)]=>4
[(1,4),(2,5),(3,7),(6,9),(8,10)]=>4
[(1,3),(2,5),(4,7),(6,9),(8,10)]=>4
[(1,2),(3,5),(4,7),(6,9),(8,10)]=>4
[(1,2),(3,6),(4,7),(5,9),(8,10)]=>4
[(1,3),(2,6),(4,7),(5,9),(8,10)]=>4
[(1,4),(2,6),(3,7),(5,9),(8,10)]=>4
[(1,5),(2,6),(3,7),(4,9),(8,10)]=>4
[(1,6),(2,5),(3,7),(4,9),(8,10)]=>4
[(1,7),(2,5),(3,6),(4,9),(8,10)]=>8
[(1,8),(2,5),(3,6),(4,9),(7,10)]=>4
[(1,9),(2,5),(3,6),(4,8),(7,10)]=>4
[(1,10),(2,5),(3,6),(4,8),(7,9)]=>4
[(1,10),(2,6),(3,5),(4,8),(7,9)]=>4
[(1,9),(2,6),(3,5),(4,8),(7,10)]=>4
[(1,8),(2,6),(3,5),(4,9),(7,10)]=>4
[(1,7),(2,6),(3,5),(4,9),(8,10)]=>8
[(1,6),(2,7),(3,5),(4,9),(8,10)]=>8
[(1,5),(2,7),(3,6),(4,9),(8,10)]=>8
[(1,4),(2,7),(3,6),(5,9),(8,10)]=>8
[(1,3),(2,7),(4,6),(5,9),(8,10)]=>8
[(1,2),(3,7),(4,6),(5,9),(8,10)]=>8
[(1,2),(3,8),(4,6),(5,9),(7,10)]=>4
[(1,3),(2,8),(4,6),(5,9),(7,10)]=>4
[(1,4),(2,8),(3,6),(5,9),(7,10)]=>4
[(1,5),(2,8),(3,6),(4,9),(7,10)]=>4
[(1,6),(2,8),(3,5),(4,9),(7,10)]=>4
[(1,7),(2,8),(3,5),(4,9),(6,10)]=>2
[(1,8),(2,7),(3,5),(4,9),(6,10)]=>2
[(1,9),(2,7),(3,5),(4,8),(6,10)]=>2
[(1,10),(2,7),(3,5),(4,8),(6,9)]=>2
[(1,10),(2,8),(3,5),(4,7),(6,9)]=>2
[(1,9),(2,8),(3,5),(4,7),(6,10)]=>2
[(1,8),(2,9),(3,5),(4,7),(6,10)]=>2
[(1,7),(2,9),(3,5),(4,8),(6,10)]=>2
[(1,6),(2,9),(3,5),(4,8),(7,10)]=>4
[(1,5),(2,9),(3,6),(4,8),(7,10)]=>4
[(1,4),(2,9),(3,6),(5,8),(7,10)]=>4
[(1,3),(2,9),(4,6),(5,8),(7,10)]=>4
[(1,2),(3,9),(4,6),(5,8),(7,10)]=>4
[(1,2),(3,10),(4,6),(5,8),(7,9)]=>4
[(1,3),(2,10),(4,6),(5,8),(7,9)]=>4
[(1,4),(2,10),(3,6),(5,8),(7,9)]=>4
[(1,5),(2,10),(3,6),(4,8),(7,9)]=>4
[(1,6),(2,10),(3,5),(4,8),(7,9)]=>4
[(1,7),(2,10),(3,5),(4,8),(6,9)]=>2
[(1,8),(2,10),(3,5),(4,7),(6,9)]=>2
[(1,9),(2,10),(3,5),(4,7),(6,8)]=>2
[(1,10),(2,9),(3,5),(4,7),(6,8)]=>2
[(1,10),(2,9),(3,4),(5,7),(6,8)]=>2
[(1,9),(2,10),(3,4),(5,7),(6,8)]=>2
[(1,8),(2,10),(3,4),(5,7),(6,9)]=>2
[(1,7),(2,10),(3,4),(5,8),(6,9)]=>2
[(1,6),(2,10),(3,4),(5,8),(7,9)]=>4
[(1,5),(2,10),(3,4),(6,8),(7,9)]=>4
[(1,4),(2,10),(3,5),(6,8),(7,9)]=>4
[(1,3),(2,10),(4,5),(6,8),(7,9)]=>4
[(1,2),(3,10),(4,5),(6,8),(7,9)]=>4
[(1,2),(3,9),(4,5),(6,8),(7,10)]=>4
[(1,3),(2,9),(4,5),(6,8),(7,10)]=>4
[(1,4),(2,9),(3,5),(6,8),(7,10)]=>4
[(1,5),(2,9),(3,4),(6,8),(7,10)]=>4
[(1,6),(2,9),(3,4),(5,8),(7,10)]=>4
[(1,7),(2,9),(3,4),(5,8),(6,10)]=>2
[(1,8),(2,9),(3,4),(5,7),(6,10)]=>2
[(1,9),(2,8),(3,4),(5,7),(6,10)]=>2
[(1,10),(2,8),(3,4),(5,7),(6,9)]=>2
[(1,10),(2,7),(3,4),(5,8),(6,9)]=>2
[(1,9),(2,7),(3,4),(5,8),(6,10)]=>2
[(1,8),(2,7),(3,4),(5,9),(6,10)]=>2
[(1,7),(2,8),(3,4),(5,9),(6,10)]=>2
[(1,6),(2,8),(3,4),(5,9),(7,10)]=>4
[(1,5),(2,8),(3,4),(6,9),(7,10)]=>4
[(1,4),(2,8),(3,5),(6,9),(7,10)]=>4
[(1,3),(2,8),(4,5),(6,9),(7,10)]=>4
[(1,2),(3,8),(4,5),(6,9),(7,10)]=>4
[(1,2),(3,7),(4,5),(6,9),(8,10)]=>8
[(1,3),(2,7),(4,5),(6,9),(8,10)]=>8
[(1,4),(2,7),(3,5),(6,9),(8,10)]=>8
[(1,5),(2,7),(3,4),(6,9),(8,10)]=>8
[(1,6),(2,7),(3,4),(5,9),(8,10)]=>8
[(1,7),(2,6),(3,4),(5,9),(8,10)]=>8
[(1,8),(2,6),(3,4),(5,9),(7,10)]=>4
[(1,9),(2,6),(3,4),(5,8),(7,10)]=>4
[(1,10),(2,6),(3,4),(5,8),(7,9)]=>4
[(1,10),(2,5),(3,4),(6,8),(7,9)]=>4
[(1,9),(2,5),(3,4),(6,8),(7,10)]=>4
[(1,8),(2,5),(3,4),(6,9),(7,10)]=>4
[(1,7),(2,5),(3,4),(6,9),(8,10)]=>8
[(1,6),(2,5),(3,4),(7,9),(8,10)]=>16
[(1,5),(2,6),(3,4),(7,9),(8,10)]=>16
[(1,4),(2,6),(3,5),(7,9),(8,10)]=>16
[(1,3),(2,6),(4,5),(7,9),(8,10)]=>16
[(1,2),(3,6),(4,5),(7,9),(8,10)]=>16
[(1,2),(3,5),(4,6),(7,9),(8,10)]=>16
[(1,3),(2,5),(4,6),(7,9),(8,10)]=>16
[(1,4),(2,5),(3,6),(7,9),(8,10)]=>16
[(1,5),(2,4),(3,6),(7,9),(8,10)]=>16
[(1,6),(2,4),(3,5),(7,9),(8,10)]=>16
[(1,7),(2,4),(3,5),(6,9),(8,10)]=>8
[(1,8),(2,4),(3,5),(6,9),(7,10)]=>4
[(1,9),(2,4),(3,5),(6,8),(7,10)]=>4
[(1,10),(2,4),(3,5),(6,8),(7,9)]=>4
[(1,10),(2,3),(4,5),(6,8),(7,9)]=>4
[(1,9),(2,3),(4,5),(6,8),(7,10)]=>4
[(1,8),(2,3),(4,5),(6,9),(7,10)]=>4
[(1,7),(2,3),(4,5),(6,9),(8,10)]=>8
[(1,6),(2,3),(4,5),(7,9),(8,10)]=>16
[(1,5),(2,3),(4,6),(7,9),(8,10)]=>16
[(1,4),(2,3),(5,6),(7,9),(8,10)]=>16
[(1,3),(2,4),(5,6),(7,9),(8,10)]=>16
[(1,2),(3,4),(5,6),(7,9),(8,10)]=>16
[(1,2),(3,4),(5,6),(7,10),(8,9)]=>16
[(1,3),(2,4),(5,6),(7,10),(8,9)]=>16
[(1,4),(2,3),(5,6),(7,10),(8,9)]=>16
[(1,5),(2,3),(4,6),(7,10),(8,9)]=>16
[(1,6),(2,3),(4,5),(7,10),(8,9)]=>16
[(1,7),(2,3),(4,5),(6,10),(8,9)]=>4
[(1,8),(2,3),(4,5),(6,10),(7,9)]=>4
[(1,9),(2,3),(4,5),(6,10),(7,8)]=>8
[(1,10),(2,3),(4,5),(6,9),(7,8)]=>8
[(1,10),(2,4),(3,5),(6,9),(7,8)]=>8
[(1,9),(2,4),(3,5),(6,10),(7,8)]=>8
[(1,8),(2,4),(3,5),(6,10),(7,9)]=>4
[(1,7),(2,4),(3,5),(6,10),(8,9)]=>4
[(1,6),(2,4),(3,5),(7,10),(8,9)]=>16
[(1,5),(2,4),(3,6),(7,10),(8,9)]=>16
[(1,4),(2,5),(3,6),(7,10),(8,9)]=>16
[(1,3),(2,5),(4,6),(7,10),(8,9)]=>16
[(1,2),(3,5),(4,6),(7,10),(8,9)]=>16
[(1,2),(3,6),(4,5),(7,10),(8,9)]=>16
[(1,3),(2,6),(4,5),(7,10),(8,9)]=>16
[(1,4),(2,6),(3,5),(7,10),(8,9)]=>16
[(1,5),(2,6),(3,4),(7,10),(8,9)]=>16
[(1,6),(2,5),(3,4),(7,10),(8,9)]=>16
[(1,7),(2,5),(3,4),(6,10),(8,9)]=>4
[(1,8),(2,5),(3,4),(6,10),(7,9)]=>4
[(1,9),(2,5),(3,4),(6,10),(7,8)]=>8
[(1,10),(2,5),(3,4),(6,9),(7,8)]=>8
[(1,10),(2,6),(3,4),(5,9),(7,8)]=>8
[(1,9),(2,6),(3,4),(5,10),(7,8)]=>8
[(1,8),(2,6),(3,4),(5,10),(7,9)]=>4
[(1,7),(2,6),(3,4),(5,10),(8,9)]=>4
[(1,6),(2,7),(3,4),(5,10),(8,9)]=>4
[(1,5),(2,7),(3,4),(6,10),(8,9)]=>4
[(1,4),(2,7),(3,5),(6,10),(8,9)]=>4
[(1,3),(2,7),(4,5),(6,10),(8,9)]=>4
[(1,2),(3,7),(4,5),(6,10),(8,9)]=>4
[(1,2),(3,8),(4,5),(6,10),(7,9)]=>4
[(1,3),(2,8),(4,5),(6,10),(7,9)]=>4
[(1,4),(2,8),(3,5),(6,10),(7,9)]=>4
[(1,5),(2,8),(3,4),(6,10),(7,9)]=>4
[(1,6),(2,8),(3,4),(5,10),(7,9)]=>4
[(1,7),(2,8),(3,4),(5,10),(6,9)]=>2
[(1,8),(2,7),(3,4),(5,10),(6,9)]=>2
[(1,9),(2,7),(3,4),(5,10),(6,8)]=>2
[(1,10),(2,7),(3,4),(5,9),(6,8)]=>2
[(1,10),(2,8),(3,4),(5,9),(6,7)]=>2
[(1,9),(2,8),(3,4),(5,10),(6,7)]=>2
[(1,8),(2,9),(3,4),(5,10),(6,7)]=>2
[(1,7),(2,9),(3,4),(5,10),(6,8)]=>2
[(1,6),(2,9),(3,4),(5,10),(7,8)]=>8
[(1,5),(2,9),(3,4),(6,10),(7,8)]=>8
[(1,4),(2,9),(3,5),(6,10),(7,8)]=>8
[(1,3),(2,9),(4,5),(6,10),(7,8)]=>8
[(1,2),(3,9),(4,5),(6,10),(7,8)]=>8
[(1,2),(3,10),(4,5),(6,9),(7,8)]=>8
[(1,3),(2,10),(4,5),(6,9),(7,8)]=>8
[(1,4),(2,10),(3,5),(6,9),(7,8)]=>8
[(1,5),(2,10),(3,4),(6,9),(7,8)]=>8
[(1,6),(2,10),(3,4),(5,9),(7,8)]=>8
[(1,7),(2,10),(3,4),(5,9),(6,8)]=>2
[(1,8),(2,10),(3,4),(5,9),(6,7)]=>2
[(1,9),(2,10),(3,4),(5,8),(6,7)]=>2
[(1,10),(2,9),(3,4),(5,8),(6,7)]=>2
[(1,10),(2,9),(3,5),(4,8),(6,7)]=>2
[(1,9),(2,10),(3,5),(4,8),(6,7)]=>2
[(1,8),(2,10),(3,5),(4,9),(6,7)]=>2
[(1,7),(2,10),(3,5),(4,9),(6,8)]=>2
[(1,6),(2,10),(3,5),(4,9),(7,8)]=>8
[(1,5),(2,10),(3,6),(4,9),(7,8)]=>8
[(1,4),(2,10),(3,6),(5,9),(7,8)]=>8
[(1,3),(2,10),(4,6),(5,9),(7,8)]=>8
[(1,2),(3,10),(4,6),(5,9),(7,8)]=>8
[(1,2),(3,9),(4,6),(5,10),(7,8)]=>8
[(1,3),(2,9),(4,6),(5,10),(7,8)]=>8
[(1,4),(2,9),(3,6),(5,10),(7,8)]=>8
[(1,5),(2,9),(3,6),(4,10),(7,8)]=>8
[(1,6),(2,9),(3,5),(4,10),(7,8)]=>8
[(1,7),(2,9),(3,5),(4,10),(6,8)]=>2
[(1,8),(2,9),(3,5),(4,10),(6,7)]=>2
[(1,9),(2,8),(3,5),(4,10),(6,7)]=>2
[(1,10),(2,8),(3,5),(4,9),(6,7)]=>2
[(1,10),(2,7),(3,5),(4,9),(6,8)]=>2
[(1,9),(2,7),(3,5),(4,10),(6,8)]=>2
[(1,8),(2,7),(3,5),(4,10),(6,9)]=>2
[(1,7),(2,8),(3,5),(4,10),(6,9)]=>2
[(1,6),(2,8),(3,5),(4,10),(7,9)]=>4
[(1,5),(2,8),(3,6),(4,10),(7,9)]=>4
[(1,4),(2,8),(3,6),(5,10),(7,9)]=>4
[(1,3),(2,8),(4,6),(5,10),(7,9)]=>4
[(1,2),(3,8),(4,6),(5,10),(7,9)]=>4
[(1,2),(3,7),(4,6),(5,10),(8,9)]=>4
[(1,3),(2,7),(4,6),(5,10),(8,9)]=>4
[(1,4),(2,7),(3,6),(5,10),(8,9)]=>4
[(1,5),(2,7),(3,6),(4,10),(8,9)]=>4
[(1,6),(2,7),(3,5),(4,10),(8,9)]=>4
[(1,7),(2,6),(3,5),(4,10),(8,9)]=>4
[(1,8),(2,6),(3,5),(4,10),(7,9)]=>4
[(1,9),(2,6),(3,5),(4,10),(7,8)]=>8
[(1,10),(2,6),(3,5),(4,9),(7,8)]=>8
[(1,10),(2,5),(3,6),(4,9),(7,8)]=>8
[(1,9),(2,5),(3,6),(4,10),(7,8)]=>8
[(1,8),(2,5),(3,6),(4,10),(7,9)]=>4
[(1,7),(2,5),(3,6),(4,10),(8,9)]=>4
[(1,6),(2,5),(3,7),(4,10),(8,9)]=>4
[(1,5),(2,6),(3,7),(4,10),(8,9)]=>4
[(1,4),(2,6),(3,7),(5,10),(8,9)]=>4
[(1,3),(2,6),(4,7),(5,10),(8,9)]=>4
[(1,2),(3,6),(4,7),(5,10),(8,9)]=>4
[(1,2),(3,5),(4,7),(6,10),(8,9)]=>4
[(1,3),(2,5),(4,7),(6,10),(8,9)]=>4
[(1,4),(2,5),(3,7),(6,10),(8,9)]=>4
[(1,5),(2,4),(3,7),(6,10),(8,9)]=>4
[(1,6),(2,4),(3,7),(5,10),(8,9)]=>4
[(1,7),(2,4),(3,6),(5,10),(8,9)]=>4
[(1,8),(2,4),(3,6),(5,10),(7,9)]=>4
[(1,9),(2,4),(3,6),(5,10),(7,8)]=>8
[(1,10),(2,4),(3,6),(5,9),(7,8)]=>8
[(1,10),(2,3),(4,6),(5,9),(7,8)]=>8
[(1,9),(2,3),(4,6),(5,10),(7,8)]=>8
[(1,8),(2,3),(4,6),(5,10),(7,9)]=>4
[(1,7),(2,3),(4,6),(5,10),(8,9)]=>4
[(1,6),(2,3),(4,7),(5,10),(8,9)]=>4
[(1,5),(2,3),(4,7),(6,10),(8,9)]=>4
[(1,4),(2,3),(5,7),(6,10),(8,9)]=>4
[(1,3),(2,4),(5,7),(6,10),(8,9)]=>4
[(1,2),(3,4),(5,7),(6,10),(8,9)]=>4
[(1,2),(3,4),(5,8),(6,10),(7,9)]=>4
[(1,3),(2,4),(5,8),(6,10),(7,9)]=>4
[(1,4),(2,3),(5,8),(6,10),(7,9)]=>4
[(1,5),(2,3),(4,8),(6,10),(7,9)]=>4
[(1,6),(2,3),(4,8),(5,10),(7,9)]=>4
[(1,7),(2,3),(4,8),(5,10),(6,9)]=>2
[(1,8),(2,3),(4,7),(5,10),(6,9)]=>2
[(1,9),(2,3),(4,7),(5,10),(6,8)]=>2
[(1,10),(2,3),(4,7),(5,9),(6,8)]=>2
[(1,10),(2,4),(3,7),(5,9),(6,8)]=>2
[(1,9),(2,4),(3,7),(5,10),(6,8)]=>2
[(1,8),(2,4),(3,7),(5,10),(6,9)]=>2
[(1,7),(2,4),(3,8),(5,10),(6,9)]=>2
[(1,6),(2,4),(3,8),(5,10),(7,9)]=>4
[(1,5),(2,4),(3,8),(6,10),(7,9)]=>4
[(1,4),(2,5),(3,8),(6,10),(7,9)]=>4
[(1,3),(2,5),(4,8),(6,10),(7,9)]=>4
[(1,2),(3,5),(4,8),(6,10),(7,9)]=>4
[(1,2),(3,6),(4,8),(5,10),(7,9)]=>4
[(1,3),(2,6),(4,8),(5,10),(7,9)]=>4
[(1,4),(2,6),(3,8),(5,10),(7,9)]=>4
[(1,5),(2,6),(3,8),(4,10),(7,9)]=>4
[(1,6),(2,5),(3,8),(4,10),(7,9)]=>4
[(1,7),(2,5),(3,8),(4,10),(6,9)]=>2
[(1,8),(2,5),(3,7),(4,10),(6,9)]=>2
[(1,9),(2,5),(3,7),(4,10),(6,8)]=>2
[(1,10),(2,5),(3,7),(4,9),(6,8)]=>2
[(1,10),(2,6),(3,7),(4,9),(5,8)]=>2
[(1,9),(2,6),(3,7),(4,10),(5,8)]=>2
[(1,8),(2,6),(3,7),(4,10),(5,9)]=>2
[(1,7),(2,6),(3,8),(4,10),(5,9)]=>2
[(1,6),(2,7),(3,8),(4,10),(5,9)]=>2
[(1,5),(2,7),(3,8),(4,10),(6,9)]=>2
[(1,4),(2,7),(3,8),(5,10),(6,9)]=>2
[(1,3),(2,7),(4,8),(5,10),(6,9)]=>2
[(1,2),(3,7),(4,8),(5,10),(6,9)]=>2
[(1,2),(3,8),(4,7),(5,10),(6,9)]=>2
[(1,3),(2,8),(4,7),(5,10),(6,9)]=>2
[(1,4),(2,8),(3,7),(5,10),(6,9)]=>2
[(1,5),(2,8),(3,7),(4,10),(6,9)]=>2
[(1,6),(2,8),(3,7),(4,10),(5,9)]=>2
[(1,7),(2,8),(3,6),(4,10),(5,9)]=>2
[(1,8),(2,7),(3,6),(4,10),(5,9)]=>2
[(1,9),(2,7),(3,6),(4,10),(5,8)]=>2
[(1,10),(2,7),(3,6),(4,9),(5,8)]=>2
[(1,10),(2,8),(3,6),(4,9),(5,7)]=>2
[(1,9),(2,8),(3,6),(4,10),(5,7)]=>2
[(1,8),(2,9),(3,6),(4,10),(5,7)]=>2
[(1,7),(2,9),(3,6),(4,10),(5,8)]=>2
[(1,6),(2,9),(3,7),(4,10),(5,8)]=>2
[(1,5),(2,9),(3,7),(4,10),(6,8)]=>2
[(1,4),(2,9),(3,7),(5,10),(6,8)]=>2
[(1,3),(2,9),(4,7),(5,10),(6,8)]=>2
[(1,2),(3,9),(4,7),(5,10),(6,8)]=>2
[(1,2),(3,10),(4,7),(5,9),(6,8)]=>2
[(1,3),(2,10),(4,7),(5,9),(6,8)]=>2
[(1,4),(2,10),(3,7),(5,9),(6,8)]=>2
[(1,5),(2,10),(3,7),(4,9),(6,8)]=>2
[(1,6),(2,10),(3,7),(4,9),(5,8)]=>2
[(1,7),(2,10),(3,6),(4,9),(5,8)]=>2
[(1,8),(2,10),(3,6),(4,9),(5,7)]=>2
[(1,9),(2,10),(3,6),(4,8),(5,7)]=>2
[(1,10),(2,9),(3,6),(4,8),(5,7)]=>2
[(1,10),(2,9),(3,7),(4,8),(5,6)]=>2
[(1,9),(2,10),(3,7),(4,8),(5,6)]=>2
[(1,8),(2,10),(3,7),(4,9),(5,6)]=>2
[(1,7),(2,10),(3,8),(4,9),(5,6)]=>2
[(1,6),(2,10),(3,8),(4,9),(5,7)]=>2
[(1,5),(2,10),(3,8),(4,9),(6,7)]=>2
[(1,4),(2,10),(3,8),(5,9),(6,7)]=>2
[(1,3),(2,10),(4,8),(5,9),(6,7)]=>2
[(1,2),(3,10),(4,8),(5,9),(6,7)]=>2
[(1,2),(3,9),(4,8),(5,10),(6,7)]=>2
[(1,3),(2,9),(4,8),(5,10),(6,7)]=>2
[(1,4),(2,9),(3,8),(5,10),(6,7)]=>2
[(1,5),(2,9),(3,8),(4,10),(6,7)]=>2
[(1,6),(2,9),(3,8),(4,10),(5,7)]=>2
[(1,7),(2,9),(3,8),(4,10),(5,6)]=>2
[(1,8),(2,9),(3,7),(4,10),(5,6)]=>2
[(1,9),(2,8),(3,7),(4,10),(5,6)]=>2
[(1,10),(2,8),(3,7),(4,9),(5,6)]=>2
[(1,10),(2,7),(3,8),(4,9),(5,6)]=>2
[(1,9),(2,7),(3,8),(4,10),(5,6)]=>2
[(1,8),(2,7),(3,9),(4,10),(5,6)]=>2
[(1,7),(2,8),(3,9),(4,10),(5,6)]=>2
[(1,6),(2,8),(3,9),(4,10),(5,7)]=>2
[(1,5),(2,8),(3,9),(4,10),(6,7)]=>2
[(1,4),(2,8),(3,9),(5,10),(6,7)]=>2
[(1,3),(2,8),(4,9),(5,10),(6,7)]=>2
[(1,2),(3,8),(4,9),(5,10),(6,7)]=>2
[(1,2),(3,7),(4,9),(5,10),(6,8)]=>2
[(1,3),(2,7),(4,9),(5,10),(6,8)]=>2
[(1,4),(2,7),(3,9),(5,10),(6,8)]=>2
[(1,5),(2,7),(3,9),(4,10),(6,8)]=>2
[(1,6),(2,7),(3,9),(4,10),(5,8)]=>2
[(1,7),(2,6),(3,9),(4,10),(5,8)]=>2
[(1,8),(2,6),(3,9),(4,10),(5,7)]=>2
[(1,9),(2,6),(3,8),(4,10),(5,7)]=>2
[(1,10),(2,6),(3,8),(4,9),(5,7)]=>2
[(1,10),(2,5),(3,8),(4,9),(6,7)]=>2
[(1,9),(2,5),(3,8),(4,10),(6,7)]=>2
[(1,8),(2,5),(3,9),(4,10),(6,7)]=>2
[(1,7),(2,5),(3,9),(4,10),(6,8)]=>2
[(1,6),(2,5),(3,9),(4,10),(7,8)]=>8
[(1,5),(2,6),(3,9),(4,10),(7,8)]=>8
[(1,4),(2,6),(3,9),(5,10),(7,8)]=>8
[(1,3),(2,6),(4,9),(5,10),(7,8)]=>8
[(1,2),(3,6),(4,9),(5,10),(7,8)]=>8
[(1,2),(3,5),(4,9),(6,10),(7,8)]=>8
[(1,3),(2,5),(4,9),(6,10),(7,8)]=>8
[(1,4),(2,5),(3,9),(6,10),(7,8)]=>8
[(1,5),(2,4),(3,9),(6,10),(7,8)]=>8
[(1,6),(2,4),(3,9),(5,10),(7,8)]=>8
[(1,7),(2,4),(3,9),(5,10),(6,8)]=>2
[(1,8),(2,4),(3,9),(5,10),(6,7)]=>2
[(1,9),(2,4),(3,8),(5,10),(6,7)]=>2
[(1,10),(2,4),(3,8),(5,9),(6,7)]=>2
[(1,10),(2,3),(4,8),(5,9),(6,7)]=>2
[(1,9),(2,3),(4,8),(5,10),(6,7)]=>2
[(1,8),(2,3),(4,9),(5,10),(6,7)]=>2
[(1,7),(2,3),(4,9),(5,10),(6,8)]=>2
[(1,6),(2,3),(4,9),(5,10),(7,8)]=>8
[(1,5),(2,3),(4,9),(6,10),(7,8)]=>8
[(1,4),(2,3),(5,9),(6,10),(7,8)]=>8
[(1,3),(2,4),(5,9),(6,10),(7,8)]=>8
[(1,2),(3,4),(5,9),(6,10),(7,8)]=>8
[(1,2),(3,4),(5,10),(6,9),(7,8)]=>8
[(1,3),(2,4),(5,10),(6,9),(7,8)]=>8
[(1,4),(2,3),(5,10),(6,9),(7,8)]=>8
[(1,5),(2,3),(4,10),(6,9),(7,8)]=>8
[(1,6),(2,3),(4,10),(5,9),(7,8)]=>8
[(1,7),(2,3),(4,10),(5,9),(6,8)]=>2
[(1,8),(2,3),(4,10),(5,9),(6,7)]=>2
[(1,9),(2,3),(4,10),(5,8),(6,7)]=>2
[(1,10),(2,3),(4,9),(5,8),(6,7)]=>2
[(1,10),(2,4),(3,9),(5,8),(6,7)]=>2
[(1,9),(2,4),(3,10),(5,8),(6,7)]=>2
[(1,8),(2,4),(3,10),(5,9),(6,7)]=>2
[(1,7),(2,4),(3,10),(5,9),(6,8)]=>2
[(1,6),(2,4),(3,10),(5,9),(7,8)]=>8
[(1,5),(2,4),(3,10),(6,9),(7,8)]=>8
[(1,4),(2,5),(3,10),(6,9),(7,8)]=>8
[(1,3),(2,5),(4,10),(6,9),(7,8)]=>8
[(1,2),(3,5),(4,10),(6,9),(7,8)]=>8
[(1,2),(3,6),(4,10),(5,9),(7,8)]=>8
[(1,3),(2,6),(4,10),(5,9),(7,8)]=>8
[(1,4),(2,6),(3,10),(5,9),(7,8)]=>8
[(1,5),(2,6),(3,10),(4,9),(7,8)]=>8
[(1,6),(2,5),(3,10),(4,9),(7,8)]=>8
[(1,7),(2,5),(3,10),(4,9),(6,8)]=>2
[(1,8),(2,5),(3,10),(4,9),(6,7)]=>2
[(1,9),(2,5),(3,10),(4,8),(6,7)]=>2
[(1,10),(2,5),(3,9),(4,8),(6,7)]=>2
[(1,10),(2,6),(3,9),(4,8),(5,7)]=>2
[(1,9),(2,6),(3,10),(4,8),(5,7)]=>2
[(1,8),(2,6),(3,10),(4,9),(5,7)]=>2
[(1,7),(2,6),(3,10),(4,9),(5,8)]=>2
[(1,6),(2,7),(3,10),(4,9),(5,8)]=>2
[(1,5),(2,7),(3,10),(4,9),(6,8)]=>2
[(1,4),(2,7),(3,10),(5,9),(6,8)]=>2
[(1,3),(2,7),(4,10),(5,9),(6,8)]=>2
[(1,2),(3,7),(4,10),(5,9),(6,8)]=>2
[(1,2),(3,8),(4,10),(5,9),(6,7)]=>2
[(1,3),(2,8),(4,10),(5,9),(6,7)]=>2
[(1,4),(2,8),(3,10),(5,9),(6,7)]=>2
[(1,5),(2,8),(3,10),(4,9),(6,7)]=>2
[(1,6),(2,8),(3,10),(4,9),(5,7)]=>2
[(1,7),(2,8),(3,10),(4,9),(5,6)]=>2
[(1,8),(2,7),(3,10),(4,9),(5,6)]=>2
[(1,9),(2,7),(3,10),(4,8),(5,6)]=>2
[(1,10),(2,7),(3,9),(4,8),(5,6)]=>2
[(1,10),(2,8),(3,9),(4,7),(5,6)]=>2
[(1,9),(2,8),(3,10),(4,7),(5,6)]=>2
[(1,8),(2,9),(3,10),(4,7),(5,6)]=>2
[(1,7),(2,9),(3,10),(4,8),(5,6)]=>2
[(1,6),(2,9),(3,10),(4,8),(5,7)]=>2
[(1,5),(2,9),(3,10),(4,8),(6,7)]=>2
[(1,4),(2,9),(3,10),(5,8),(6,7)]=>2
[(1,3),(2,9),(4,10),(5,8),(6,7)]=>2
[(1,2),(3,9),(4,10),(5,8),(6,7)]=>2
[(1,2),(3,10),(4,9),(5,8),(6,7)]=>2
[(1,3),(2,10),(4,9),(5,8),(6,7)]=>2
[(1,4),(2,10),(3,9),(5,8),(6,7)]=>2
[(1,5),(2,10),(3,9),(4,8),(6,7)]=>2
[(1,6),(2,10),(3,9),(4,8),(5,7)]=>2
[(1,7),(2,10),(3,9),(4,8),(5,6)]=>2
[(1,8),(2,10),(3,9),(4,7),(5,6)]=>2
[(1,9),(2,10),(3,8),(4,7),(5,6)]=>2
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>2
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>8
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>8
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>16
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>16
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>16
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>16
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>8
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>4
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>8
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>4
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>16
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>16
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>16
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>8
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)]=>8
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]=>16
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)]=>8
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)]=>8
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)]=>16
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)]=>8
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)]=>16
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)]=>8
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)]=>8
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)]=>4
[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)]=>4
[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)]=>4
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)]=>4
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)]=>16
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)]=>8
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)]=>16
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)]=>8
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)]=>8
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)]=>16
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)]=>8
[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)]=>16
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)]=>8
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)]=>8
[(1,2),(3,4),(5,6),(7,9),(8,12),(10,11)]=>8
[(1,2),(3,4),(5,6),(7,10),(8,12),(9,11)]=>8
[(1,2),(3,4),(5,6),(7,11),(8,9),(10,12)]=>16
[(1,2),(3,4),(5,6),(7,11),(8,10),(9,12)]=>16
[(1,2),(3,4),(5,6),(7,11),(8,12),(9,10)]=>16
[(1,2),(3,4),(5,6),(7,12),(8,10),(9,11)]=>16
[(1,2),(3,4),(5,7),(6,8),(9,12),(10,11)]=>8
[(1,2),(3,4),(5,7),(6,9),(8,12),(10,11)]=>8
[(1,2),(3,4),(5,7),(6,10),(8,9),(11,12)]=>16
[(1,2),(3,4),(5,7),(6,10),(8,12),(9,11)]=>8
[(1,2),(3,4),(5,7),(6,11),(8,9),(10,12)]=>16
[(1,2),(3,4),(5,7),(6,11),(8,10),(9,12)]=>16
[(1,2),(3,4),(5,7),(6,11),(8,12),(9,10)]=>16
[(1,2),(3,4),(5,7),(6,12),(8,9),(10,11)]=>16
[(1,2),(3,4),(5,7),(6,12),(8,10),(9,11)]=>16
[(1,2),(3,4),(5,7),(6,12),(8,11),(9,10)]=>16
[(1,2),(3,4),(5,8),(6,7),(9,11),(10,12)]=>16
[(1,2),(3,4),(5,8),(6,9),(7,12),(10,11)]=>8
[(1,2),(3,4),(5,8),(6,10),(7,12),(9,11)]=>4
[(1,2),(3,4),(5,8),(6,10),(7,9),(11,12)]=>4
[(1,2),(3,4),(5,8),(6,11),(7,12),(9,10)]=>4
[(1,2),(3,4),(5,8),(6,11),(7,10),(9,12)]=>4
[(1,2),(3,4),(5,8),(6,11),(7,9),(10,12)]=>4
[(1,2),(3,4),(5,8),(6,12),(7,11),(9,10)]=>4
[(1,2),(3,4),(5,8),(6,12),(7,10),(9,11)]=>4
[(1,2),(3,4),(5,8),(6,12),(7,9),(10,11)]=>8
[(1,2),(3,4),(5,9),(6,7),(8,10),(11,12)]=>8
[(1,2),(3,4),(5,9),(6,7),(8,11),(10,12)]=>16
[(1,2),(3,4),(5,9),(6,7),(8,12),(10,11)]=>8
[(1,2),(3,4),(5,9),(6,8),(7,12),(10,11)]=>8
[(1,2),(3,4),(5,9),(6,8),(7,11),(10,12)]=>4
[(1,2),(3,4),(5,9),(6,8),(7,10),(11,12)]=>4
[(1,2),(3,4),(5,9),(6,10),(7,12),(8,11)]=>4
[(1,2),(3,4),(5,9),(6,10),(7,8),(11,12)]=>4
[(1,2),(3,4),(5,9),(6,11),(7,12),(8,10)]=>4
[(1,2),(3,4),(5,9),(6,11),(7,10),(8,12)]=>4
[(1,2),(3,4),(5,9),(6,11),(7,8),(10,12)]=>4
[(1,2),(3,4),(5,9),(6,12),(7,11),(8,10)]=>4
[(1,2),(3,4),(5,9),(6,12),(7,10),(8,11)]=>4
[(1,2),(3,4),(5,9),(6,12),(7,8),(10,11)]=>8
[(1,2),(3,4),(5,10),(6,7),(8,11),(9,12)]=>8
[(1,2),(3,4),(5,10),(6,7),(8,12),(9,11)]=>8
[(1,2),(3,4),(5,10),(6,8),(7,12),(9,11)]=>4
[(1,2),(3,4),(5,10),(6,8),(7,11),(9,12)]=>4
[(1,2),(3,4),(5,10),(6,8),(7,9),(11,12)]=>4
[(1,2),(3,4),(5,10),(6,9),(7,12),(8,11)]=>4
[(1,2),(3,4),(5,10),(6,9),(7,11),(8,12)]=>4
[(1,2),(3,4),(5,10),(6,11),(7,12),(8,9)]=>8
[(1,2),(3,4),(5,10),(6,11),(7,9),(8,12)]=>4
[(1,2),(3,4),(5,10),(6,11),(7,8),(9,12)]=>4
[(1,2),(3,4),(5,10),(6,12),(7,11),(8,9)]=>8
[(1,2),(3,4),(5,10),(6,12),(7,9),(8,11)]=>4
[(1,2),(3,4),(5,10),(6,12),(7,8),(9,11)]=>4
[(1,2),(3,4),(5,11),(6,7),(8,9),(10,12)]=>16
[(1,2),(3,4),(5,11),(6,7),(8,10),(9,12)]=>16
[(1,2),(3,4),(5,11),(6,7),(8,12),(9,10)]=>16
[(1,2),(3,4),(5,11),(6,8),(7,12),(9,10)]=>4
[(1,2),(3,4),(5,11),(6,8),(7,10),(9,12)]=>4
[(1,2),(3,4),(5,11),(6,8),(7,9),(10,12)]=>4
[(1,2),(3,4),(5,11),(6,9),(7,12),(8,10)]=>4
[(1,2),(3,4),(5,11),(6,9),(7,10),(8,12)]=>4
[(1,2),(3,4),(5,11),(6,9),(7,8),(10,12)]=>4
[(1,2),(3,4),(5,11),(6,10),(7,12),(8,9)]=>8
[(1,2),(3,4),(5,11),(6,10),(7,9),(8,12)]=>4
[(1,2),(3,4),(5,11),(6,10),(7,8),(9,12)]=>4
[(1,2),(3,4),(5,11),(6,12),(7,10),(8,9)]=>8
[(1,2),(3,4),(5,11),(6,12),(7,9),(8,10)]=>4
[(1,2),(3,4),(5,11),(6,12),(7,8),(9,10)]=>4
[(1,2),(3,4),(5,12),(6,7),(8,10),(9,11)]=>16
[(1,2),(3,4),(5,12),(6,8),(7,11),(9,10)]=>4
[(1,2),(3,4),(5,12),(6,8),(7,10),(9,11)]=>4
[(1,2),(3,4),(5,12),(6,8),(7,9),(10,11)]=>8
[(1,2),(3,4),(5,12),(6,9),(7,11),(8,10)]=>4
[(1,2),(3,4),(5,12),(6,9),(7,10),(8,11)]=>4
[(1,2),(3,4),(5,12),(6,10),(7,11),(8,9)]=>8
[(1,2),(3,4),(5,12),(6,10),(7,9),(8,11)]=>4
[(1,2),(3,4),(5,12),(6,10),(7,8),(9,11)]=>4
[(1,2),(3,4),(5,12),(6,11),(7,9),(8,10)]=>4
[(1,2),(3,5),(4,6),(7,8),(9,12),(10,11)]=>8
[(1,2),(3,5),(4,6),(7,9),(8,12),(10,11)]=>8
[(1,2),(3,5),(4,6),(7,10),(8,9),(11,12)]=>16
[(1,2),(3,5),(4,6),(7,10),(8,12),(9,11)]=>8
[(1,2),(3,5),(4,6),(7,11),(8,9),(10,12)]=>16
[(1,2),(3,5),(4,6),(7,11),(8,10),(9,12)]=>16
[(1,2),(3,5),(4,6),(7,11),(8,12),(9,10)]=>16
[(1,2),(3,5),(4,6),(7,12),(8,9),(10,11)]=>16
[(1,2),(3,5),(4,6),(7,12),(8,10),(9,11)]=>16
[(1,2),(3,5),(4,6),(7,12),(8,11),(9,10)]=>16
[(1,2),(3,5),(4,7),(6,8),(9,12),(10,11)]=>8
[(1,2),(3,5),(4,7),(6,9),(8,12),(10,11)]=>8
[(1,2),(3,5),(4,7),(6,10),(8,9),(11,12)]=>16
[(1,2),(3,5),(4,7),(6,10),(8,12),(9,11)]=>8
[(1,2),(3,5),(4,7),(6,11),(8,9),(10,12)]=>16
[(1,2),(3,5),(4,7),(6,11),(8,10),(9,12)]=>16
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Description
The size of the automorphism group of the leaf labelled binary unordered tree associated with the perfect matching.
The bijection between perfect matchings of $\{1,\dots,2n\}$ and trees with $n+1$ leaves is described in Example 5.2.6 of [1]. This statistic is the number of permutations on $n+1$ letters acting trivially on the tree.
The bijection between perfect matchings of $\{1,\dots,2n\}$ and trees with $n+1$ leaves is described in Example 5.2.6 of [1]. This statistic is the number of permutations on $n+1$ letters acting trivially on the tree.
References
[1] Stanley, R. P. Enumerative combinatorics. Vol. 2 MathSciNet:1676282
Code
def statistic(m):
def aux(T):
if T.node_number() == 1:
return 1
if T[0] == T[1]:
return 2*aux(T[0])^2
return aux(T[0])*aux(T[1])
return aux(matching_to_tree(m).shape())
def matching_to_tree(m):
"""
INPUT:
- m, a PerfectMatching on {1,...,2n}.
OUTPUT:
a decreasingly labelled, unordered full binary tree with n+1 leaves.
EXAMPLES::
sage: m = PerfectMatching([(1,4),(2,9),(3,10),(5,7),(6,8),(11,12)])
sage: ascii_art(matching_to_tree(m))
"""
if not m:
return LabelledRootedTree([])
# the children of the smallest label are the largest remaining
# element and its partner
trees = [LabelledRootedTree([LabelledRootedTree([], label=i),
LabelledRootedTree([], label=j)]) for i, j in m]
max_label = m.size()//2+1 # last labelled node
while len(trees) > 1:
max_label += 1
# find tree with smallest child and both children smaller than max_label
A = sorted([T for T in trees if max(T[0].label(), T[1].label()) < max_label],
key = lambda T: min(T[0].label(), T[1].label()))[0]
trees.remove(A)
# give it's root node the new label
A = LabelledRootedTree(A, label=max_label)
# find tree with child having label max_label
B = next(T for T in trees
if T[0].label() == max_label or T[1].label() == max_label)
trees.remove(B)
# replace B with [B[0], A] or [B[1], A]
if B[0].label() == max_label:
C = LabelledRootedTree([A, B[1]])
else:
C = LabelledRootedTree([A, B[0]])
trees.append(C)
return trees[0]
Created
Nov 08, 2017 at 21:10 by Martin Rubey
Updated
Feb 02, 2023 at 23:32 by Martin Rubey
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