- FindStat

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Identifier

St001830: Perfect matchings ⟶ ℤ

Values

=>
                            Cc0012;cc-rep
                            
                            
                            

                        [(1,2)]=>1
[(1,2),(3,4)]=>1
[(1,3),(2,4)]=>2
[(1,4),(2,3)]=>1
[(1,2),(3,4),(5,6)]=>1
[(1,3),(2,4),(5,6)]=>2
[(1,4),(2,3),(5,6)]=>1
[(1,5),(2,3),(4,6)]=>2
[(1,6),(2,3),(4,5)]=>1
[(1,6),(2,4),(3,5)]=>2
[(1,5),(2,4),(3,6)]=>4
[(1,4),(2,5),(3,6)]=>5
[(1,3),(2,5),(4,6)]=>4
[(1,2),(3,5),(4,6)]=>2
[(1,2),(3,6),(4,5)]=>1
[(1,3),(2,6),(4,5)]=>2
[(1,4),(2,6),(3,5)]=>4
[(1,5),(2,6),(3,4)]=>2
[(1,6),(2,5),(3,4)]=>1
[(1,2),(3,4),(5,6),(7,8)]=>1
[(1,3),(2,4),(5,6),(7,8)]=>2
[(1,4),(2,3),(5,6),(7,8)]=>1
[(1,5),(2,3),(4,6),(7,8)]=>2
[(1,6),(2,3),(4,5),(7,8)]=>1
[(1,7),(2,3),(4,5),(6,8)]=>2
[(1,8),(2,3),(4,5),(6,7)]=>1
[(1,8),(2,4),(3,5),(6,7)]=>2
[(1,7),(2,4),(3,5),(6,8)]=>4
[(1,6),(2,4),(3,5),(7,8)]=>2
[(1,5),(2,4),(3,6),(7,8)]=>4
[(1,4),(2,5),(3,6),(7,8)]=>5
[(1,3),(2,5),(4,6),(7,8)]=>4
[(1,2),(3,5),(4,6),(7,8)]=>2
[(1,2),(3,6),(4,5),(7,8)]=>1
[(1,3),(2,6),(4,5),(7,8)]=>2
[(1,4),(2,6),(3,5),(7,8)]=>4
[(1,5),(2,6),(3,4),(7,8)]=>2
[(1,6),(2,5),(3,4),(7,8)]=>1
[(1,7),(2,5),(3,4),(6,8)]=>2
[(1,8),(2,5),(3,4),(6,7)]=>1
[(1,8),(2,6),(3,4),(5,7)]=>2
[(1,7),(2,6),(3,4),(5,8)]=>4
[(1,6),(2,7),(3,4),(5,8)]=>5
[(1,5),(2,7),(3,4),(6,8)]=>4
[(1,4),(2,7),(3,5),(6,8)]=>8
[(1,3),(2,7),(4,5),(6,8)]=>4
[(1,2),(3,7),(4,5),(6,8)]=>2
[(1,2),(3,8),(4,5),(6,7)]=>1
[(1,3),(2,8),(4,5),(6,7)]=>2
[(1,4),(2,8),(3,5),(6,7)]=>4
[(1,5),(2,8),(3,4),(6,7)]=>2
[(1,6),(2,8),(3,4),(5,7)]=>4
[(1,7),(2,8),(3,4),(5,6)]=>2
[(1,8),(2,7),(3,4),(5,6)]=>1
[(1,8),(2,7),(3,5),(4,6)]=>2
[(1,7),(2,8),(3,5),(4,6)]=>4
[(1,6),(2,8),(3,5),(4,7)]=>8
[(1,5),(2,8),(3,6),(4,7)]=>10
[(1,4),(2,8),(3,6),(5,7)]=>8
[(1,3),(2,8),(4,6),(5,7)]=>4
[(1,2),(3,8),(4,6),(5,7)]=>2
[(1,2),(3,7),(4,6),(5,8)]=>4
[(1,3),(2,7),(4,6),(5,8)]=>8
[(1,4),(2,7),(3,6),(5,8)]=>13
[(1,5),(2,7),(3,6),(4,8)]=>14
[(1,6),(2,7),(3,5),(4,8)]=>10
[(1,7),(2,6),(3,5),(4,8)]=>8
[(1,8),(2,6),(3,5),(4,7)]=>4
[(1,8),(2,5),(3,6),(4,7)]=>5
[(1,7),(2,5),(3,6),(4,8)]=>10
[(1,6),(2,5),(3,7),(4,8)]=>14
[(1,5),(2,6),(3,7),(4,8)]=>16
[(1,4),(2,6),(3,7),(5,8)]=>14
[(1,3),(2,6),(4,7),(5,8)]=>10
[(1,2),(3,6),(4,7),(5,8)]=>5
[(1,2),(3,5),(4,7),(6,8)]=>4
[(1,3),(2,5),(4,7),(6,8)]=>8
[(1,4),(2,5),(3,7),(6,8)]=>10
[(1,5),(2,4),(3,7),(6,8)]=>8
[(1,6),(2,4),(3,7),(5,8)]=>10
[(1,7),(2,4),(3,6),(5,8)]=>8
[(1,8),(2,4),(3,6),(5,7)]=>4
[(1,8),(2,3),(4,6),(5,7)]=>2
[(1,7),(2,3),(4,6),(5,8)]=>4
[(1,6),(2,3),(4,7),(5,8)]=>5
[(1,5),(2,3),(4,7),(6,8)]=>4
[(1,4),(2,3),(5,7),(6,8)]=>2
[(1,3),(2,4),(5,7),(6,8)]=>4
[(1,2),(3,4),(5,7),(6,8)]=>2
[(1,2),(3,4),(5,8),(6,7)]=>1
[(1,3),(2,4),(5,8),(6,7)]=>2
[(1,4),(2,3),(5,8),(6,7)]=>1
[(1,5),(2,3),(4,8),(6,7)]=>2
[(1,6),(2,3),(4,8),(5,7)]=>4
[(1,7),(2,3),(4,8),(5,6)]=>2
[(1,8),(2,3),(4,7),(5,6)]=>1
[(1,8),(2,4),(3,7),(5,6)]=>2
[(1,7),(2,4),(3,8),(5,6)]=>4
[(1,6),(2,4),(3,8),(5,7)]=>8
[(1,5),(2,4),(3,8),(6,7)]=>4
[(1,4),(2,5),(3,8),(6,7)]=>5
[(1,3),(2,5),(4,8),(6,7)]=>4
[(1,2),(3,5),(4,8),(6,7)]=>2
[(1,2),(3,6),(4,8),(5,7)]=>4
[(1,3),(2,6),(4,8),(5,7)]=>8
[(1,4),(2,6),(3,8),(5,7)]=>10
[(1,5),(2,6),(3,8),(4,7)]=>14
[(1,6),(2,5),(3,8),(4,7)]=>13
[(1,7),(2,5),(3,8),(4,6)]=>8
[(1,8),(2,5),(3,7),(4,6)]=>4
[(1,8),(2,6),(3,7),(4,5)]=>2
[(1,7),(2,6),(3,8),(4,5)]=>4
[(1,6),(2,7),(3,8),(4,5)]=>5
[(1,5),(2,7),(3,8),(4,6)]=>10
[(1,4),(2,7),(3,8),(5,6)]=>5
[(1,3),(2,7),(4,8),(5,6)]=>4
[(1,2),(3,7),(4,8),(5,6)]=>2
[(1,2),(3,8),(4,7),(5,6)]=>1
[(1,3),(2,8),(4,7),(5,6)]=>2
[(1,4),(2,8),(3,7),(5,6)]=>4
[(1,5),(2,8),(3,7),(4,6)]=>8
[(1,6),(2,8),(3,7),(4,5)]=>4
[(1,7),(2,8),(3,6),(4,5)]=>2
[(1,8),(2,7),(3,6),(4,5)]=>1
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>1
[(1,3),(2,4),(5,6),(7,8),(9,10)]=>2
[(1,4),(2,3),(5,6),(7,8),(9,10)]=>1
[(1,5),(2,3),(4,6),(7,8),(9,10)]=>2
[(1,6),(2,3),(4,5),(7,8),(9,10)]=>1
[(1,7),(2,3),(4,5),(6,8),(9,10)]=>2
[(1,8),(2,3),(4,5),(6,7),(9,10)]=>1
[(1,9),(2,3),(4,5),(6,7),(8,10)]=>2
[(1,10),(2,3),(4,5),(6,7),(8,9)]=>1
[(1,10),(2,4),(3,5),(6,7),(8,9)]=>2
[(1,9),(2,4),(3,5),(6,7),(8,10)]=>4
[(1,8),(2,4),(3,5),(6,7),(9,10)]=>2
[(1,7),(2,4),(3,5),(6,8),(9,10)]=>4
[(1,6),(2,4),(3,5),(7,8),(9,10)]=>2
[(1,5),(2,4),(3,6),(7,8),(9,10)]=>4
[(1,4),(2,5),(3,6),(7,8),(9,10)]=>5
[(1,3),(2,5),(4,6),(7,8),(9,10)]=>4
[(1,2),(3,5),(4,6),(7,8),(9,10)]=>2
[(1,2),(3,6),(4,5),(7,8),(9,10)]=>1
[(1,3),(2,6),(4,5),(7,8),(9,10)]=>2
[(1,4),(2,6),(3,5),(7,8),(9,10)]=>4
[(1,5),(2,6),(3,4),(7,8),(9,10)]=>2
[(1,6),(2,5),(3,4),(7,8),(9,10)]=>1
[(1,7),(2,5),(3,4),(6,8),(9,10)]=>2
[(1,8),(2,5),(3,4),(6,7),(9,10)]=>1
[(1,9),(2,5),(3,4),(6,7),(8,10)]=>2
[(1,10),(2,5),(3,4),(6,7),(8,9)]=>1
[(1,10),(2,6),(3,4),(5,7),(8,9)]=>2
[(1,9),(2,6),(3,4),(5,7),(8,10)]=>4
[(1,8),(2,6),(3,4),(5,7),(9,10)]=>2
[(1,7),(2,6),(3,4),(5,8),(9,10)]=>4
[(1,6),(2,7),(3,4),(5,8),(9,10)]=>5
[(1,5),(2,7),(3,4),(6,8),(9,10)]=>4
[(1,4),(2,7),(3,5),(6,8),(9,10)]=>8
[(1,3),(2,7),(4,5),(6,8),(9,10)]=>4
[(1,2),(3,7),(4,5),(6,8),(9,10)]=>2
[(1,2),(3,8),(4,5),(6,7),(9,10)]=>1
[(1,3),(2,8),(4,5),(6,7),(9,10)]=>2
[(1,4),(2,8),(3,5),(6,7),(9,10)]=>4
[(1,5),(2,8),(3,4),(6,7),(9,10)]=>2
[(1,6),(2,8),(3,4),(5,7),(9,10)]=>4
[(1,7),(2,8),(3,4),(5,6),(9,10)]=>2
[(1,8),(2,7),(3,4),(5,6),(9,10)]=>1
[(1,9),(2,7),(3,4),(5,6),(8,10)]=>2
[(1,10),(2,7),(3,4),(5,6),(8,9)]=>1
[(1,10),(2,8),(3,4),(5,6),(7,9)]=>2
[(1,9),(2,8),(3,4),(5,6),(7,10)]=>4
[(1,8),(2,9),(3,4),(5,6),(7,10)]=>5
[(1,7),(2,9),(3,4),(5,6),(8,10)]=>4
[(1,6),(2,9),(3,4),(5,7),(8,10)]=>8
[(1,5),(2,9),(3,4),(6,7),(8,10)]=>4
[(1,4),(2,9),(3,5),(6,7),(8,10)]=>8
[(1,3),(2,9),(4,5),(6,7),(8,10)]=>4
[(1,2),(3,9),(4,5),(6,7),(8,10)]=>2
[(1,2),(3,10),(4,5),(6,7),(8,9)]=>1
[(1,3),(2,10),(4,5),(6,7),(8,9)]=>2
[(1,4),(2,10),(3,5),(6,7),(8,9)]=>4
[(1,5),(2,10),(3,4),(6,7),(8,9)]=>2
[(1,6),(2,10),(3,4),(5,7),(8,9)]=>4
[(1,7),(2,10),(3,4),(5,6),(8,9)]=>2
[(1,8),(2,10),(3,4),(5,6),(7,9)]=>4
[(1,9),(2,10),(3,4),(5,6),(7,8)]=>2
[(1,10),(2,9),(3,4),(5,6),(7,8)]=>1
[(1,10),(2,9),(3,5),(4,6),(7,8)]=>2
[(1,9),(2,10),(3,5),(4,6),(7,8)]=>4
[(1,8),(2,10),(3,5),(4,6),(7,9)]=>8
[(1,7),(2,10),(3,5),(4,6),(8,9)]=>4
[(1,6),(2,10),(3,5),(4,7),(8,9)]=>8
[(1,5),(2,10),(3,6),(4,7),(8,9)]=>10
[(1,4),(2,10),(3,6),(5,7),(8,9)]=>8
[(1,3),(2,10),(4,6),(5,7),(8,9)]=>4
[(1,2),(3,10),(4,6),(5,7),(8,9)]=>2
[(1,2),(3,9),(4,6),(5,7),(8,10)]=>4
[(1,3),(2,9),(4,6),(5,7),(8,10)]=>8
[(1,4),(2,9),(3,6),(5,7),(8,10)]=>16
[(1,5),(2,9),(3,6),(4,7),(8,10)]=>20
[(1,6),(2,9),(3,5),(4,7),(8,10)]=>16
[(1,7),(2,9),(3,5),(4,6),(8,10)]=>8
[(1,8),(2,9),(3,5),(4,6),(7,10)]=>10
[(1,9),(2,8),(3,5),(4,6),(7,10)]=>8
[(1,10),(2,8),(3,5),(4,6),(7,9)]=>4
[(1,10),(2,7),(3,5),(4,6),(8,9)]=>2
[(1,9),(2,7),(3,5),(4,6),(8,10)]=>4
[(1,8),(2,7),(3,5),(4,6),(9,10)]=>2
[(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)]=>10
[(1,4),(2,8),(3,6),(5,7),(9,10)]=>8
[(1,3),(2,8),(4,6),(5,7),(9,10)]=>4
[(1,2),(3,8),(4,6),(5,7),(9,10)]=>2
[(1,2),(3,7),(4,6),(5,8),(9,10)]=>4
[(1,3),(2,7),(4,6),(5,8),(9,10)]=>8
[(1,4),(2,7),(3,6),(5,8),(9,10)]=>13
[(1,5),(2,7),(3,6),(4,8),(9,10)]=>14
[(1,6),(2,7),(3,5),(4,8),(9,10)]=>10
[(1,7),(2,6),(3,5),(4,8),(9,10)]=>8
[(1,8),(2,6),(3,5),(4,7),(9,10)]=>4
[(1,9),(2,6),(3,5),(4,7),(8,10)]=>8
[(1,10),(2,6),(3,5),(4,7),(8,9)]=>4
[(1,10),(2,5),(3,6),(4,7),(8,9)]=>5
[(1,9),(2,5),(3,6),(4,7),(8,10)]=>10
[(1,8),(2,5),(3,6),(4,7),(9,10)]=>5
[(1,7),(2,5),(3,6),(4,8),(9,10)]=>10
[(1,6),(2,5),(3,7),(4,8),(9,10)]=>14
[(1,5),(2,6),(3,7),(4,8),(9,10)]=>16
[(1,4),(2,6),(3,7),(5,8),(9,10)]=>14
[(1,3),(2,6),(4,7),(5,8),(9,10)]=>10
[(1,2),(3,6),(4,7),(5,8),(9,10)]=>5
[(1,2),(3,5),(4,7),(6,8),(9,10)]=>4
[(1,3),(2,5),(4,7),(6,8),(9,10)]=>8
[(1,4),(2,5),(3,7),(6,8),(9,10)]=>10
[(1,5),(2,4),(3,7),(6,8),(9,10)]=>8
[(1,6),(2,4),(3,7),(5,8),(9,10)]=>10
[(1,7),(2,4),(3,6),(5,8),(9,10)]=>8
[(1,8),(2,4),(3,6),(5,7),(9,10)]=>4
[(1,9),(2,4),(3,6),(5,7),(8,10)]=>8
[(1,10),(2,4),(3,6),(5,7),(8,9)]=>4
[(1,10),(2,3),(4,6),(5,7),(8,9)]=>2
[(1,9),(2,3),(4,6),(5,7),(8,10)]=>4
[(1,8),(2,3),(4,6),(5,7),(9,10)]=>2
[(1,7),(2,3),(4,6),(5,8),(9,10)]=>4
[(1,6),(2,3),(4,7),(5,8),(9,10)]=>5
[(1,5),(2,3),(4,7),(6,8),(9,10)]=>4
[(1,4),(2,3),(5,7),(6,8),(9,10)]=>2
[(1,3),(2,4),(5,7),(6,8),(9,10)]=>4
[(1,2),(3,4),(5,7),(6,8),(9,10)]=>2
[(1,2),(3,4),(5,8),(6,7),(9,10)]=>1
[(1,3),(2,4),(5,8),(6,7),(9,10)]=>2
[(1,4),(2,3),(5,8),(6,7),(9,10)]=>1
[(1,5),(2,3),(4,8),(6,7),(9,10)]=>2
[(1,6),(2,3),(4,8),(5,7),(9,10)]=>4
[(1,7),(2,3),(4,8),(5,6),(9,10)]=>2
[(1,8),(2,3),(4,7),(5,6),(9,10)]=>1
[(1,9),(2,3),(4,7),(5,6),(8,10)]=>2
[(1,10),(2,3),(4,7),(5,6),(8,9)]=>1
[(1,10),(2,4),(3,7),(5,6),(8,9)]=>2
[(1,9),(2,4),(3,7),(5,6),(8,10)]=>4
[(1,8),(2,4),(3,7),(5,6),(9,10)]=>2
[(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)]=>4
[(1,4),(2,5),(3,8),(6,7),(9,10)]=>5
[(1,3),(2,5),(4,8),(6,7),(9,10)]=>4
[(1,2),(3,5),(4,8),(6,7),(9,10)]=>2
[(1,2),(3,6),(4,8),(5,7),(9,10)]=>4
[(1,3),(2,6),(4,8),(5,7),(9,10)]=>8
[(1,4),(2,6),(3,8),(5,7),(9,10)]=>10
[(1,5),(2,6),(3,8),(4,7),(9,10)]=>14
[(1,6),(2,5),(3,8),(4,7),(9,10)]=>13
[(1,7),(2,5),(3,8),(4,6),(9,10)]=>8
[(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)]=>2
[(1,9),(2,6),(3,7),(4,5),(8,10)]=>4
[(1,8),(2,6),(3,7),(4,5),(9,10)]=>2
[(1,7),(2,6),(3,8),(4,5),(9,10)]=>4
[(1,6),(2,7),(3,8),(4,5),(9,10)]=>5
[(1,5),(2,7),(3,8),(4,6),(9,10)]=>10
[(1,4),(2,7),(3,8),(5,6),(9,10)]=>5
[(1,3),(2,7),(4,8),(5,6),(9,10)]=>4
[(1,2),(3,7),(4,8),(5,6),(9,10)]=>2
[(1,2),(3,8),(4,7),(5,6),(9,10)]=>1
[(1,3),(2,8),(4,7),(5,6),(9,10)]=>2
[(1,4),(2,8),(3,7),(5,6),(9,10)]=>4
[(1,5),(2,8),(3,7),(4,6),(9,10)]=>8
[(1,6),(2,8),(3,7),(4,5),(9,10)]=>4
[(1,7),(2,8),(3,6),(4,5),(9,10)]=>2
[(1,8),(2,7),(3,6),(4,5),(9,10)]=>1
[(1,9),(2,7),(3,6),(4,5),(8,10)]=>2
[(1,10),(2,7),(3,6),(4,5),(8,9)]=>1
[(1,10),(2,8),(3,6),(4,5),(7,9)]=>2
[(1,9),(2,8),(3,6),(4,5),(7,10)]=>4
[(1,8),(2,9),(3,6),(4,5),(7,10)]=>5
[(1,7),(2,9),(3,6),(4,5),(8,10)]=>4
[(1,6),(2,9),(3,7),(4,5),(8,10)]=>8
[(1,5),(2,9),(3,7),(4,6),(8,10)]=>16
[(1,4),(2,9),(3,7),(5,6),(8,10)]=>8
[(1,3),(2,9),(4,7),(5,6),(8,10)]=>4
[(1,2),(3,9),(4,7),(5,6),(8,10)]=>2
[(1,2),(3,10),(4,7),(5,6),(8,9)]=>1
[(1,3),(2,10),(4,7),(5,6),(8,9)]=>2
[(1,4),(2,10),(3,7),(5,6),(8,9)]=>4
[(1,5),(2,10),(3,7),(4,6),(8,9)]=>8
[(1,6),(2,10),(3,7),(4,5),(8,9)]=>4
[(1,7),(2,10),(3,6),(4,5),(8,9)]=>2
[(1,8),(2,10),(3,6),(4,5),(7,9)]=>4
[(1,9),(2,10),(3,6),(4,5),(7,8)]=>2
[(1,10),(2,9),(3,6),(4,5),(7,8)]=>1
[(1,10),(2,9),(3,7),(4,5),(6,8)]=>2
[(1,9),(2,10),(3,7),(4,5),(6,8)]=>4
[(1,8),(2,10),(3,7),(4,5),(6,9)]=>8
[(1,7),(2,10),(3,8),(4,5),(6,9)]=>10
[(1,6),(2,10),(3,8),(4,5),(7,9)]=>8
[(1,5),(2,10),(3,8),(4,6),(7,9)]=>16
[(1,4),(2,10),(3,8),(5,6),(7,9)]=>8
[(1,3),(2,10),(4,8),(5,6),(7,9)]=>4
[(1,2),(3,10),(4,8),(5,6),(7,9)]=>2
[(1,2),(3,9),(4,8),(5,6),(7,10)]=>4
[(1,3),(2,9),(4,8),(5,6),(7,10)]=>8
[(1,4),(2,9),(3,8),(5,6),(7,10)]=>13
[(1,5),(2,9),(3,8),(4,6),(7,10)]=>26
[(1,6),(2,9),(3,8),(4,5),(7,10)]=>13
[(1,7),(2,9),(3,8),(4,5),(6,10)]=>14
[(1,8),(2,9),(3,7),(4,5),(6,10)]=>10
[(1,9),(2,8),(3,7),(4,5),(6,10)]=>8
[(1,10),(2,8),(3,7),(4,5),(6,9)]=>4
[(1,10),(2,7),(3,8),(4,5),(6,9)]=>5
[(1,9),(2,7),(3,8),(4,5),(6,10)]=>10
[(1,8),(2,7),(3,9),(4,5),(6,10)]=>14
[(1,7),(2,8),(3,9),(4,5),(6,10)]=>16
[(1,6),(2,8),(3,9),(4,5),(7,10)]=>14
[(1,5),(2,8),(3,9),(4,6),(7,10)]=>28
[(1,4),(2,8),(3,9),(5,6),(7,10)]=>14
[(1,3),(2,8),(4,9),(5,6),(7,10)]=>10
[(1,2),(3,8),(4,9),(5,6),(7,10)]=>5
[(1,2),(3,7),(4,9),(5,6),(8,10)]=>4
[(1,3),(2,7),(4,9),(5,6),(8,10)]=>8
[(1,4),(2,7),(3,9),(5,6),(8,10)]=>10
[(1,5),(2,7),(3,9),(4,6),(8,10)]=>20
[(1,6),(2,7),(3,9),(4,5),(8,10)]=>10
[(1,7),(2,6),(3,9),(4,5),(8,10)]=>8
[(1,8),(2,6),(3,9),(4,5),(7,10)]=>10
[(1,9),(2,6),(3,8),(4,5),(7,10)]=>8
[(1,10),(2,6),(3,8),(4,5),(7,9)]=>4
[(1,10),(2,5),(3,8),(4,6),(7,9)]=>8
[(1,9),(2,5),(3,8),(4,6),(7,10)]=>16
[(1,8),(2,5),(3,9),(4,6),(7,10)]=>20
[(1,7),(2,5),(3,9),(4,6),(8,10)]=>16
[(1,6),(2,5),(3,9),(4,7),(8,10)]=>26
[(1,5),(2,6),(3,9),(4,7),(8,10)]=>28
[(1,4),(2,6),(3,9),(5,7),(8,10)]=>20
[(1,3),(2,6),(4,9),(5,7),(8,10)]=>16
[(1,2),(3,6),(4,9),(5,7),(8,10)]=>8
[(1,2),(3,5),(4,9),(6,7),(8,10)]=>4
[(1,3),(2,5),(4,9),(6,7),(8,10)]=>8
[(1,4),(2,5),(3,9),(6,7),(8,10)]=>10
[(1,5),(2,4),(3,9),(6,7),(8,10)]=>8
[(1,6),(2,4),(3,9),(5,7),(8,10)]=>16
[(1,7),(2,4),(3,9),(5,6),(8,10)]=>8
[(1,8),(2,4),(3,9),(5,6),(7,10)]=>10
[(1,9),(2,4),(3,8),(5,6),(7,10)]=>8
[(1,10),(2,4),(3,8),(5,6),(7,9)]=>4
[(1,10),(2,3),(4,8),(5,6),(7,9)]=>2
[(1,9),(2,3),(4,8),(5,6),(7,10)]=>4
[(1,8),(2,3),(4,9),(5,6),(7,10)]=>5
[(1,7),(2,3),(4,9),(5,6),(8,10)]=>4
[(1,6),(2,3),(4,9),(5,7),(8,10)]=>8
[(1,5),(2,3),(4,9),(6,7),(8,10)]=>4
[(1,4),(2,3),(5,9),(6,7),(8,10)]=>2
[(1,3),(2,4),(5,9),(6,7),(8,10)]=>4
[(1,2),(3,4),(5,9),(6,7),(8,10)]=>2
[(1,2),(3,4),(5,10),(6,7),(8,9)]=>1
[(1,3),(2,4),(5,10),(6,7),(8,9)]=>2
[(1,4),(2,3),(5,10),(6,7),(8,9)]=>1
[(1,5),(2,3),(4,10),(6,7),(8,9)]=>2
[(1,6),(2,3),(4,10),(5,7),(8,9)]=>4
[(1,7),(2,3),(4,10),(5,6),(8,9)]=>2
[(1,8),(2,3),(4,10),(5,6),(7,9)]=>4
[(1,9),(2,3),(4,10),(5,6),(7,8)]=>2
[(1,10),(2,3),(4,9),(5,6),(7,8)]=>1
[(1,10),(2,4),(3,9),(5,6),(7,8)]=>2
[(1,9),(2,4),(3,10),(5,6),(7,8)]=>4
[(1,8),(2,4),(3,10),(5,6),(7,9)]=>8
[(1,7),(2,4),(3,10),(5,6),(8,9)]=>4
[(1,6),(2,4),(3,10),(5,7),(8,9)]=>8
[(1,5),(2,4),(3,10),(6,7),(8,9)]=>4
[(1,4),(2,5),(3,10),(6,7),(8,9)]=>5
[(1,3),(2,5),(4,10),(6,7),(8,9)]=>4
[(1,2),(3,5),(4,10),(6,7),(8,9)]=>2
[(1,2),(3,6),(4,10),(5,7),(8,9)]=>4
[(1,3),(2,6),(4,10),(5,7),(8,9)]=>8
[(1,4),(2,6),(3,10),(5,7),(8,9)]=>10
[(1,5),(2,6),(3,10),(4,7),(8,9)]=>14
[(1,6),(2,5),(3,10),(4,7),(8,9)]=>13
[(1,7),(2,5),(3,10),(4,6),(8,9)]=>8
[(1,8),(2,5),(3,10),(4,6),(7,9)]=>16
[(1,9),(2,5),(3,10),(4,6),(7,8)]=>8
[(1,10),(2,5),(3,9),(4,6),(7,8)]=>4
[(1,10),(2,6),(3,9),(4,5),(7,8)]=>2
[(1,9),(2,6),(3,10),(4,5),(7,8)]=>4
[(1,8),(2,6),(3,10),(4,5),(7,9)]=>8
[(1,7),(2,6),(3,10),(4,5),(8,9)]=>4
[(1,6),(2,7),(3,10),(4,5),(8,9)]=>5
[(1,5),(2,7),(3,10),(4,6),(8,9)]=>10
[(1,4),(2,7),(3,10),(5,6),(8,9)]=>5
[(1,3),(2,7),(4,10),(5,6),(8,9)]=>4
[(1,2),(3,7),(4,10),(5,6),(8,9)]=>2
[(1,2),(3,8),(4,10),(5,6),(7,9)]=>4
[(1,3),(2,8),(4,10),(5,6),(7,9)]=>8
[(1,4),(2,8),(3,10),(5,6),(7,9)]=>10
[(1,5),(2,8),(3,10),(4,6),(7,9)]=>20
[(1,6),(2,8),(3,10),(4,5),(7,9)]=>10
[(1,7),(2,8),(3,10),(4,5),(6,9)]=>14
[(1,8),(2,7),(3,10),(4,5),(6,9)]=>13
[(1,9),(2,7),(3,10),(4,5),(6,8)]=>8
[(1,10),(2,7),(3,9),(4,5),(6,8)]=>4
[(1,10),(2,8),(3,9),(4,5),(6,7)]=>2
[(1,9),(2,8),(3,10),(4,5),(6,7)]=>4
[(1,8),(2,9),(3,10),(4,5),(6,7)]=>5
[(1,7),(2,9),(3,10),(4,5),(6,8)]=>10
[(1,6),(2,9),(3,10),(4,5),(7,8)]=>5
[(1,5),(2,9),(3,10),(4,6),(7,8)]=>10
[(1,4),(2,9),(3,10),(5,6),(7,8)]=>5
[(1,3),(2,9),(4,10),(5,6),(7,8)]=>4
[(1,2),(3,9),(4,10),(5,6),(7,8)]=>2
[(1,2),(3,10),(4,9),(5,6),(7,8)]=>1
[(1,3),(2,10),(4,9),(5,6),(7,8)]=>2
[(1,4),(2,10),(3,9),(5,6),(7,8)]=>4
[(1,5),(2,10),(3,9),(4,6),(7,8)]=>8
[(1,6),(2,10),(3,9),(4,5),(7,8)]=>4
[(1,7),(2,10),(3,9),(4,5),(6,8)]=>8
[(1,8),(2,10),(3,9),(4,5),(6,7)]=>4
[(1,9),(2,10),(3,8),(4,5),(6,7)]=>2
[(1,10),(2,9),(3,8),(4,5),(6,7)]=>1
[(1,10),(2,9),(3,8),(4,6),(5,7)]=>2
[(1,9),(2,10),(3,8),(4,6),(5,7)]=>4
[(1,8),(2,10),(3,9),(4,6),(5,7)]=>8
[(1,7),(2,10),(3,9),(4,6),(5,8)]=>16
[(1,6),(2,10),(3,9),(4,7),(5,8)]=>20
[(1,5),(2,10),(3,9),(4,7),(6,8)]=>16
[(1,4),(2,10),(3,9),(5,7),(6,8)]=>8
[(1,3),(2,10),(4,9),(5,7),(6,8)]=>4
[(1,2),(3,10),(4,9),(5,7),(6,8)]=>2
[(1,2),(3,9),(4,10),(5,7),(6,8)]=>4
[(1,3),(2,9),(4,10),(5,7),(6,8)]=>8
[(1,4),(2,9),(3,10),(5,7),(6,8)]=>10
[(1,5),(2,9),(3,10),(4,7),(6,8)]=>20
[(1,6),(2,9),(3,10),(4,7),(5,8)]=>25
[(1,7),(2,9),(3,10),(4,6),(5,8)]=>20
[(1,8),(2,9),(3,10),(4,6),(5,7)]=>10
[(1,9),(2,8),(3,10),(4,6),(5,7)]=>8
[(1,10),(2,8),(3,9),(4,6),(5,7)]=>4
[(1,10),(2,7),(3,9),(4,6),(5,8)]=>8
[(1,9),(2,7),(3,10),(4,6),(5,8)]=>16
[(1,8),(2,7),(3,10),(4,6),(5,9)]=>26
[(1,7),(2,8),(3,10),(4,6),(5,9)]=>28
[(1,6),(2,8),(3,10),(4,7),(5,9)]=>38
[(1,5),(2,8),(3,10),(4,7),(6,9)]=>34
[(1,4),(2,8),(3,10),(5,7),(6,9)]=>20
[(1,3),(2,8),(4,10),(5,7),(6,9)]=>16
[(1,2),(3,8),(4,10),(5,7),(6,9)]=>8
[(1,2),(3,7),(4,10),(5,8),(6,9)]=>10
[(1,3),(2,7),(4,10),(5,8),(6,9)]=>20
[(1,4),(2,7),(3,10),(5,8),(6,9)]=>25
[(1,5),(2,7),(3,10),(4,8),(6,9)]=>38
[(1,6),(2,7),(3,10),(4,8),(5,9)]=>46
[(1,7),(2,6),(3,10),(4,8),(5,9)]=>44
[(1,8),(2,6),(3,10),(4,7),(5,9)]=>34
[(1,9),(2,6),(3,10),(4,7),(5,8)]=>20
[(1,10),(2,6),(3,9),(4,7),(5,8)]=>10
[(1,10),(2,5),(3,9),(4,7),(6,8)]=>8
[(1,9),(2,5),(3,10),(4,7),(6,8)]=>16
[(1,8),(2,5),(3,10),(4,7),(6,9)]=>29
[(1,7),(2,5),(3,10),(4,8),(6,9)]=>34
[(1,6),(2,5),(3,10),(4,8),(7,9)]=>26
[(1,5),(2,6),(3,10),(4,8),(7,9)]=>28
[(1,4),(2,6),(3,10),(5,8),(7,9)]=>20
[(1,3),(2,6),(4,10),(5,8),(7,9)]=>16
[(1,2),(3,6),(4,10),(5,8),(7,9)]=>8
[(1,2),(3,5),(4,10),(6,8),(7,9)]=>4
[(1,3),(2,5),(4,10),(6,8),(7,9)]=>8
[(1,4),(2,5),(3,10),(6,8),(7,9)]=>10
[(1,5),(2,4),(3,10),(6,8),(7,9)]=>8
[(1,6),(2,4),(3,10),(5,8),(7,9)]=>16
[(1,7),(2,4),(3,10),(5,8),(6,9)]=>20
[(1,8),(2,4),(3,10),(5,7),(6,9)]=>16
[(1,9),(2,4),(3,10),(5,7),(6,8)]=>8
[(1,10),(2,4),(3,9),(5,7),(6,8)]=>4
[(1,10),(2,3),(4,9),(5,7),(6,8)]=>2
[(1,9),(2,3),(4,10),(5,7),(6,8)]=>4
[(1,8),(2,3),(4,10),(5,7),(6,9)]=>8
[(1,7),(2,3),(4,10),(5,8),(6,9)]=>10
[(1,6),(2,3),(4,10),(5,8),(7,9)]=>8
[(1,5),(2,3),(4,10),(6,8),(7,9)]=>4
[(1,4),(2,3),(5,10),(6,8),(7,9)]=>2
[(1,3),(2,4),(5,10),(6,8),(7,9)]=>4
[(1,2),(3,4),(5,10),(6,8),(7,9)]=>2
[(1,2),(3,4),(5,9),(6,8),(7,10)]=>4
[(1,3),(2,4),(5,9),(6,8),(7,10)]=>8
[(1,4),(2,3),(5,9),(6,8),(7,10)]=>4
[(1,5),(2,3),(4,9),(6,8),(7,10)]=>8
[(1,6),(2,3),(4,9),(5,8),(7,10)]=>13
[(1,7),(2,3),(4,9),(5,8),(6,10)]=>14
[(1,8),(2,3),(4,9),(5,7),(6,10)]=>10
[(1,9),(2,3),(4,8),(5,7),(6,10)]=>8
[(1,10),(2,3),(4,8),(5,7),(6,9)]=>4
[(1,10),(2,4),(3,8),(5,7),(6,9)]=>8
[(1,9),(2,4),(3,8),(5,7),(6,10)]=>16
[(1,8),(2,4),(3,9),(5,7),(6,10)]=>20
[(1,7),(2,4),(3,9),(5,8),(6,10)]=>28
[(1,6),(2,4),(3,9),(5,8),(7,10)]=>26
[(1,5),(2,4),(3,9),(6,8),(7,10)]=>16
[(1,4),(2,5),(3,9),(6,8),(7,10)]=>20
[(1,3),(2,5),(4,9),(6,8),(7,10)]=>16
[(1,2),(3,5),(4,9),(6,8),(7,10)]=>8
[(1,2),(3,6),(4,9),(5,8),(7,10)]=>13
[(1,3),(2,6),(4,9),(5,8),(7,10)]=>26
[(1,4),(2,6),(3,9),(5,8),(7,10)]=>34
[(1,5),(2,6),(3,9),(4,8),(7,10)]=>44
[(1,6),(2,5),(3,9),(4,8),(7,10)]=>40
[(1,7),(2,5),(3,9),(4,8),(6,10)]=>44
[(1,8),(2,5),(3,9),(4,7),(6,10)]=>34
[(1,9),(2,5),(3,8),(4,7),(6,10)]=>26
[(1,10),(2,5),(3,8),(4,7),(6,9)]=>13
[(1,10),(2,6),(3,8),(4,7),(5,9)]=>14
[(1,9),(2,6),(3,8),(4,7),(5,10)]=>28
[(1,8),(2,6),(3,9),(4,7),(5,10)]=>38
[(1,7),(2,6),(3,9),(4,8),(5,10)]=>52
[(1,6),(2,7),(3,9),(4,8),(5,10)]=>56
[(1,5),(2,7),(3,9),(4,8),(6,10)]=>52
[(1,4),(2,7),(3,9),(5,8),(6,10)]=>38
[(1,3),(2,7),(4,9),(5,8),(6,10)]=>28
[(1,2),(3,7),(4,9),(5,8),(6,10)]=>14
[(1,2),(3,8),(4,9),(5,7),(6,10)]=>10
[(1,3),(2,8),(4,9),(5,7),(6,10)]=>20
[(1,4),(2,8),(3,9),(5,7),(6,10)]=>28
[(1,5),(2,8),(3,9),(4,7),(6,10)]=>44
[(1,6),(2,8),(3,9),(4,7),(5,10)]=>46
[(1,7),(2,8),(3,9),(4,6),(5,10)]=>32
[(1,8),(2,7),(3,9),(4,6),(5,10)]=>28
[(1,9),(2,7),(3,8),(4,6),(5,10)]=>20
[(1,10),(2,7),(3,8),(4,6),(5,9)]=>10
[(1,10),(2,8),(3,7),(4,6),(5,9)]=>8
[(1,9),(2,8),(3,7),(4,6),(5,10)]=>16
[(1,8),(2,9),(3,7),(4,6),(5,10)]=>20
[(1,7),(2,9),(3,8),(4,6),(5,10)]=>28
[(1,6),(2,9),(3,8),(4,7),(5,10)]=>41
[(1,5),(2,9),(3,8),(4,7),(6,10)]=>40
[(1,4),(2,9),(3,8),(5,7),(6,10)]=>26
[(1,3),(2,9),(4,8),(5,7),(6,10)]=>16
[(1,2),(3,9),(4,8),(5,7),(6,10)]=>8
[(1,2),(3,10),(4,8),(5,7),(6,9)]=>4
[(1,3),(2,10),(4,8),(5,7),(6,9)]=>8
[(1,4),(2,10),(3,8),(5,7),(6,9)]=>16
[(1,5),(2,10),(3,8),(4,7),(6,9)]=>26
[(1,6),(2,10),(3,8),(4,7),(5,9)]=>28
[(1,7),(2,10),(3,8),(4,6),(5,9)]=>20
[(1,8),(2,10),(3,7),(4,6),(5,9)]=>16
[(1,9),(2,10),(3,7),(4,6),(5,8)]=>8
[(1,10),(2,9),(3,7),(4,6),(5,8)]=>4
[(1,10),(2,9),(3,6),(4,7),(5,8)]=>5
[(1,9),(2,10),(3,6),(4,7),(5,8)]=>10
[(1,8),(2,10),(3,6),(4,7),(5,9)]=>20
[(1,7),(2,10),(3,6),(4,8),(5,9)]=>28
[(1,6),(2,10),(3,7),(4,8),(5,9)]=>32
[(1,5),(2,10),(3,7),(4,8),(6,9)]=>28
[(1,4),(2,10),(3,7),(5,8),(6,9)]=>20
[(1,3),(2,10),(4,7),(5,8),(6,9)]=>10
[(1,2),(3,10),(4,7),(5,8),(6,9)]=>5
[(1,2),(3,9),(4,7),(5,8),(6,10)]=>10
[(1,3),(2,9),(4,7),(5,8),(6,10)]=>20
[(1,4),(2,9),(3,7),(5,8),(6,10)]=>34
[(1,5),(2,9),(3,7),(4,8),(6,10)]=>44
[(1,6),(2,9),(3,7),(4,8),(5,10)]=>46
[(1,7),(2,9),(3,6),(4,8),(5,10)]=>38
[(1,8),(2,9),(3,6),(4,7),(5,10)]=>25
[(1,9),(2,8),(3,6),(4,7),(5,10)]=>20
[(1,10),(2,8),(3,6),(4,7),(5,9)]=>10
[(1,10),(2,7),(3,6),(4,8),(5,9)]=>14
[(1,9),(2,7),(3,6),(4,8),(5,10)]=>28
[(1,8),(2,7),(3,6),(4,9),(5,10)]=>41
[(1,7),(2,8),(3,6),(4,9),(5,10)]=>46
[(1,6),(2,8),(3,7),(4,9),(5,10)]=>56
[(1,5),(2,8),(3,7),(4,9),(6,10)]=>52
[(1,4),(2,8),(3,7),(5,9),(6,10)]=>44
[(1,3),(2,8),(4,7),(5,9),(6,10)]=>28
[(1,2),(3,8),(4,7),(5,9),(6,10)]=>14
[(1,2),(3,7),(4,8),(5,9),(6,10)]=>16
[(1,3),(2,7),(4,8),(5,9),(6,10)]=>32
[(1,4),(2,7),(3,8),(5,9),(6,10)]=>46
[(1,5),(2,7),(3,8),(4,9),(6,10)]=>56
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>61
[(1,7),(2,6),(3,8),(4,9),(5,10)]=>56
[(1,8),(2,6),(3,7),(4,9),(5,10)]=>46
[(1,9),(2,6),(3,7),(4,8),(5,10)]=>32
[(1,10),(2,6),(3,7),(4,8),(5,9)]=>16
[(1,10),(2,5),(3,7),(4,8),(6,9)]=>14
[(1,9),(2,5),(3,7),(4,8),(6,10)]=>28
[(1,8),(2,5),(3,7),(4,9),(6,10)]=>38
[(1,7),(2,5),(3,8),(4,9),(6,10)]=>46
[(1,6),(2,5),(3,8),(4,9),(7,10)]=>41
[(1,5),(2,6),(3,8),(4,9),(7,10)]=>46
[(1,4),(2,6),(3,8),(5,9),(7,10)]=>38
[(1,3),(2,6),(4,8),(5,9),(7,10)]=>28
[(1,2),(3,6),(4,8),(5,9),(7,10)]=>14
[(1,2),(3,5),(4,8),(6,9),(7,10)]=>10
[(1,3),(2,5),(4,8),(6,9),(7,10)]=>20
[(1,4),(2,5),(3,8),(6,9),(7,10)]=>25
[(1,5),(2,4),(3,8),(6,9),(7,10)]=>20
[(1,6),(2,4),(3,8),(5,9),(7,10)]=>28
[(1,7),(2,4),(3,8),(5,9),(6,10)]=>32
[(1,8),(2,4),(3,7),(5,9),(6,10)]=>28
[(1,9),(2,4),(3,7),(5,8),(6,10)]=>20
[(1,10),(2,4),(3,7),(5,8),(6,9)]=>10
[(1,10),(2,3),(4,7),(5,8),(6,9)]=>5
[(1,9),(2,3),(4,7),(5,8),(6,10)]=>10
[(1,8),(2,3),(4,7),(5,9),(6,10)]=>14
[(1,7),(2,3),(4,8),(5,9),(6,10)]=>16
[(1,6),(2,3),(4,8),(5,9),(7,10)]=>14
[(1,5),(2,3),(4,8),(6,9),(7,10)]=>10
[(1,4),(2,3),(5,8),(6,9),(7,10)]=>5
[(1,3),(2,4),(5,8),(6,9),(7,10)]=>10
[(1,2),(3,4),(5,8),(6,9),(7,10)]=>5
[(1,2),(3,4),(5,7),(6,9),(8,10)]=>4
[(1,3),(2,4),(5,7),(6,9),(8,10)]=>8
[(1,4),(2,3),(5,7),(6,9),(8,10)]=>4
[(1,5),(2,3),(4,7),(6,9),(8,10)]=>8
[(1,6),(2,3),(4,7),(5,9),(8,10)]=>10
[(1,7),(2,3),(4,6),(5,9),(8,10)]=>8
[(1,8),(2,3),(4,6),(5,9),(7,10)]=>10
[(1,9),(2,3),(4,6),(5,8),(7,10)]=>8
[(1,10),(2,3),(4,6),(5,8),(7,9)]=>4
[(1,10),(2,4),(3,6),(5,8),(7,9)]=>8
[(1,9),(2,4),(3,6),(5,8),(7,10)]=>16
[(1,8),(2,4),(3,6),(5,9),(7,10)]=>20
[(1,7),(2,4),(3,6),(5,9),(8,10)]=>16
[(1,6),(2,4),(3,7),(5,9),(8,10)]=>20
[(1,5),(2,4),(3,7),(6,9),(8,10)]=>16
[(1,4),(2,5),(3,7),(6,9),(8,10)]=>20
[(1,3),(2,5),(4,7),(6,9),(8,10)]=>16
[(1,2),(3,5),(4,7),(6,9),(8,10)]=>8
[(1,2),(3,6),(4,7),(5,9),(8,10)]=>10
[(1,3),(2,6),(4,7),(5,9),(8,10)]=>20
[(1,4),(2,6),(3,7),(5,9),(8,10)]=>28
[(1,5),(2,6),(3,7),(4,9),(8,10)]=>32
[(1,6),(2,5),(3,7),(4,9),(8,10)]=>28
[(1,7),(2,5),(3,6),(4,9),(8,10)]=>20
[(1,8),(2,5),(3,6),(4,9),(7,10)]=>25
[(1,9),(2,5),(3,6),(4,8),(7,10)]=>20
[(1,10),(2,5),(3,6),(4,8),(7,9)]=>10
[(1,10),(2,6),(3,5),(4,8),(7,9)]=>8
[(1,9),(2,6),(3,5),(4,8),(7,10)]=>16
[(1,8),(2,6),(3,5),(4,9),(7,10)]=>20
[(1,7),(2,6),(3,5),(4,9),(8,10)]=>16
[(1,6),(2,7),(3,5),(4,9),(8,10)]=>20
[(1,5),(2,7),(3,6),(4,9),(8,10)]=>28
[(1,4),(2,7),(3,6),(5,9),(8,10)]=>26
[(1,3),(2,7),(4,6),(5,9),(8,10)]=>16
[(1,2),(3,7),(4,6),(5,9),(8,10)]=>8
[(1,2),(3,8),(4,6),(5,9),(7,10)]=>10
[(1,3),(2,8),(4,6),(5,9),(7,10)]=>20
[(1,4),(2,8),(3,6),(5,9),(7,10)]=>34
[(1,5),(2,8),(3,6),(4,9),(7,10)]=>38
[(1,6),(2,8),(3,5),(4,9),(7,10)]=>28
[(1,7),(2,8),(3,5),(4,9),(6,10)]=>32
[(1,8),(2,7),(3,5),(4,9),(6,10)]=>28
[(1,9),(2,7),(3,5),(4,8),(6,10)]=>20
[(1,10),(2,7),(3,5),(4,8),(6,9)]=>10
[(1,10),(2,8),(3,5),(4,7),(6,9)]=>8
[(1,9),(2,8),(3,5),(4,7),(6,10)]=>16
[(1,8),(2,9),(3,5),(4,7),(6,10)]=>20
[(1,7),(2,9),(3,5),(4,8),(6,10)]=>28
[(1,6),(2,9),(3,5),(4,8),(7,10)]=>26
[(1,5),(2,9),(3,6),(4,8),(7,10)]=>34
[(1,4),(2,9),(3,6),(5,8),(7,10)]=>29
[(1,3),(2,9),(4,6),(5,8),(7,10)]=>16
[(1,2),(3,9),(4,6),(5,8),(7,10)]=>8
[(1,2),(3,10),(4,6),(5,8),(7,9)]=>4
[(1,3),(2,10),(4,6),(5,8),(7,9)]=>8
[(1,4),(2,10),(3,6),(5,8),(7,9)]=>16
[(1,5),(2,10),(3,6),(4,8),(7,9)]=>20
[(1,6),(2,10),(3,5),(4,8),(7,9)]=>16
[(1,7),(2,10),(3,5),(4,8),(6,9)]=>20
[(1,8),(2,10),(3,5),(4,7),(6,9)]=>16
[(1,9),(2,10),(3,5),(4,7),(6,8)]=>8
[(1,10),(2,9),(3,5),(4,7),(6,8)]=>4
[(1,10),(2,9),(3,4),(5,7),(6,8)]=>2
[(1,9),(2,10),(3,4),(5,7),(6,8)]=>4
[(1,8),(2,10),(3,4),(5,7),(6,9)]=>8
[(1,7),(2,10),(3,4),(5,8),(6,9)]=>10
[(1,6),(2,10),(3,4),(5,8),(7,9)]=>8
[(1,5),(2,10),(3,4),(6,8),(7,9)]=>4
[(1,4),(2,10),(3,5),(6,8),(7,9)]=>8
[(1,3),(2,10),(4,5),(6,8),(7,9)]=>4
[(1,2),(3,10),(4,5),(6,8),(7,9)]=>2
[(1,2),(3,9),(4,5),(6,8),(7,10)]=>4
[(1,3),(2,9),(4,5),(6,8),(7,10)]=>8
[(1,4),(2,9),(3,5),(6,8),(7,10)]=>16
[(1,5),(2,9),(3,4),(6,8),(7,10)]=>8
[(1,6),(2,9),(3,4),(5,8),(7,10)]=>13
[(1,7),(2,9),(3,4),(5,8),(6,10)]=>14
[(1,8),(2,9),(3,4),(5,7),(6,10)]=>10
[(1,9),(2,8),(3,4),(5,7),(6,10)]=>8
[(1,10),(2,8),(3,4),(5,7),(6,9)]=>4
[(1,10),(2,7),(3,4),(5,8),(6,9)]=>5
[(1,9),(2,7),(3,4),(5,8),(6,10)]=>10
[(1,8),(2,7),(3,4),(5,9),(6,10)]=>14
[(1,7),(2,8),(3,4),(5,9),(6,10)]=>16
[(1,6),(2,8),(3,4),(5,9),(7,10)]=>14
[(1,5),(2,8),(3,4),(6,9),(7,10)]=>10
[(1,4),(2,8),(3,5),(6,9),(7,10)]=>20
[(1,3),(2,8),(4,5),(6,9),(7,10)]=>10
[(1,2),(3,8),(4,5),(6,9),(7,10)]=>5
[(1,2),(3,7),(4,5),(6,9),(8,10)]=>4
[(1,3),(2,7),(4,5),(6,9),(8,10)]=>8
[(1,4),(2,7),(3,5),(6,9),(8,10)]=>16
[(1,5),(2,7),(3,4),(6,9),(8,10)]=>8
[(1,6),(2,7),(3,4),(5,9),(8,10)]=>10
[(1,7),(2,6),(3,4),(5,9),(8,10)]=>8
[(1,8),(2,6),(3,4),(5,9),(7,10)]=>10
[(1,9),(2,6),(3,4),(5,8),(7,10)]=>8
[(1,10),(2,6),(3,4),(5,8),(7,9)]=>4
[(1,10),(2,5),(3,4),(6,8),(7,9)]=>2
[(1,9),(2,5),(3,4),(6,8),(7,10)]=>4
[(1,8),(2,5),(3,4),(6,9),(7,10)]=>5
[(1,7),(2,5),(3,4),(6,9),(8,10)]=>4
[(1,6),(2,5),(3,4),(7,9),(8,10)]=>2
[(1,5),(2,6),(3,4),(7,9),(8,10)]=>4
[(1,4),(2,6),(3,5),(7,9),(8,10)]=>8
[(1,3),(2,6),(4,5),(7,9),(8,10)]=>4
[(1,2),(3,6),(4,5),(7,9),(8,10)]=>2
[(1,2),(3,5),(4,6),(7,9),(8,10)]=>4
[(1,3),(2,5),(4,6),(7,9),(8,10)]=>8
[(1,4),(2,5),(3,6),(7,9),(8,10)]=>10
[(1,5),(2,4),(3,6),(7,9),(8,10)]=>8
[(1,6),(2,4),(3,5),(7,9),(8,10)]=>4
[(1,7),(2,4),(3,5),(6,9),(8,10)]=>8
[(1,8),(2,4),(3,5),(6,9),(7,10)]=>10
[(1,9),(2,4),(3,5),(6,8),(7,10)]=>8
[(1,10),(2,4),(3,5),(6,8),(7,9)]=>4
[(1,10),(2,3),(4,5),(6,8),(7,9)]=>2
[(1,9),(2,3),(4,5),(6,8),(7,10)]=>4
[(1,8),(2,3),(4,5),(6,9),(7,10)]=>5
[(1,7),(2,3),(4,5),(6,9),(8,10)]=>4
[(1,6),(2,3),(4,5),(7,9),(8,10)]=>2
[(1,5),(2,3),(4,6),(7,9),(8,10)]=>4
[(1,4),(2,3),(5,6),(7,9),(8,10)]=>2
[(1,3),(2,4),(5,6),(7,9),(8,10)]=>4
[(1,2),(3,4),(5,6),(7,9),(8,10)]=>2
[(1,2),(3,4),(5,6),(7,10),(8,9)]=>1
[(1,3),(2,4),(5,6),(7,10),(8,9)]=>2
[(1,4),(2,3),(5,6),(7,10),(8,9)]=>1
[(1,5),(2,3),(4,6),(7,10),(8,9)]=>2
[(1,6),(2,3),(4,5),(7,10),(8,9)]=>1
[(1,7),(2,3),(4,5),(6,10),(8,9)]=>2
[(1,8),(2,3),(4,5),(6,10),(7,9)]=>4
[(1,9),(2,3),(4,5),(6,10),(7,8)]=>2
[(1,10),(2,3),(4,5),(6,9),(7,8)]=>1
[(1,10),(2,4),(3,5),(6,9),(7,8)]=>2
[(1,9),(2,4),(3,5),(6,10),(7,8)]=>4
[(1,8),(2,4),(3,5),(6,10),(7,9)]=>8
[(1,7),(2,4),(3,5),(6,10),(8,9)]=>4
[(1,6),(2,4),(3,5),(7,10),(8,9)]=>2
[(1,5),(2,4),(3,6),(7,10),(8,9)]=>4
[(1,4),(2,5),(3,6),(7,10),(8,9)]=>5
[(1,3),(2,5),(4,6),(7,10),(8,9)]=>4
[(1,2),(3,5),(4,6),(7,10),(8,9)]=>2
[(1,2),(3,6),(4,5),(7,10),(8,9)]=>1
[(1,3),(2,6),(4,5),(7,10),(8,9)]=>2
[(1,4),(2,6),(3,5),(7,10),(8,9)]=>4
[(1,5),(2,6),(3,4),(7,10),(8,9)]=>2
[(1,6),(2,5),(3,4),(7,10),(8,9)]=>1
[(1,7),(2,5),(3,4),(6,10),(8,9)]=>2
[(1,8),(2,5),(3,4),(6,10),(7,9)]=>4
[(1,9),(2,5),(3,4),(6,10),(7,8)]=>2
[(1,10),(2,5),(3,4),(6,9),(7,8)]=>1
[(1,10),(2,6),(3,4),(5,9),(7,8)]=>2
[(1,9),(2,6),(3,4),(5,10),(7,8)]=>4
[(1,8),(2,6),(3,4),(5,10),(7,9)]=>8
[(1,7),(2,6),(3,4),(5,10),(8,9)]=>4
[(1,6),(2,7),(3,4),(5,10),(8,9)]=>5
[(1,5),(2,7),(3,4),(6,10),(8,9)]=>4
[(1,4),(2,7),(3,5),(6,10),(8,9)]=>8
[(1,3),(2,7),(4,5),(6,10),(8,9)]=>4
[(1,2),(3,7),(4,5),(6,10),(8,9)]=>2
[(1,2),(3,8),(4,5),(6,10),(7,9)]=>4
[(1,3),(2,8),(4,5),(6,10),(7,9)]=>8
[(1,4),(2,8),(3,5),(6,10),(7,9)]=>16
[(1,5),(2,8),(3,4),(6,10),(7,9)]=>8
[(1,6),(2,8),(3,4),(5,10),(7,9)]=>10
[(1,7),(2,8),(3,4),(5,10),(6,9)]=>14
[(1,8),(2,7),(3,4),(5,10),(6,9)]=>13
[(1,9),(2,7),(3,4),(5,10),(6,8)]=>8
[(1,10),(2,7),(3,4),(5,9),(6,8)]=>4
[(1,10),(2,8),(3,4),(5,9),(6,7)]=>2
[(1,9),(2,8),(3,4),(5,10),(6,7)]=>4
[(1,8),(2,9),(3,4),(5,10),(6,7)]=>5
[(1,7),(2,9),(3,4),(5,10),(6,8)]=>10
[(1,6),(2,9),(3,4),(5,10),(7,8)]=>5
[(1,5),(2,9),(3,4),(6,10),(7,8)]=>4
[(1,4),(2,9),(3,5),(6,10),(7,8)]=>8
[(1,3),(2,9),(4,5),(6,10),(7,8)]=>4
[(1,2),(3,9),(4,5),(6,10),(7,8)]=>2
[(1,2),(3,10),(4,5),(6,9),(7,8)]=>1
[(1,3),(2,10),(4,5),(6,9),(7,8)]=>2
[(1,4),(2,10),(3,5),(6,9),(7,8)]=>4
[(1,5),(2,10),(3,4),(6,9),(7,8)]=>2
[(1,6),(2,10),(3,4),(5,9),(7,8)]=>4
[(1,7),(2,10),(3,4),(5,9),(6,8)]=>8
[(1,8),(2,10),(3,4),(5,9),(6,7)]=>4
[(1,9),(2,10),(3,4),(5,8),(6,7)]=>2
[(1,10),(2,9),(3,4),(5,8),(6,7)]=>1
[(1,10),(2,9),(3,5),(4,8),(6,7)]=>2
[(1,9),(2,10),(3,5),(4,8),(6,7)]=>4
[(1,8),(2,10),(3,5),(4,9),(6,7)]=>8
[(1,7),(2,10),(3,5),(4,9),(6,8)]=>16
[(1,6),(2,10),(3,5),(4,9),(7,8)]=>8
[(1,5),(2,10),(3,6),(4,9),(7,8)]=>10
[(1,4),(2,10),(3,6),(5,9),(7,8)]=>8
[(1,3),(2,10),(4,6),(5,9),(7,8)]=>4
[(1,2),(3,10),(4,6),(5,9),(7,8)]=>2
[(1,2),(3,9),(4,6),(5,10),(7,8)]=>4
[(1,3),(2,9),(4,6),(5,10),(7,8)]=>8
[(1,4),(2,9),(3,6),(5,10),(7,8)]=>13
[(1,5),(2,9),(3,6),(4,10),(7,8)]=>14
[(1,6),(2,9),(3,5),(4,10),(7,8)]=>10
[(1,7),(2,9),(3,5),(4,10),(6,8)]=>20
[(1,8),(2,9),(3,5),(4,10),(6,7)]=>10
[(1,9),(2,8),(3,5),(4,10),(6,7)]=>8
[(1,10),(2,8),(3,5),(4,9),(6,7)]=>4
[(1,10),(2,7),(3,5),(4,9),(6,8)]=>8
[(1,9),(2,7),(3,5),(4,10),(6,8)]=>16
[(1,8),(2,7),(3,5),(4,10),(6,9)]=>26
[(1,7),(2,8),(3,5),(4,10),(6,9)]=>28
[(1,6),(2,8),(3,5),(4,10),(7,9)]=>20
[(1,5),(2,8),(3,6),(4,10),(7,9)]=>28
[(1,4),(2,8),(3,6),(5,10),(7,9)]=>26
[(1,3),(2,8),(4,6),(5,10),(7,9)]=>16
[(1,2),(3,8),(4,6),(5,10),(7,9)]=>8
[(1,2),(3,7),(4,6),(5,10),(8,9)]=>4
[(1,3),(2,7),(4,6),(5,10),(8,9)]=>8
[(1,4),(2,7),(3,6),(5,10),(8,9)]=>13
[(1,5),(2,7),(3,6),(4,10),(8,9)]=>14
[(1,6),(2,7),(3,5),(4,10),(8,9)]=>10
[(1,7),(2,6),(3,5),(4,10),(8,9)]=>8
[(1,8),(2,6),(3,5),(4,10),(7,9)]=>16
[(1,9),(2,6),(3,5),(4,10),(7,8)]=>8
[(1,10),(2,6),(3,5),(4,9),(7,8)]=>4
[(1,10),(2,5),(3,6),(4,9),(7,8)]=>5
[(1,9),(2,5),(3,6),(4,10),(7,8)]=>10
[(1,8),(2,5),(3,6),(4,10),(7,9)]=>20
[(1,7),(2,5),(3,6),(4,10),(8,9)]=>10
[(1,6),(2,5),(3,7),(4,10),(8,9)]=>14
[(1,5),(2,6),(3,7),(4,10),(8,9)]=>16
[(1,4),(2,6),(3,7),(5,10),(8,9)]=>14
[(1,3),(2,6),(4,7),(5,10),(8,9)]=>10
[(1,2),(3,6),(4,7),(5,10),(8,9)]=>5
[(1,2),(3,5),(4,7),(6,10),(8,9)]=>4
[(1,3),(2,5),(4,7),(6,10),(8,9)]=>8
[(1,4),(2,5),(3,7),(6,10),(8,9)]=>10
[(1,5),(2,4),(3,7),(6,10),(8,9)]=>8
[(1,6),(2,4),(3,7),(5,10),(8,9)]=>10
[(1,7),(2,4),(3,6),(5,10),(8,9)]=>8
[(1,8),(2,4),(3,6),(5,10),(7,9)]=>16
[(1,9),(2,4),(3,6),(5,10),(7,8)]=>8
[(1,10),(2,4),(3,6),(5,9),(7,8)]=>4
[(1,10),(2,3),(4,6),(5,9),(7,8)]=>2
[(1,9),(2,3),(4,6),(5,10),(7,8)]=>4
[(1,8),(2,3),(4,6),(5,10),(7,9)]=>8
[(1,7),(2,3),(4,6),(5,10),(8,9)]=>4
[(1,6),(2,3),(4,7),(5,10),(8,9)]=>5
[(1,5),(2,3),(4,7),(6,10),(8,9)]=>4
[(1,4),(2,3),(5,7),(6,10),(8,9)]=>2
[(1,3),(2,4),(5,7),(6,10),(8,9)]=>4
[(1,2),(3,4),(5,7),(6,10),(8,9)]=>2
[(1,2),(3,4),(5,8),(6,10),(7,9)]=>4
[(1,3),(2,4),(5,8),(6,10),(7,9)]=>8
[(1,4),(2,3),(5,8),(6,10),(7,9)]=>4
[(1,5),(2,3),(4,8),(6,10),(7,9)]=>8
[(1,6),(2,3),(4,8),(5,10),(7,9)]=>10
[(1,7),(2,3),(4,8),(5,10),(6,9)]=>14
[(1,8),(2,3),(4,7),(5,10),(6,9)]=>13
[(1,9),(2,3),(4,7),(5,10),(6,8)]=>8
[(1,10),(2,3),(4,7),(5,9),(6,8)]=>4
[(1,10),(2,4),(3,7),(5,9),(6,8)]=>8
[(1,9),(2,4),(3,7),(5,10),(6,8)]=>16
[(1,8),(2,4),(3,7),(5,10),(6,9)]=>26
[(1,7),(2,4),(3,8),(5,10),(6,9)]=>28
[(1,6),(2,4),(3,8),(5,10),(7,9)]=>20
[(1,5),(2,4),(3,8),(6,10),(7,9)]=>16
[(1,4),(2,5),(3,8),(6,10),(7,9)]=>20
[(1,3),(2,5),(4,8),(6,10),(7,9)]=>16
[(1,2),(3,5),(4,8),(6,10),(7,9)]=>8
[(1,2),(3,6),(4,8),(5,10),(7,9)]=>10
[(1,3),(2,6),(4,8),(5,10),(7,9)]=>20
[(1,4),(2,6),(3,8),(5,10),(7,9)]=>28
[(1,5),(2,6),(3,8),(4,10),(7,9)]=>32
[(1,6),(2,5),(3,8),(4,10),(7,9)]=>28
[(1,7),(2,5),(3,8),(4,10),(6,9)]=>38
[(1,8),(2,5),(3,7),(4,10),(6,9)]=>34
[(1,9),(2,5),(3,7),(4,10),(6,8)]=>20
[(1,10),(2,5),(3,7),(4,9),(6,8)]=>10
[(1,10),(2,6),(3,7),(4,9),(5,8)]=>14
[(1,9),(2,6),(3,7),(4,10),(5,8)]=>28
[(1,8),(2,6),(3,7),(4,10),(5,9)]=>44
[(1,7),(2,6),(3,8),(4,10),(5,9)]=>52
[(1,6),(2,7),(3,8),(4,10),(5,9)]=>56
[(1,5),(2,7),(3,8),(4,10),(6,9)]=>46
[(1,4),(2,7),(3,8),(5,10),(6,9)]=>41
[(1,3),(2,7),(4,8),(5,10),(6,9)]=>28
[(1,2),(3,7),(4,8),(5,10),(6,9)]=>14
[(1,2),(3,8),(4,7),(5,10),(6,9)]=>13
[(1,3),(2,8),(4,7),(5,10),(6,9)]=>26
[(1,4),(2,8),(3,7),(5,10),(6,9)]=>40
[(1,5),(2,8),(3,7),(4,10),(6,9)]=>44
[(1,6),(2,8),(3,7),(4,10),(5,9)]=>52
[(1,7),(2,8),(3,6),(4,10),(5,9)]=>44
[(1,8),(2,7),(3,6),(4,10),(5,9)]=>40
[(1,9),(2,7),(3,6),(4,10),(5,8)]=>26
[(1,10),(2,7),(3,6),(4,9),(5,8)]=>13
[(1,10),(2,8),(3,6),(4,9),(5,7)]=>8
[(1,9),(2,8),(3,6),(4,10),(5,7)]=>16
[(1,8),(2,9),(3,6),(4,10),(5,7)]=>20
[(1,7),(2,9),(3,6),(4,10),(5,8)]=>34
[(1,6),(2,9),(3,7),(4,10),(5,8)]=>38
[(1,5),(2,9),(3,7),(4,10),(6,8)]=>28
[(1,4),(2,9),(3,7),(5,10),(6,8)]=>26
[(1,3),(2,9),(4,7),(5,10),(6,8)]=>16
[(1,2),(3,9),(4,7),(5,10),(6,8)]=>8
[(1,2),(3,10),(4,7),(5,9),(6,8)]=>4
[(1,3),(2,10),(4,7),(5,9),(6,8)]=>8
[(1,4),(2,10),(3,7),(5,9),(6,8)]=>16
[(1,5),(2,10),(3,7),(4,9),(6,8)]=>20
[(1,6),(2,10),(3,7),(4,9),(5,8)]=>28
[(1,7),(2,10),(3,6),(4,9),(5,8)]=>26
[(1,8),(2,10),(3,6),(4,9),(5,7)]=>16
[(1,9),(2,10),(3,6),(4,8),(5,7)]=>8
[(1,10),(2,9),(3,6),(4,8),(5,7)]=>4
[(1,10),(2,9),(3,7),(4,8),(5,6)]=>2
[(1,9),(2,10),(3,7),(4,8),(5,6)]=>4
[(1,8),(2,10),(3,7),(4,9),(5,6)]=>8
[(1,7),(2,10),(3,8),(4,9),(5,6)]=>10
[(1,6),(2,10),(3,8),(4,9),(5,7)]=>20
[(1,5),(2,10),(3,8),(4,9),(6,7)]=>10
[(1,4),(2,10),(3,8),(5,9),(6,7)]=>8
[(1,3),(2,10),(4,8),(5,9),(6,7)]=>4
[(1,2),(3,10),(4,8),(5,9),(6,7)]=>2
[(1,2),(3,9),(4,8),(5,10),(6,7)]=>4
[(1,3),(2,9),(4,8),(5,10),(6,7)]=>8
[(1,4),(2,9),(3,8),(5,10),(6,7)]=>13
[(1,5),(2,9),(3,8),(4,10),(6,7)]=>14
[(1,6),(2,9),(3,8),(4,10),(5,7)]=>28
[(1,7),(2,9),(3,8),(4,10),(5,6)]=>14
[(1,8),(2,9),(3,7),(4,10),(5,6)]=>10
[(1,9),(2,8),(3,7),(4,10),(5,6)]=>8
[(1,10),(2,8),(3,7),(4,9),(5,6)]=>4
[(1,10),(2,7),(3,8),(4,9),(5,6)]=>5
[(1,9),(2,7),(3,8),(4,10),(5,6)]=>10
[(1,8),(2,7),(3,9),(4,10),(5,6)]=>14
[(1,7),(2,8),(3,9),(4,10),(5,6)]=>16
[(1,6),(2,8),(3,9),(4,10),(5,7)]=>32
[(1,5),(2,8),(3,9),(4,10),(6,7)]=>16
[(1,4),(2,8),(3,9),(5,10),(6,7)]=>14
[(1,3),(2,8),(4,9),(5,10),(6,7)]=>10
[(1,2),(3,8),(4,9),(5,10),(6,7)]=>5
[(1,2),(3,7),(4,9),(5,10),(6,8)]=>10
[(1,3),(2,7),(4,9),(5,10),(6,8)]=>20
[(1,4),(2,7),(3,9),(5,10),(6,8)]=>28
[(1,5),(2,7),(3,9),(4,10),(6,8)]=>32
[(1,6),(2,7),(3,9),(4,10),(5,8)]=>46
[(1,7),(2,6),(3,9),(4,10),(5,8)]=>44
[(1,8),(2,6),(3,9),(4,10),(5,7)]=>28
[(1,9),(2,6),(3,8),(4,10),(5,7)]=>20
[(1,10),(2,6),(3,8),(4,9),(5,7)]=>10
[(1,10),(2,5),(3,8),(4,9),(6,7)]=>5
[(1,9),(2,5),(3,8),(4,10),(6,7)]=>10
[(1,8),(2,5),(3,9),(4,10),(6,7)]=>14
[(1,7),(2,5),(3,9),(4,10),(6,8)]=>28
[(1,6),(2,5),(3,9),(4,10),(7,8)]=>14
[(1,5),(2,6),(3,9),(4,10),(7,8)]=>16
[(1,4),(2,6),(3,9),(5,10),(7,8)]=>14
[(1,3),(2,6),(4,9),(5,10),(7,8)]=>10
[(1,2),(3,6),(4,9),(5,10),(7,8)]=>5
[(1,2),(3,5),(4,9),(6,10),(7,8)]=>4
[(1,3),(2,5),(4,9),(6,10),(7,8)]=>8
[(1,4),(2,5),(3,9),(6,10),(7,8)]=>10
[(1,5),(2,4),(3,9),(6,10),(7,8)]=>8
[(1,6),(2,4),(3,9),(5,10),(7,8)]=>10
[(1,7),(2,4),(3,9),(5,10),(6,8)]=>20
[(1,8),(2,4),(3,9),(5,10),(6,7)]=>10
[(1,9),(2,4),(3,8),(5,10),(6,7)]=>8
[(1,10),(2,4),(3,8),(5,9),(6,7)]=>4
[(1,10),(2,3),(4,8),(5,9),(6,7)]=>2
[(1,9),(2,3),(4,8),(5,10),(6,7)]=>4
[(1,8),(2,3),(4,9),(5,10),(6,7)]=>5
[(1,7),(2,3),(4,9),(5,10),(6,8)]=>10
[(1,6),(2,3),(4,9),(5,10),(7,8)]=>5
[(1,5),(2,3),(4,9),(6,10),(7,8)]=>4
[(1,4),(2,3),(5,9),(6,10),(7,8)]=>2
[(1,3),(2,4),(5,9),(6,10),(7,8)]=>4
[(1,2),(3,4),(5,9),(6,10),(7,8)]=>2
[(1,2),(3,4),(5,10),(6,9),(7,8)]=>1
[(1,3),(2,4),(5,10),(6,9),(7,8)]=>2
[(1,4),(2,3),(5,10),(6,9),(7,8)]=>1
[(1,5),(2,3),(4,10),(6,9),(7,8)]=>2
[(1,6),(2,3),(4,10),(5,9),(7,8)]=>4
[(1,7),(2,3),(4,10),(5,9),(6,8)]=>8
[(1,8),(2,3),(4,10),(5,9),(6,7)]=>4
[(1,9),(2,3),(4,10),(5,8),(6,7)]=>2
[(1,10),(2,3),(4,9),(5,8),(6,7)]=>1
[(1,10),(2,4),(3,9),(5,8),(6,7)]=>2
[(1,9),(2,4),(3,10),(5,8),(6,7)]=>4
[(1,8),(2,4),(3,10),(5,9),(6,7)]=>8
[(1,7),(2,4),(3,10),(5,9),(6,8)]=>16
[(1,6),(2,4),(3,10),(5,9),(7,8)]=>8
[(1,5),(2,4),(3,10),(6,9),(7,8)]=>4
[(1,4),(2,5),(3,10),(6,9),(7,8)]=>5
[(1,3),(2,5),(4,10),(6,9),(7,8)]=>4
[(1,2),(3,5),(4,10),(6,9),(7,8)]=>2
[(1,2),(3,6),(4,10),(5,9),(7,8)]=>4
[(1,3),(2,6),(4,10),(5,9),(7,8)]=>8
[(1,4),(2,6),(3,10),(5,9),(7,8)]=>10
[(1,5),(2,6),(3,10),(4,9),(7,8)]=>14
[(1,6),(2,5),(3,10),(4,9),(7,8)]=>13
[(1,7),(2,5),(3,10),(4,9),(6,8)]=>26
[(1,8),(2,5),(3,10),(4,9),(6,7)]=>13
[(1,9),(2,5),(3,10),(4,8),(6,7)]=>8
[(1,10),(2,5),(3,9),(4,8),(6,7)]=>4
[(1,10),(2,6),(3,9),(4,8),(5,7)]=>8
[(1,9),(2,6),(3,10),(4,8),(5,7)]=>16
[(1,8),(2,6),(3,10),(4,9),(5,7)]=>26
[(1,7),(2,6),(3,10),(4,9),(5,8)]=>40
[(1,6),(2,7),(3,10),(4,9),(5,8)]=>41
[(1,5),(2,7),(3,10),(4,9),(6,8)]=>28
[(1,4),(2,7),(3,10),(5,9),(6,8)]=>20
[(1,3),(2,7),(4,10),(5,9),(6,8)]=>16
[(1,2),(3,7),(4,10),(5,9),(6,8)]=>8
[(1,2),(3,8),(4,10),(5,9),(6,7)]=>4
[(1,3),(2,8),(4,10),(5,9),(6,7)]=>8
[(1,4),(2,8),(3,10),(5,9),(6,7)]=>10
[(1,5),(2,8),(3,10),(4,9),(6,7)]=>14
[(1,6),(2,8),(3,10),(4,9),(5,7)]=>28
[(1,7),(2,8),(3,10),(4,9),(5,6)]=>14
[(1,8),(2,7),(3,10),(4,9),(5,6)]=>13
[(1,9),(2,7),(3,10),(4,8),(5,6)]=>8
[(1,10),(2,7),(3,9),(4,8),(5,6)]=>4
[(1,10),(2,8),(3,9),(4,7),(5,6)]=>2
[(1,9),(2,8),(3,10),(4,7),(5,6)]=>4
[(1,8),(2,9),(3,10),(4,7),(5,6)]=>5
[(1,7),(2,9),(3,10),(4,8),(5,6)]=>10
[(1,6),(2,9),(3,10),(4,8),(5,7)]=>20
[(1,5),(2,9),(3,10),(4,8),(6,7)]=>10
[(1,4),(2,9),(3,10),(5,8),(6,7)]=>5
[(1,3),(2,9),(4,10),(5,8),(6,7)]=>4
[(1,2),(3,9),(4,10),(5,8),(6,7)]=>2
[(1,2),(3,10),(4,9),(5,8),(6,7)]=>1
[(1,3),(2,10),(4,9),(5,8),(6,7)]=>2
[(1,4),(2,10),(3,9),(5,8),(6,7)]=>4
[(1,5),(2,10),(3,9),(4,8),(6,7)]=>8
[(1,6),(2,10),(3,9),(4,8),(5,7)]=>16
[(1,7),(2,10),(3,9),(4,8),(5,6)]=>8
[(1,8),(2,10),(3,9),(4,7),(5,6)]=>4
[(1,9),(2,10),(3,8),(4,7),(5,6)]=>2
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>1
                    

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Description

The chord expansion number of a perfect matching.
Given a perfect matching, we obtain a formal sum of non-crossing perfect matchings by replacing recursively every matching $M$ that has a crossing $(a, c), (b, d)$ with $a < b < c < d$ with the sum of the two matchings $(M\setminus \{(a,c), (b,d)\})\cup \{(a,b), (c,d)\}$ and $(M\setminus \{(a,c), (b,d)\})\cup \{(a,d), (b,c)\}$.
This statistic is the sum of the coefficients in the formal sum.

Code

def expand(M, ac, bd):
    a, c = ac
    b, d = bd
    m = list(M)
    m.remove(frozenset(ac))
    m.remove(frozenset(bd))
    m1 = m + [frozenset([a, b]), frozenset([c, d])]
    m2 = m + [frozenset([a, d]), frozenset([b, c])]
    return PerfectMatching(m1), PerfectMatching(m2)

def expansion(M):
    input = {M: 1}
    output = {}
    while input:
        m, e = input.popitem()
        try:
            ac, bd = next(m.crossings_iterator())
        except StopIteration:
            output[m] = output.get(m, 0) + e
        else:
            m1, m2 = expand(m, ac, bd)
            input[m1] = input.get(m1, 0) + e
            input[m2] = input.get(m2, 0) + e
    return output

def statistic(M):
    return sum(expansion(M).values())

Created

Aug 31, 2022 at 17:42 by Martin Rubey

Updated

Aug 31, 2022 at 17:42 by Martin Rubey