Identifier
- St001831: Perfect matchings ⟶ ℤ
Values
=>
Cc0012;cc-rep
[(1,2)]=>1
[(1,2),(3,4)]=>1
[(1,3),(2,4)]=>1
[(1,4),(2,3)]=>0
[(1,2),(3,4),(5,6)]=>1
[(1,3),(2,4),(5,6)]=>1
[(1,4),(2,3),(5,6)]=>0
[(1,5),(2,3),(4,6)]=>0
[(1,6),(2,3),(4,5)]=>0
[(1,6),(2,4),(3,5)]=>0
[(1,5),(2,4),(3,6)]=>1
[(1,4),(2,5),(3,6)]=>1
[(1,3),(2,5),(4,6)]=>1
[(1,2),(3,5),(4,6)]=>1
[(1,2),(3,6),(4,5)]=>0
[(1,3),(2,6),(4,5)]=>0
[(1,4),(2,6),(3,5)]=>1
[(1,5),(2,6),(3,4)]=>1
[(1,6),(2,5),(3,4)]=>0
[(1,2),(3,4),(5,6),(7,8)]=>1
[(1,3),(2,4),(5,6),(7,8)]=>1
[(1,4),(2,3),(5,6),(7,8)]=>0
[(1,5),(2,3),(4,6),(7,8)]=>0
[(1,6),(2,3),(4,5),(7,8)]=>0
[(1,7),(2,3),(4,5),(6,8)]=>0
[(1,8),(2,3),(4,5),(6,7)]=>0
[(1,8),(2,4),(3,5),(6,7)]=>0
[(1,7),(2,4),(3,5),(6,8)]=>0
[(1,6),(2,4),(3,5),(7,8)]=>0
[(1,5),(2,4),(3,6),(7,8)]=>1
[(1,4),(2,5),(3,6),(7,8)]=>1
[(1,3),(2,5),(4,6),(7,8)]=>1
[(1,2),(3,5),(4,6),(7,8)]=>1
[(1,2),(3,6),(4,5),(7,8)]=>0
[(1,3),(2,6),(4,5),(7,8)]=>0
[(1,4),(2,6),(3,5),(7,8)]=>1
[(1,5),(2,6),(3,4),(7,8)]=>1
[(1,6),(2,5),(3,4),(7,8)]=>0
[(1,7),(2,5),(3,4),(6,8)]=>0
[(1,8),(2,5),(3,4),(6,7)]=>0
[(1,8),(2,6),(3,4),(5,7)]=>0
[(1,7),(2,6),(3,4),(5,8)]=>1
[(1,6),(2,7),(3,4),(5,8)]=>1
[(1,5),(2,7),(3,4),(6,8)]=>1
[(1,4),(2,7),(3,5),(6,8)]=>1
[(1,3),(2,7),(4,5),(6,8)]=>0
[(1,2),(3,7),(4,5),(6,8)]=>0
[(1,2),(3,8),(4,5),(6,7)]=>0
[(1,3),(2,8),(4,5),(6,7)]=>0
[(1,4),(2,8),(3,5),(6,7)]=>0
[(1,5),(2,8),(3,4),(6,7)]=>0
[(1,6),(2,8),(3,4),(5,7)]=>1
[(1,7),(2,8),(3,4),(5,6)]=>1
[(1,8),(2,7),(3,4),(5,6)]=>0
[(1,8),(2,7),(3,5),(4,6)]=>0
[(1,7),(2,8),(3,5),(4,6)]=>1
[(1,6),(2,8),(3,5),(4,7)]=>1
[(1,5),(2,8),(3,6),(4,7)]=>1
[(1,4),(2,8),(3,6),(5,7)]=>1
[(1,3),(2,8),(4,6),(5,7)]=>0
[(1,2),(3,8),(4,6),(5,7)]=>0
[(1,2),(3,7),(4,6),(5,8)]=>1
[(1,3),(2,7),(4,6),(5,8)]=>1
[(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)]=>1
[(1,7),(2,6),(3,5),(4,8)]=>1
[(1,8),(2,6),(3,5),(4,7)]=>0
[(1,8),(2,5),(3,6),(4,7)]=>0
[(1,7),(2,5),(3,6),(4,8)]=>1
[(1,6),(2,5),(3,7),(4,8)]=>1
[(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)]=>1
[(1,2),(3,6),(4,7),(5,8)]=>1
[(1,2),(3,5),(4,7),(6,8)]=>1
[(1,3),(2,5),(4,7),(6,8)]=>1
[(1,4),(2,5),(3,7),(6,8)]=>1
[(1,5),(2,4),(3,7),(6,8)]=>1
[(1,6),(2,4),(3,7),(5,8)]=>1
[(1,7),(2,4),(3,6),(5,8)]=>1
[(1,8),(2,4),(3,6),(5,7)]=>0
[(1,8),(2,3),(4,6),(5,7)]=>0
[(1,7),(2,3),(4,6),(5,8)]=>0
[(1,6),(2,3),(4,7),(5,8)]=>0
[(1,5),(2,3),(4,7),(6,8)]=>0
[(1,4),(2,3),(5,7),(6,8)]=>0
[(1,3),(2,4),(5,7),(6,8)]=>1
[(1,2),(3,4),(5,7),(6,8)]=>1
[(1,2),(3,4),(5,8),(6,7)]=>0
[(1,3),(2,4),(5,8),(6,7)]=>0
[(1,4),(2,3),(5,8),(6,7)]=>0
[(1,5),(2,3),(4,8),(6,7)]=>0
[(1,6),(2,3),(4,8),(5,7)]=>0
[(1,7),(2,3),(4,8),(5,6)]=>0
[(1,8),(2,3),(4,7),(5,6)]=>0
[(1,8),(2,4),(3,7),(5,6)]=>0
[(1,7),(2,4),(3,8),(5,6)]=>1
[(1,6),(2,4),(3,8),(5,7)]=>1
[(1,5),(2,4),(3,8),(6,7)]=>0
[(1,4),(2,5),(3,8),(6,7)]=>0
[(1,3),(2,5),(4,8),(6,7)]=>0
[(1,2),(3,5),(4,8),(6,7)]=>0
[(1,2),(3,6),(4,8),(5,7)]=>1
[(1,3),(2,6),(4,8),(5,7)]=>1
[(1,4),(2,6),(3,8),(5,7)]=>1
[(1,5),(2,6),(3,8),(4,7)]=>1
[(1,6),(2,5),(3,8),(4,7)]=>1
[(1,7),(2,5),(3,8),(4,6)]=>1
[(1,8),(2,5),(3,7),(4,6)]=>0
[(1,8),(2,6),(3,7),(4,5)]=>0
[(1,7),(2,6),(3,8),(4,5)]=>0
[(1,6),(2,7),(3,8),(4,5)]=>0
[(1,5),(2,7),(3,8),(4,6)]=>1
[(1,4),(2,7),(3,8),(5,6)]=>1
[(1,3),(2,7),(4,8),(5,6)]=>1
[(1,2),(3,7),(4,8),(5,6)]=>1
[(1,2),(3,8),(4,7),(5,6)]=>0
[(1,3),(2,8),(4,7),(5,6)]=>0
[(1,4),(2,8),(3,7),(5,6)]=>1
[(1,5),(2,8),(3,7),(4,6)]=>1
[(1,6),(2,8),(3,7),(4,5)]=>0
[(1,7),(2,8),(3,6),(4,5)]=>0
[(1,8),(2,7),(3,6),(4,5)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>1
[(1,3),(2,4),(5,6),(7,8),(9,10)]=>1
[(1,4),(2,3),(5,6),(7,8),(9,10)]=>0
[(1,5),(2,3),(4,6),(7,8),(9,10)]=>0
[(1,6),(2,3),(4,5),(7,8),(9,10)]=>0
[(1,7),(2,3),(4,5),(6,8),(9,10)]=>0
[(1,8),(2,3),(4,5),(6,7),(9,10)]=>0
[(1,9),(2,3),(4,5),(6,7),(8,10)]=>0
[(1,10),(2,3),(4,5),(6,7),(8,9)]=>0
[(1,10),(2,4),(3,5),(6,7),(8,9)]=>0
[(1,9),(2,4),(3,5),(6,7),(8,10)]=>0
[(1,8),(2,4),(3,5),(6,7),(9,10)]=>0
[(1,7),(2,4),(3,5),(6,8),(9,10)]=>0
[(1,6),(2,4),(3,5),(7,8),(9,10)]=>0
[(1,5),(2,4),(3,6),(7,8),(9,10)]=>1
[(1,4),(2,5),(3,6),(7,8),(9,10)]=>1
[(1,3),(2,5),(4,6),(7,8),(9,10)]=>1
[(1,2),(3,5),(4,6),(7,8),(9,10)]=>1
[(1,2),(3,6),(4,5),(7,8),(9,10)]=>0
[(1,3),(2,6),(4,5),(7,8),(9,10)]=>0
[(1,4),(2,6),(3,5),(7,8),(9,10)]=>1
[(1,5),(2,6),(3,4),(7,8),(9,10)]=>1
[(1,6),(2,5),(3,4),(7,8),(9,10)]=>0
[(1,7),(2,5),(3,4),(6,8),(9,10)]=>0
[(1,8),(2,5),(3,4),(6,7),(9,10)]=>0
[(1,9),(2,5),(3,4),(6,7),(8,10)]=>0
[(1,10),(2,5),(3,4),(6,7),(8,9)]=>0
[(1,10),(2,6),(3,4),(5,7),(8,9)]=>0
[(1,9),(2,6),(3,4),(5,7),(8,10)]=>0
[(1,8),(2,6),(3,4),(5,7),(9,10)]=>0
[(1,7),(2,6),(3,4),(5,8),(9,10)]=>1
[(1,6),(2,7),(3,4),(5,8),(9,10)]=>1
[(1,5),(2,7),(3,4),(6,8),(9,10)]=>1
[(1,4),(2,7),(3,5),(6,8),(9,10)]=>1
[(1,3),(2,7),(4,5),(6,8),(9,10)]=>0
[(1,2),(3,7),(4,5),(6,8),(9,10)]=>0
[(1,2),(3,8),(4,5),(6,7),(9,10)]=>0
[(1,3),(2,8),(4,5),(6,7),(9,10)]=>0
[(1,4),(2,8),(3,5),(6,7),(9,10)]=>0
[(1,5),(2,8),(3,4),(6,7),(9,10)]=>0
[(1,6),(2,8),(3,4),(5,7),(9,10)]=>1
[(1,7),(2,8),(3,4),(5,6),(9,10)]=>1
[(1,8),(2,7),(3,4),(5,6),(9,10)]=>0
[(1,9),(2,7),(3,4),(5,6),(8,10)]=>0
[(1,10),(2,7),(3,4),(5,6),(8,9)]=>0
[(1,10),(2,8),(3,4),(5,6),(7,9)]=>0
[(1,9),(2,8),(3,4),(5,6),(7,10)]=>1
[(1,8),(2,9),(3,4),(5,6),(7,10)]=>1
[(1,7),(2,9),(3,4),(5,6),(8,10)]=>1
[(1,6),(2,9),(3,4),(5,7),(8,10)]=>1
[(1,5),(2,9),(3,4),(6,7),(8,10)]=>0
[(1,4),(2,9),(3,5),(6,7),(8,10)]=>0
[(1,3),(2,9),(4,5),(6,7),(8,10)]=>0
[(1,2),(3,9),(4,5),(6,7),(8,10)]=>0
[(1,2),(3,10),(4,5),(6,7),(8,9)]=>0
[(1,3),(2,10),(4,5),(6,7),(8,9)]=>0
[(1,4),(2,10),(3,5),(6,7),(8,9)]=>0
[(1,5),(2,10),(3,4),(6,7),(8,9)]=>0
[(1,6),(2,10),(3,4),(5,7),(8,9)]=>0
[(1,7),(2,10),(3,4),(5,6),(8,9)]=>0
[(1,8),(2,10),(3,4),(5,6),(7,9)]=>1
[(1,9),(2,10),(3,4),(5,6),(7,8)]=>1
[(1,10),(2,9),(3,4),(5,6),(7,8)]=>0
[(1,10),(2,9),(3,5),(4,6),(7,8)]=>0
[(1,9),(2,10),(3,5),(4,6),(7,8)]=>1
[(1,8),(2,10),(3,5),(4,6),(7,9)]=>1
[(1,7),(2,10),(3,5),(4,6),(8,9)]=>0
[(1,6),(2,10),(3,5),(4,7),(8,9)]=>0
[(1,5),(2,10),(3,6),(4,7),(8,9)]=>0
[(1,4),(2,10),(3,6),(5,7),(8,9)]=>0
[(1,3),(2,10),(4,6),(5,7),(8,9)]=>0
[(1,2),(3,10),(4,6),(5,7),(8,9)]=>0
[(1,2),(3,9),(4,6),(5,7),(8,10)]=>0
[(1,3),(2,9),(4,6),(5,7),(8,10)]=>0
[(1,4),(2,9),(3,6),(5,7),(8,10)]=>1
[(1,5),(2,9),(3,6),(4,7),(8,10)]=>1
[(1,6),(2,9),(3,5),(4,7),(8,10)]=>1
[(1,7),(2,9),(3,5),(4,6),(8,10)]=>1
[(1,8),(2,9),(3,5),(4,6),(7,10)]=>1
[(1,9),(2,8),(3,5),(4,6),(7,10)]=>1
[(1,10),(2,8),(3,5),(4,6),(7,9)]=>0
[(1,10),(2,7),(3,5),(4,6),(8,9)]=>0
[(1,9),(2,7),(3,5),(4,6),(8,10)]=>0
[(1,8),(2,7),(3,5),(4,6),(9,10)]=>0
[(1,7),(2,8),(3,5),(4,6),(9,10)]=>1
[(1,6),(2,8),(3,5),(4,7),(9,10)]=>1
[(1,5),(2,8),(3,6),(4,7),(9,10)]=>1
[(1,4),(2,8),(3,6),(5,7),(9,10)]=>1
[(1,3),(2,8),(4,6),(5,7),(9,10)]=>0
[(1,2),(3,8),(4,6),(5,7),(9,10)]=>0
[(1,2),(3,7),(4,6),(5,8),(9,10)]=>1
[(1,3),(2,7),(4,6),(5,8),(9,10)]=>1
[(1,4),(2,7),(3,6),(5,8),(9,10)]=>2
[(1,5),(2,7),(3,6),(4,8),(9,10)]=>2
[(1,6),(2,7),(3,5),(4,8),(9,10)]=>1
[(1,7),(2,6),(3,5),(4,8),(9,10)]=>1
[(1,8),(2,6),(3,5),(4,7),(9,10)]=>0
[(1,9),(2,6),(3,5),(4,7),(8,10)]=>0
[(1,10),(2,6),(3,5),(4,7),(8,9)]=>0
[(1,10),(2,5),(3,6),(4,7),(8,9)]=>0
[(1,9),(2,5),(3,6),(4,7),(8,10)]=>0
[(1,8),(2,5),(3,6),(4,7),(9,10)]=>0
[(1,7),(2,5),(3,6),(4,8),(9,10)]=>1
[(1,6),(2,5),(3,7),(4,8),(9,10)]=>1
[(1,5),(2,6),(3,7),(4,8),(9,10)]=>2
[(1,4),(2,6),(3,7),(5,8),(9,10)]=>2
[(1,3),(2,6),(4,7),(5,8),(9,10)]=>1
[(1,2),(3,6),(4,7),(5,8),(9,10)]=>1
[(1,2),(3,5),(4,7),(6,8),(9,10)]=>1
[(1,3),(2,5),(4,7),(6,8),(9,10)]=>1
[(1,4),(2,5),(3,7),(6,8),(9,10)]=>1
[(1,5),(2,4),(3,7),(6,8),(9,10)]=>1
[(1,6),(2,4),(3,7),(5,8),(9,10)]=>1
[(1,7),(2,4),(3,6),(5,8),(9,10)]=>1
[(1,8),(2,4),(3,6),(5,7),(9,10)]=>0
[(1,9),(2,4),(3,6),(5,7),(8,10)]=>0
[(1,10),(2,4),(3,6),(5,7),(8,9)]=>0
[(1,10),(2,3),(4,6),(5,7),(8,9)]=>0
[(1,9),(2,3),(4,6),(5,7),(8,10)]=>0
[(1,8),(2,3),(4,6),(5,7),(9,10)]=>0
[(1,7),(2,3),(4,6),(5,8),(9,10)]=>0
[(1,6),(2,3),(4,7),(5,8),(9,10)]=>0
[(1,5),(2,3),(4,7),(6,8),(9,10)]=>0
[(1,4),(2,3),(5,7),(6,8),(9,10)]=>0
[(1,3),(2,4),(5,7),(6,8),(9,10)]=>1
[(1,2),(3,4),(5,7),(6,8),(9,10)]=>1
[(1,2),(3,4),(5,8),(6,7),(9,10)]=>0
[(1,3),(2,4),(5,8),(6,7),(9,10)]=>0
[(1,4),(2,3),(5,8),(6,7),(9,10)]=>0
[(1,5),(2,3),(4,8),(6,7),(9,10)]=>0
[(1,6),(2,3),(4,8),(5,7),(9,10)]=>0
[(1,7),(2,3),(4,8),(5,6),(9,10)]=>0
[(1,8),(2,3),(4,7),(5,6),(9,10)]=>0
[(1,9),(2,3),(4,7),(5,6),(8,10)]=>0
[(1,10),(2,3),(4,7),(5,6),(8,9)]=>0
[(1,10),(2,4),(3,7),(5,6),(8,9)]=>0
[(1,9),(2,4),(3,7),(5,6),(8,10)]=>0
[(1,8),(2,4),(3,7),(5,6),(9,10)]=>0
[(1,7),(2,4),(3,8),(5,6),(9,10)]=>1
[(1,6),(2,4),(3,8),(5,7),(9,10)]=>1
[(1,5),(2,4),(3,8),(6,7),(9,10)]=>0
[(1,4),(2,5),(3,8),(6,7),(9,10)]=>0
[(1,3),(2,5),(4,8),(6,7),(9,10)]=>0
[(1,2),(3,5),(4,8),(6,7),(9,10)]=>0
[(1,2),(3,6),(4,8),(5,7),(9,10)]=>1
[(1,3),(2,6),(4,8),(5,7),(9,10)]=>1
[(1,4),(2,6),(3,8),(5,7),(9,10)]=>1
[(1,5),(2,6),(3,8),(4,7),(9,10)]=>1
[(1,6),(2,5),(3,8),(4,7),(9,10)]=>1
[(1,7),(2,5),(3,8),(4,6),(9,10)]=>1
[(1,8),(2,5),(3,7),(4,6),(9,10)]=>0
[(1,9),(2,5),(3,7),(4,6),(8,10)]=>0
[(1,10),(2,5),(3,7),(4,6),(8,9)]=>0
[(1,10),(2,6),(3,7),(4,5),(8,9)]=>0
[(1,9),(2,6),(3,7),(4,5),(8,10)]=>0
[(1,8),(2,6),(3,7),(4,5),(9,10)]=>0
[(1,7),(2,6),(3,8),(4,5),(9,10)]=>0
[(1,6),(2,7),(3,8),(4,5),(9,10)]=>0
[(1,5),(2,7),(3,8),(4,6),(9,10)]=>1
[(1,4),(2,7),(3,8),(5,6),(9,10)]=>1
[(1,3),(2,7),(4,8),(5,6),(9,10)]=>1
[(1,2),(3,7),(4,8),(5,6),(9,10)]=>1
[(1,2),(3,8),(4,7),(5,6),(9,10)]=>0
[(1,3),(2,8),(4,7),(5,6),(9,10)]=>0
[(1,4),(2,8),(3,7),(5,6),(9,10)]=>1
[(1,5),(2,8),(3,7),(4,6),(9,10)]=>1
[(1,6),(2,8),(3,7),(4,5),(9,10)]=>0
[(1,7),(2,8),(3,6),(4,5),(9,10)]=>0
[(1,8),(2,7),(3,6),(4,5),(9,10)]=>0
[(1,9),(2,7),(3,6),(4,5),(8,10)]=>0
[(1,10),(2,7),(3,6),(4,5),(8,9)]=>0
[(1,10),(2,8),(3,6),(4,5),(7,9)]=>0
[(1,9),(2,8),(3,6),(4,5),(7,10)]=>0
[(1,8),(2,9),(3,6),(4,5),(7,10)]=>0
[(1,7),(2,9),(3,6),(4,5),(8,10)]=>0
[(1,6),(2,9),(3,7),(4,5),(8,10)]=>0
[(1,5),(2,9),(3,7),(4,6),(8,10)]=>1
[(1,4),(2,9),(3,7),(5,6),(8,10)]=>1
[(1,3),(2,9),(4,7),(5,6),(8,10)]=>0
[(1,2),(3,9),(4,7),(5,6),(8,10)]=>0
[(1,2),(3,10),(4,7),(5,6),(8,9)]=>0
[(1,3),(2,10),(4,7),(5,6),(8,9)]=>0
[(1,4),(2,10),(3,7),(5,6),(8,9)]=>0
[(1,5),(2,10),(3,7),(4,6),(8,9)]=>0
[(1,6),(2,10),(3,7),(4,5),(8,9)]=>0
[(1,7),(2,10),(3,6),(4,5),(8,9)]=>0
[(1,8),(2,10),(3,6),(4,5),(7,9)]=>0
[(1,9),(2,10),(3,6),(4,5),(7,8)]=>0
[(1,10),(2,9),(3,6),(4,5),(7,8)]=>0
[(1,10),(2,9),(3,7),(4,5),(6,8)]=>0
[(1,9),(2,10),(3,7),(4,5),(6,8)]=>0
[(1,8),(2,10),(3,7),(4,5),(6,9)]=>0
[(1,7),(2,10),(3,8),(4,5),(6,9)]=>0
[(1,6),(2,10),(3,8),(4,5),(7,9)]=>0
[(1,5),(2,10),(3,8),(4,6),(7,9)]=>1
[(1,4),(2,10),(3,8),(5,6),(7,9)]=>1
[(1,3),(2,10),(4,8),(5,6),(7,9)]=>0
[(1,2),(3,10),(4,8),(5,6),(7,9)]=>0
[(1,2),(3,9),(4,8),(5,6),(7,10)]=>1
[(1,3),(2,9),(4,8),(5,6),(7,10)]=>1
[(1,4),(2,9),(3,8),(5,6),(7,10)]=>2
[(1,5),(2,9),(3,8),(4,6),(7,10)]=>2
[(1,6),(2,9),(3,8),(4,5),(7,10)]=>0
[(1,7),(2,9),(3,8),(4,5),(6,10)]=>0
[(1,8),(2,9),(3,7),(4,5),(6,10)]=>0
[(1,9),(2,8),(3,7),(4,5),(6,10)]=>0
[(1,10),(2,8),(3,7),(4,5),(6,9)]=>0
[(1,10),(2,7),(3,8),(4,5),(6,9)]=>0
[(1,9),(2,7),(3,8),(4,5),(6,10)]=>0
[(1,8),(2,7),(3,9),(4,5),(6,10)]=>0
[(1,7),(2,8),(3,9),(4,5),(6,10)]=>0
[(1,6),(2,8),(3,9),(4,5),(7,10)]=>0
[(1,5),(2,8),(3,9),(4,6),(7,10)]=>2
[(1,4),(2,8),(3,9),(5,6),(7,10)]=>2
[(1,3),(2,8),(4,9),(5,6),(7,10)]=>1
[(1,2),(3,8),(4,9),(5,6),(7,10)]=>1
[(1,2),(3,7),(4,9),(5,6),(8,10)]=>1
[(1,3),(2,7),(4,9),(5,6),(8,10)]=>1
[(1,4),(2,7),(3,9),(5,6),(8,10)]=>1
[(1,5),(2,7),(3,9),(4,6),(8,10)]=>1
[(1,6),(2,7),(3,9),(4,5),(8,10)]=>0
[(1,7),(2,6),(3,9),(4,5),(8,10)]=>0
[(1,8),(2,6),(3,9),(4,5),(7,10)]=>0
[(1,9),(2,6),(3,8),(4,5),(7,10)]=>0
[(1,10),(2,6),(3,8),(4,5),(7,9)]=>0
[(1,10),(2,5),(3,8),(4,6),(7,9)]=>0
[(1,9),(2,5),(3,8),(4,6),(7,10)]=>1
[(1,8),(2,5),(3,9),(4,6),(7,10)]=>1
[(1,7),(2,5),(3,9),(4,6),(8,10)]=>1
[(1,6),(2,5),(3,9),(4,7),(8,10)]=>1
[(1,5),(2,6),(3,9),(4,7),(8,10)]=>1
[(1,4),(2,6),(3,9),(5,7),(8,10)]=>1
[(1,3),(2,6),(4,9),(5,7),(8,10)]=>1
[(1,2),(3,6),(4,9),(5,7),(8,10)]=>1
[(1,2),(3,5),(4,9),(6,7),(8,10)]=>0
[(1,3),(2,5),(4,9),(6,7),(8,10)]=>0
[(1,4),(2,5),(3,9),(6,7),(8,10)]=>0
[(1,5),(2,4),(3,9),(6,7),(8,10)]=>0
[(1,6),(2,4),(3,9),(5,7),(8,10)]=>1
[(1,7),(2,4),(3,9),(5,6),(8,10)]=>1
[(1,8),(2,4),(3,9),(5,6),(7,10)]=>1
[(1,9),(2,4),(3,8),(5,6),(7,10)]=>1
[(1,10),(2,4),(3,8),(5,6),(7,9)]=>0
[(1,10),(2,3),(4,8),(5,6),(7,9)]=>0
[(1,9),(2,3),(4,8),(5,6),(7,10)]=>0
[(1,8),(2,3),(4,9),(5,6),(7,10)]=>0
[(1,7),(2,3),(4,9),(5,6),(8,10)]=>0
[(1,6),(2,3),(4,9),(5,7),(8,10)]=>0
[(1,5),(2,3),(4,9),(6,7),(8,10)]=>0
[(1,4),(2,3),(5,9),(6,7),(8,10)]=>0
[(1,3),(2,4),(5,9),(6,7),(8,10)]=>0
[(1,2),(3,4),(5,9),(6,7),(8,10)]=>0
[(1,2),(3,4),(5,10),(6,7),(8,9)]=>0
[(1,3),(2,4),(5,10),(6,7),(8,9)]=>0
[(1,4),(2,3),(5,10),(6,7),(8,9)]=>0
[(1,5),(2,3),(4,10),(6,7),(8,9)]=>0
[(1,6),(2,3),(4,10),(5,7),(8,9)]=>0
[(1,7),(2,3),(4,10),(5,6),(8,9)]=>0
[(1,8),(2,3),(4,10),(5,6),(7,9)]=>0
[(1,9),(2,3),(4,10),(5,6),(7,8)]=>0
[(1,10),(2,3),(4,9),(5,6),(7,8)]=>0
[(1,10),(2,4),(3,9),(5,6),(7,8)]=>0
[(1,9),(2,4),(3,10),(5,6),(7,8)]=>1
[(1,8),(2,4),(3,10),(5,6),(7,9)]=>1
[(1,7),(2,4),(3,10),(5,6),(8,9)]=>0
[(1,6),(2,4),(3,10),(5,7),(8,9)]=>0
[(1,5),(2,4),(3,10),(6,7),(8,9)]=>0
[(1,4),(2,5),(3,10),(6,7),(8,9)]=>0
[(1,3),(2,5),(4,10),(6,7),(8,9)]=>0
[(1,2),(3,5),(4,10),(6,7),(8,9)]=>0
[(1,2),(3,6),(4,10),(5,7),(8,9)]=>0
[(1,3),(2,6),(4,10),(5,7),(8,9)]=>0
[(1,4),(2,6),(3,10),(5,7),(8,9)]=>0
[(1,5),(2,6),(3,10),(4,7),(8,9)]=>0
[(1,6),(2,5),(3,10),(4,7),(8,9)]=>0
[(1,7),(2,5),(3,10),(4,6),(8,9)]=>0
[(1,8),(2,5),(3,10),(4,6),(7,9)]=>1
[(1,9),(2,5),(3,10),(4,6),(7,8)]=>1
[(1,10),(2,5),(3,9),(4,6),(7,8)]=>0
[(1,10),(2,6),(3,9),(4,5),(7,8)]=>0
[(1,9),(2,6),(3,10),(4,5),(7,8)]=>0
[(1,8),(2,6),(3,10),(4,5),(7,9)]=>0
[(1,7),(2,6),(3,10),(4,5),(8,9)]=>0
[(1,6),(2,7),(3,10),(4,5),(8,9)]=>0
[(1,5),(2,7),(3,10),(4,6),(8,9)]=>0
[(1,4),(2,7),(3,10),(5,6),(8,9)]=>0
[(1,3),(2,7),(4,10),(5,6),(8,9)]=>0
[(1,2),(3,7),(4,10),(5,6),(8,9)]=>0
[(1,2),(3,8),(4,10),(5,6),(7,9)]=>1
[(1,3),(2,8),(4,10),(5,6),(7,9)]=>1
[(1,4),(2,8),(3,10),(5,6),(7,9)]=>1
[(1,5),(2,8),(3,10),(4,6),(7,9)]=>1
[(1,6),(2,8),(3,10),(4,5),(7,9)]=>0
[(1,7),(2,8),(3,10),(4,5),(6,9)]=>0
[(1,8),(2,7),(3,10),(4,5),(6,9)]=>0
[(1,9),(2,7),(3,10),(4,5),(6,8)]=>0
[(1,10),(2,7),(3,9),(4,5),(6,8)]=>0
[(1,10),(2,8),(3,9),(4,5),(6,7)]=>0
[(1,9),(2,8),(3,10),(4,5),(6,7)]=>0
[(1,8),(2,9),(3,10),(4,5),(6,7)]=>0
[(1,7),(2,9),(3,10),(4,5),(6,8)]=>0
[(1,6),(2,9),(3,10),(4,5),(7,8)]=>0
[(1,5),(2,9),(3,10),(4,6),(7,8)]=>1
[(1,4),(2,9),(3,10),(5,6),(7,8)]=>1
[(1,3),(2,9),(4,10),(5,6),(7,8)]=>1
[(1,2),(3,9),(4,10),(5,6),(7,8)]=>1
[(1,2),(3,10),(4,9),(5,6),(7,8)]=>0
[(1,3),(2,10),(4,9),(5,6),(7,8)]=>0
[(1,4),(2,10),(3,9),(5,6),(7,8)]=>1
[(1,5),(2,10),(3,9),(4,6),(7,8)]=>1
[(1,6),(2,10),(3,9),(4,5),(7,8)]=>0
[(1,7),(2,10),(3,9),(4,5),(6,8)]=>0
[(1,8),(2,10),(3,9),(4,5),(6,7)]=>0
[(1,9),(2,10),(3,8),(4,5),(6,7)]=>0
[(1,10),(2,9),(3,8),(4,5),(6,7)]=>0
[(1,10),(2,9),(3,8),(4,6),(5,7)]=>0
[(1,9),(2,10),(3,8),(4,6),(5,7)]=>0
[(1,8),(2,10),(3,9),(4,6),(5,7)]=>0
[(1,7),(2,10),(3,9),(4,6),(5,8)]=>1
[(1,6),(2,10),(3,9),(4,7),(5,8)]=>1
[(1,5),(2,10),(3,9),(4,7),(6,8)]=>1
[(1,4),(2,10),(3,9),(5,7),(6,8)]=>1
[(1,3),(2,10),(4,9),(5,7),(6,8)]=>0
[(1,2),(3,10),(4,9),(5,7),(6,8)]=>0
[(1,2),(3,9),(4,10),(5,7),(6,8)]=>1
[(1,3),(2,9),(4,10),(5,7),(6,8)]=>1
[(1,4),(2,9),(3,10),(5,7),(6,8)]=>1
[(1,5),(2,9),(3,10),(4,7),(6,8)]=>1
[(1,6),(2,9),(3,10),(4,7),(5,8)]=>1
[(1,7),(2,9),(3,10),(4,6),(5,8)]=>1
[(1,8),(2,9),(3,10),(4,6),(5,7)]=>0
[(1,9),(2,8),(3,10),(4,6),(5,7)]=>0
[(1,10),(2,8),(3,9),(4,6),(5,7)]=>0
[(1,10),(2,7),(3,9),(4,6),(5,8)]=>0
[(1,9),(2,7),(3,10),(4,6),(5,8)]=>1
[(1,8),(2,7),(3,10),(4,6),(5,9)]=>1
[(1,7),(2,8),(3,10),(4,6),(5,9)]=>1
[(1,6),(2,8),(3,10),(4,7),(5,9)]=>1
[(1,5),(2,8),(3,10),(4,7),(6,9)]=>1
[(1,4),(2,8),(3,10),(5,7),(6,9)]=>1
[(1,3),(2,8),(4,10),(5,7),(6,9)]=>1
[(1,2),(3,8),(4,10),(5,7),(6,9)]=>1
[(1,2),(3,7),(4,10),(5,8),(6,9)]=>1
[(1,3),(2,7),(4,10),(5,8),(6,9)]=>1
[(1,4),(2,7),(3,10),(5,8),(6,9)]=>1
[(1,5),(2,7),(3,10),(4,8),(6,9)]=>1
[(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)]=>1
[(1,9),(2,6),(3,10),(4,7),(5,8)]=>1
[(1,10),(2,6),(3,9),(4,7),(5,8)]=>0
[(1,10),(2,5),(3,9),(4,7),(6,8)]=>0
[(1,9),(2,5),(3,10),(4,7),(6,8)]=>1
[(1,8),(2,5),(3,10),(4,7),(6,9)]=>1
[(1,7),(2,5),(3,10),(4,8),(6,9)]=>1
[(1,6),(2,5),(3,10),(4,8),(7,9)]=>1
[(1,5),(2,6),(3,10),(4,8),(7,9)]=>1
[(1,4),(2,6),(3,10),(5,8),(7,9)]=>1
[(1,3),(2,6),(4,10),(5,8),(7,9)]=>1
[(1,2),(3,6),(4,10),(5,8),(7,9)]=>1
[(1,2),(3,5),(4,10),(6,8),(7,9)]=>0
[(1,3),(2,5),(4,10),(6,8),(7,9)]=>0
[(1,4),(2,5),(3,10),(6,8),(7,9)]=>0
[(1,5),(2,4),(3,10),(6,8),(7,9)]=>0
[(1,6),(2,4),(3,10),(5,8),(7,9)]=>1
[(1,7),(2,4),(3,10),(5,8),(6,9)]=>1
[(1,8),(2,4),(3,10),(5,7),(6,9)]=>1
[(1,9),(2,4),(3,10),(5,7),(6,8)]=>1
[(1,10),(2,4),(3,9),(5,7),(6,8)]=>0
[(1,10),(2,3),(4,9),(5,7),(6,8)]=>0
[(1,9),(2,3),(4,10),(5,7),(6,8)]=>0
[(1,8),(2,3),(4,10),(5,7),(6,9)]=>0
[(1,7),(2,3),(4,10),(5,8),(6,9)]=>0
[(1,6),(2,3),(4,10),(5,8),(7,9)]=>0
[(1,5),(2,3),(4,10),(6,8),(7,9)]=>0
[(1,4),(2,3),(5,10),(6,8),(7,9)]=>0
[(1,3),(2,4),(5,10),(6,8),(7,9)]=>0
[(1,2),(3,4),(5,10),(6,8),(7,9)]=>0
[(1,2),(3,4),(5,9),(6,8),(7,10)]=>1
[(1,3),(2,4),(5,9),(6,8),(7,10)]=>1
[(1,4),(2,3),(5,9),(6,8),(7,10)]=>0
[(1,5),(2,3),(4,9),(6,8),(7,10)]=>0
[(1,6),(2,3),(4,9),(5,8),(7,10)]=>0
[(1,7),(2,3),(4,9),(5,8),(6,10)]=>0
[(1,8),(2,3),(4,9),(5,7),(6,10)]=>0
[(1,9),(2,3),(4,8),(5,7),(6,10)]=>0
[(1,10),(2,3),(4,8),(5,7),(6,9)]=>0
[(1,10),(2,4),(3,8),(5,7),(6,9)]=>0
[(1,9),(2,4),(3,8),(5,7),(6,10)]=>1
[(1,8),(2,4),(3,9),(5,7),(6,10)]=>1
[(1,7),(2,4),(3,9),(5,8),(6,10)]=>2
[(1,6),(2,4),(3,9),(5,8),(7,10)]=>2
[(1,5),(2,4),(3,9),(6,8),(7,10)]=>1
[(1,4),(2,5),(3,9),(6,8),(7,10)]=>1
[(1,3),(2,5),(4,9),(6,8),(7,10)]=>1
[(1,2),(3,5),(4,9),(6,8),(7,10)]=>1
[(1,2),(3,6),(4,9),(5,8),(7,10)]=>2
[(1,3),(2,6),(4,9),(5,8),(7,10)]=>2
[(1,4),(2,6),(3,9),(5,8),(7,10)]=>3
[(1,5),(2,6),(3,9),(4,8),(7,10)]=>3
[(1,6),(2,5),(3,9),(4,8),(7,10)]=>2
[(1,7),(2,5),(3,9),(4,8),(6,10)]=>2
[(1,8),(2,5),(3,9),(4,7),(6,10)]=>1
[(1,9),(2,5),(3,8),(4,7),(6,10)]=>1
[(1,10),(2,5),(3,8),(4,7),(6,9)]=>0
[(1,10),(2,6),(3,8),(4,7),(5,9)]=>0
[(1,9),(2,6),(3,8),(4,7),(5,10)]=>1
[(1,8),(2,6),(3,9),(4,7),(5,10)]=>1
[(1,7),(2,6),(3,9),(4,8),(5,10)]=>3
[(1,6),(2,7),(3,9),(4,8),(5,10)]=>3
[(1,5),(2,7),(3,9),(4,8),(6,10)]=>3
[(1,4),(2,7),(3,9),(5,8),(6,10)]=>3
[(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)]=>1
[(1,3),(2,8),(4,9),(5,7),(6,10)]=>1
[(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)]=>1
[(1,9),(2,7),(3,8),(4,6),(5,10)]=>1
[(1,10),(2,7),(3,8),(4,6),(5,9)]=>0
[(1,10),(2,8),(3,7),(4,6),(5,9)]=>0
[(1,9),(2,8),(3,7),(4,6),(5,10)]=>1
[(1,8),(2,9),(3,7),(4,6),(5,10)]=>1
[(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)]=>1
[(1,2),(3,9),(4,8),(5,7),(6,10)]=>1
[(1,2),(3,10),(4,8),(5,7),(6,9)]=>0
[(1,3),(2,10),(4,8),(5,7),(6,9)]=>0
[(1,4),(2,10),(3,8),(5,7),(6,9)]=>1
[(1,5),(2,10),(3,8),(4,7),(6,9)]=>1
[(1,6),(2,10),(3,8),(4,7),(5,9)]=>1
[(1,7),(2,10),(3,8),(4,6),(5,9)]=>1
[(1,8),(2,10),(3,7),(4,6),(5,9)]=>1
[(1,9),(2,10),(3,7),(4,6),(5,8)]=>1
[(1,10),(2,9),(3,7),(4,6),(5,8)]=>0
[(1,10),(2,9),(3,6),(4,7),(5,8)]=>0
[(1,9),(2,10),(3,6),(4,7),(5,8)]=>1
[(1,8),(2,10),(3,6),(4,7),(5,9)]=>1
[(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)]=>1
[(1,4),(2,10),(3,7),(5,8),(6,9)]=>1
[(1,3),(2,10),(4,7),(5,8),(6,9)]=>0
[(1,2),(3,10),(4,7),(5,8),(6,9)]=>0
[(1,2),(3,9),(4,7),(5,8),(6,10)]=>1
[(1,3),(2,9),(4,7),(5,8),(6,10)]=>1
[(1,4),(2,9),(3,7),(5,8),(6,10)]=>3
[(1,5),(2,9),(3,7),(4,8),(6,10)]=>3
[(1,6),(2,9),(3,7),(4,8),(5,10)]=>3
[(1,7),(2,9),(3,6),(4,8),(5,10)]=>3
[(1,8),(2,9),(3,6),(4,7),(5,10)]=>1
[(1,9),(2,8),(3,6),(4,7),(5,10)]=>1
[(1,10),(2,8),(3,6),(4,7),(5,9)]=>0
[(1,10),(2,7),(3,6),(4,8),(5,9)]=>0
[(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)]=>3
[(1,6),(2,8),(3,7),(4,9),(5,10)]=>3
[(1,5),(2,8),(3,7),(4,9),(6,10)]=>3
[(1,4),(2,8),(3,7),(5,9),(6,10)]=>3
[(1,3),(2,8),(4,7),(5,9),(6,10)]=>1
[(1,2),(3,8),(4,7),(5,9),(6,10)]=>1
[(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)]=>3
[(1,5),(2,7),(3,8),(4,9),(6,10)]=>3
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>3
[(1,7),(2,6),(3,8),(4,9),(5,10)]=>3
[(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)]=>0
[(1,10),(2,5),(3,7),(4,8),(6,9)]=>0
[(1,9),(2,5),(3,7),(4,8),(6,10)]=>1
[(1,8),(2,5),(3,7),(4,9),(6,10)]=>1
[(1,7),(2,5),(3,8),(4,9),(6,10)]=>2
[(1,6),(2,5),(3,8),(4,9),(7,10)]=>2
[(1,5),(2,6),(3,8),(4,9),(7,10)]=>3
[(1,4),(2,6),(3,8),(5,9),(7,10)]=>3
[(1,3),(2,6),(4,8),(5,9),(7,10)]=>2
[(1,2),(3,6),(4,8),(5,9),(7,10)]=>2
[(1,2),(3,5),(4,8),(6,9),(7,10)]=>1
[(1,3),(2,5),(4,8),(6,9),(7,10)]=>1
[(1,4),(2,5),(3,8),(6,9),(7,10)]=>1
[(1,5),(2,4),(3,8),(6,9),(7,10)]=>1
[(1,6),(2,4),(3,8),(5,9),(7,10)]=>2
[(1,7),(2,4),(3,8),(5,9),(6,10)]=>2
[(1,8),(2,4),(3,7),(5,9),(6,10)]=>1
[(1,9),(2,4),(3,7),(5,8),(6,10)]=>1
[(1,10),(2,4),(3,7),(5,8),(6,9)]=>0
[(1,10),(2,3),(4,7),(5,8),(6,9)]=>0
[(1,9),(2,3),(4,7),(5,8),(6,10)]=>0
[(1,8),(2,3),(4,7),(5,9),(6,10)]=>0
[(1,7),(2,3),(4,8),(5,9),(6,10)]=>0
[(1,6),(2,3),(4,8),(5,9),(7,10)]=>0
[(1,5),(2,3),(4,8),(6,9),(7,10)]=>0
[(1,4),(2,3),(5,8),(6,9),(7,10)]=>0
[(1,3),(2,4),(5,8),(6,9),(7,10)]=>1
[(1,2),(3,4),(5,8),(6,9),(7,10)]=>1
[(1,2),(3,4),(5,7),(6,9),(8,10)]=>1
[(1,3),(2,4),(5,7),(6,9),(8,10)]=>1
[(1,4),(2,3),(5,7),(6,9),(8,10)]=>0
[(1,5),(2,3),(4,7),(6,9),(8,10)]=>0
[(1,6),(2,3),(4,7),(5,9),(8,10)]=>0
[(1,7),(2,3),(4,6),(5,9),(8,10)]=>0
[(1,8),(2,3),(4,6),(5,9),(7,10)]=>0
[(1,9),(2,3),(4,6),(5,8),(7,10)]=>0
[(1,10),(2,3),(4,6),(5,8),(7,9)]=>0
[(1,10),(2,4),(3,6),(5,8),(7,9)]=>0
[(1,9),(2,4),(3,6),(5,8),(7,10)]=>1
[(1,8),(2,4),(3,6),(5,9),(7,10)]=>1
[(1,7),(2,4),(3,6),(5,9),(8,10)]=>1
[(1,6),(2,4),(3,7),(5,9),(8,10)]=>1
[(1,5),(2,4),(3,7),(6,9),(8,10)]=>1
[(1,4),(2,5),(3,7),(6,9),(8,10)]=>1
[(1,3),(2,5),(4,7),(6,9),(8,10)]=>1
[(1,2),(3,5),(4,7),(6,9),(8,10)]=>1
[(1,2),(3,6),(4,7),(5,9),(8,10)]=>1
[(1,3),(2,6),(4,7),(5,9),(8,10)]=>1
[(1,4),(2,6),(3,7),(5,9),(8,10)]=>2
[(1,5),(2,6),(3,7),(4,9),(8,10)]=>2
[(1,6),(2,5),(3,7),(4,9),(8,10)]=>1
[(1,7),(2,5),(3,6),(4,9),(8,10)]=>1
[(1,8),(2,5),(3,6),(4,9),(7,10)]=>1
[(1,9),(2,5),(3,6),(4,8),(7,10)]=>1
[(1,10),(2,5),(3,6),(4,8),(7,9)]=>0
[(1,10),(2,6),(3,5),(4,8),(7,9)]=>0
[(1,9),(2,6),(3,5),(4,8),(7,10)]=>1
[(1,8),(2,6),(3,5),(4,9),(7,10)]=>1
[(1,7),(2,6),(3,5),(4,9),(8,10)]=>1
[(1,6),(2,7),(3,5),(4,9),(8,10)]=>1
[(1,5),(2,7),(3,6),(4,9),(8,10)]=>2
[(1,4),(2,7),(3,6),(5,9),(8,10)]=>2
[(1,3),(2,7),(4,6),(5,9),(8,10)]=>1
[(1,2),(3,7),(4,6),(5,9),(8,10)]=>1
[(1,2),(3,8),(4,6),(5,9),(7,10)]=>1
[(1,3),(2,8),(4,6),(5,9),(7,10)]=>1
[(1,4),(2,8),(3,6),(5,9),(7,10)]=>3
[(1,5),(2,8),(3,6),(4,9),(7,10)]=>3
[(1,6),(2,8),(3,5),(4,9),(7,10)]=>2
[(1,7),(2,8),(3,5),(4,9),(6,10)]=>2
[(1,8),(2,7),(3,5),(4,9),(6,10)]=>1
[(1,9),(2,7),(3,5),(4,8),(6,10)]=>1
[(1,10),(2,7),(3,5),(4,8),(6,9)]=>0
[(1,10),(2,8),(3,5),(4,7),(6,9)]=>0
[(1,9),(2,8),(3,5),(4,7),(6,10)]=>1
[(1,8),(2,9),(3,5),(4,7),(6,10)]=>1
[(1,7),(2,9),(3,5),(4,8),(6,10)]=>2
[(1,6),(2,9),(3,5),(4,8),(7,10)]=>2
[(1,5),(2,9),(3,6),(4,8),(7,10)]=>3
[(1,4),(2,9),(3,6),(5,8),(7,10)]=>3
[(1,3),(2,9),(4,6),(5,8),(7,10)]=>1
[(1,2),(3,9),(4,6),(5,8),(7,10)]=>1
[(1,2),(3,10),(4,6),(5,8),(7,9)]=>0
[(1,3),(2,10),(4,6),(5,8),(7,9)]=>0
[(1,4),(2,10),(3,6),(5,8),(7,9)]=>1
[(1,5),(2,10),(3,6),(4,8),(7,9)]=>1
[(1,6),(2,10),(3,5),(4,8),(7,9)]=>1
[(1,7),(2,10),(3,5),(4,8),(6,9)]=>1
[(1,8),(2,10),(3,5),(4,7),(6,9)]=>1
[(1,9),(2,10),(3,5),(4,7),(6,8)]=>1
[(1,10),(2,9),(3,5),(4,7),(6,8)]=>0
[(1,10),(2,9),(3,4),(5,7),(6,8)]=>0
[(1,9),(2,10),(3,4),(5,7),(6,8)]=>1
[(1,8),(2,10),(3,4),(5,7),(6,9)]=>1
[(1,7),(2,10),(3,4),(5,8),(6,9)]=>1
[(1,6),(2,10),(3,4),(5,8),(7,9)]=>1
[(1,5),(2,10),(3,4),(6,8),(7,9)]=>0
[(1,4),(2,10),(3,5),(6,8),(7,9)]=>0
[(1,3),(2,10),(4,5),(6,8),(7,9)]=>0
[(1,2),(3,10),(4,5),(6,8),(7,9)]=>0
[(1,2),(3,9),(4,5),(6,8),(7,10)]=>0
[(1,3),(2,9),(4,5),(6,8),(7,10)]=>0
[(1,4),(2,9),(3,5),(6,8),(7,10)]=>1
[(1,5),(2,9),(3,4),(6,8),(7,10)]=>1
[(1,6),(2,9),(3,4),(5,8),(7,10)]=>2
[(1,7),(2,9),(3,4),(5,8),(6,10)]=>2
[(1,8),(2,9),(3,4),(5,7),(6,10)]=>1
[(1,9),(2,8),(3,4),(5,7),(6,10)]=>1
[(1,10),(2,8),(3,4),(5,7),(6,9)]=>0
[(1,10),(2,7),(3,4),(5,8),(6,9)]=>0
[(1,9),(2,7),(3,4),(5,8),(6,10)]=>1
[(1,8),(2,7),(3,4),(5,9),(6,10)]=>1
[(1,7),(2,8),(3,4),(5,9),(6,10)]=>2
[(1,6),(2,8),(3,4),(5,9),(7,10)]=>2
[(1,5),(2,8),(3,4),(6,9),(7,10)]=>1
[(1,4),(2,8),(3,5),(6,9),(7,10)]=>1
[(1,3),(2,8),(4,5),(6,9),(7,10)]=>0
[(1,2),(3,8),(4,5),(6,9),(7,10)]=>0
[(1,2),(3,7),(4,5),(6,9),(8,10)]=>0
[(1,3),(2,7),(4,5),(6,9),(8,10)]=>0
[(1,4),(2,7),(3,5),(6,9),(8,10)]=>1
[(1,5),(2,7),(3,4),(6,9),(8,10)]=>1
[(1,6),(2,7),(3,4),(5,9),(8,10)]=>1
[(1,7),(2,6),(3,4),(5,9),(8,10)]=>1
[(1,8),(2,6),(3,4),(5,9),(7,10)]=>1
[(1,9),(2,6),(3,4),(5,8),(7,10)]=>1
[(1,10),(2,6),(3,4),(5,8),(7,9)]=>0
[(1,10),(2,5),(3,4),(6,8),(7,9)]=>0
[(1,9),(2,5),(3,4),(6,8),(7,10)]=>0
[(1,8),(2,5),(3,4),(6,9),(7,10)]=>0
[(1,7),(2,5),(3,4),(6,9),(8,10)]=>0
[(1,6),(2,5),(3,4),(7,9),(8,10)]=>0
[(1,5),(2,6),(3,4),(7,9),(8,10)]=>1
[(1,4),(2,6),(3,5),(7,9),(8,10)]=>1
[(1,3),(2,6),(4,5),(7,9),(8,10)]=>0
[(1,2),(3,6),(4,5),(7,9),(8,10)]=>0
[(1,2),(3,5),(4,6),(7,9),(8,10)]=>1
[(1,3),(2,5),(4,6),(7,9),(8,10)]=>1
[(1,4),(2,5),(3,6),(7,9),(8,10)]=>1
[(1,5),(2,4),(3,6),(7,9),(8,10)]=>1
[(1,6),(2,4),(3,5),(7,9),(8,10)]=>0
[(1,7),(2,4),(3,5),(6,9),(8,10)]=>0
[(1,8),(2,4),(3,5),(6,9),(7,10)]=>0
[(1,9),(2,4),(3,5),(6,8),(7,10)]=>0
[(1,10),(2,4),(3,5),(6,8),(7,9)]=>0
[(1,10),(2,3),(4,5),(6,8),(7,9)]=>0
[(1,9),(2,3),(4,5),(6,8),(7,10)]=>0
[(1,8),(2,3),(4,5),(6,9),(7,10)]=>0
[(1,7),(2,3),(4,5),(6,9),(8,10)]=>0
[(1,6),(2,3),(4,5),(7,9),(8,10)]=>0
[(1,5),(2,3),(4,6),(7,9),(8,10)]=>0
[(1,4),(2,3),(5,6),(7,9),(8,10)]=>0
[(1,3),(2,4),(5,6),(7,9),(8,10)]=>1
[(1,2),(3,4),(5,6),(7,9),(8,10)]=>1
[(1,2),(3,4),(5,6),(7,10),(8,9)]=>0
[(1,3),(2,4),(5,6),(7,10),(8,9)]=>0
[(1,4),(2,3),(5,6),(7,10),(8,9)]=>0
[(1,5),(2,3),(4,6),(7,10),(8,9)]=>0
[(1,6),(2,3),(4,5),(7,10),(8,9)]=>0
[(1,7),(2,3),(4,5),(6,10),(8,9)]=>0
[(1,8),(2,3),(4,5),(6,10),(7,9)]=>0
[(1,9),(2,3),(4,5),(6,10),(7,8)]=>0
[(1,10),(2,3),(4,5),(6,9),(7,8)]=>0
[(1,10),(2,4),(3,5),(6,9),(7,8)]=>0
[(1,9),(2,4),(3,5),(6,10),(7,8)]=>0
[(1,8),(2,4),(3,5),(6,10),(7,9)]=>0
[(1,7),(2,4),(3,5),(6,10),(8,9)]=>0
[(1,6),(2,4),(3,5),(7,10),(8,9)]=>0
[(1,5),(2,4),(3,6),(7,10),(8,9)]=>0
[(1,4),(2,5),(3,6),(7,10),(8,9)]=>0
[(1,3),(2,5),(4,6),(7,10),(8,9)]=>0
[(1,2),(3,5),(4,6),(7,10),(8,9)]=>0
[(1,2),(3,6),(4,5),(7,10),(8,9)]=>0
[(1,3),(2,6),(4,5),(7,10),(8,9)]=>0
[(1,4),(2,6),(3,5),(7,10),(8,9)]=>0
[(1,5),(2,6),(3,4),(7,10),(8,9)]=>0
[(1,6),(2,5),(3,4),(7,10),(8,9)]=>0
[(1,7),(2,5),(3,4),(6,10),(8,9)]=>0
[(1,8),(2,5),(3,4),(6,10),(7,9)]=>0
[(1,9),(2,5),(3,4),(6,10),(7,8)]=>0
[(1,10),(2,5),(3,4),(6,9),(7,8)]=>0
[(1,10),(2,6),(3,4),(5,9),(7,8)]=>0
[(1,9),(2,6),(3,4),(5,10),(7,8)]=>1
[(1,8),(2,6),(3,4),(5,10),(7,9)]=>1
[(1,7),(2,6),(3,4),(5,10),(8,9)]=>0
[(1,6),(2,7),(3,4),(5,10),(8,9)]=>0
[(1,5),(2,7),(3,4),(6,10),(8,9)]=>0
[(1,4),(2,7),(3,5),(6,10),(8,9)]=>0
[(1,3),(2,7),(4,5),(6,10),(8,9)]=>0
[(1,2),(3,7),(4,5),(6,10),(8,9)]=>0
[(1,2),(3,8),(4,5),(6,10),(7,9)]=>0
[(1,3),(2,8),(4,5),(6,10),(7,9)]=>0
[(1,4),(2,8),(3,5),(6,10),(7,9)]=>1
[(1,5),(2,8),(3,4),(6,10),(7,9)]=>1
[(1,6),(2,8),(3,4),(5,10),(7,9)]=>1
[(1,7),(2,8),(3,4),(5,10),(6,9)]=>1
[(1,8),(2,7),(3,4),(5,10),(6,9)]=>1
[(1,9),(2,7),(3,4),(5,10),(6,8)]=>1
[(1,10),(2,7),(3,4),(5,9),(6,8)]=>0
[(1,10),(2,8),(3,4),(5,9),(6,7)]=>0
[(1,9),(2,8),(3,4),(5,10),(6,7)]=>0
[(1,8),(2,9),(3,4),(5,10),(6,7)]=>0
[(1,7),(2,9),(3,4),(5,10),(6,8)]=>1
[(1,6),(2,9),(3,4),(5,10),(7,8)]=>1
[(1,5),(2,9),(3,4),(6,10),(7,8)]=>1
[(1,4),(2,9),(3,5),(6,10),(7,8)]=>1
[(1,3),(2,9),(4,5),(6,10),(7,8)]=>0
[(1,2),(3,9),(4,5),(6,10),(7,8)]=>0
[(1,2),(3,10),(4,5),(6,9),(7,8)]=>0
[(1,3),(2,10),(4,5),(6,9),(7,8)]=>0
[(1,4),(2,10),(3,5),(6,9),(7,8)]=>0
[(1,5),(2,10),(3,4),(6,9),(7,8)]=>0
[(1,6),(2,10),(3,4),(5,9),(7,8)]=>1
[(1,7),(2,10),(3,4),(5,9),(6,8)]=>1
[(1,8),(2,10),(3,4),(5,9),(6,7)]=>0
[(1,9),(2,10),(3,4),(5,8),(6,7)]=>0
[(1,10),(2,9),(3,4),(5,8),(6,7)]=>0
[(1,10),(2,9),(3,5),(4,8),(6,7)]=>0
[(1,9),(2,10),(3,5),(4,8),(6,7)]=>0
[(1,8),(2,10),(3,5),(4,9),(6,7)]=>0
[(1,7),(2,10),(3,5),(4,9),(6,8)]=>1
[(1,6),(2,10),(3,5),(4,9),(7,8)]=>1
[(1,5),(2,10),(3,6),(4,9),(7,8)]=>1
[(1,4),(2,10),(3,6),(5,9),(7,8)]=>1
[(1,3),(2,10),(4,6),(5,9),(7,8)]=>0
[(1,2),(3,10),(4,6),(5,9),(7,8)]=>0
[(1,2),(3,9),(4,6),(5,10),(7,8)]=>1
[(1,3),(2,9),(4,6),(5,10),(7,8)]=>1
[(1,4),(2,9),(3,6),(5,10),(7,8)]=>2
[(1,5),(2,9),(3,6),(4,10),(7,8)]=>2
[(1,6),(2,9),(3,5),(4,10),(7,8)]=>1
[(1,7),(2,9),(3,5),(4,10),(6,8)]=>1
[(1,8),(2,9),(3,5),(4,10),(6,7)]=>0
[(1,9),(2,8),(3,5),(4,10),(6,7)]=>0
[(1,10),(2,8),(3,5),(4,9),(6,7)]=>0
[(1,10),(2,7),(3,5),(4,9),(6,8)]=>0
[(1,9),(2,7),(3,5),(4,10),(6,8)]=>1
[(1,8),(2,7),(3,5),(4,10),(6,9)]=>1
[(1,7),(2,8),(3,5),(4,10),(6,9)]=>1
[(1,6),(2,8),(3,5),(4,10),(7,9)]=>1
[(1,5),(2,8),(3,6),(4,10),(7,9)]=>2
[(1,4),(2,8),(3,6),(5,10),(7,9)]=>2
[(1,3),(2,8),(4,6),(5,10),(7,9)]=>1
[(1,2),(3,8),(4,6),(5,10),(7,9)]=>1
[(1,2),(3,7),(4,6),(5,10),(8,9)]=>0
[(1,3),(2,7),(4,6),(5,10),(8,9)]=>0
[(1,4),(2,7),(3,6),(5,10),(8,9)]=>0
[(1,5),(2,7),(3,6),(4,10),(8,9)]=>0
[(1,6),(2,7),(3,5),(4,10),(8,9)]=>0
[(1,7),(2,6),(3,5),(4,10),(8,9)]=>0
[(1,8),(2,6),(3,5),(4,10),(7,9)]=>1
[(1,9),(2,6),(3,5),(4,10),(7,8)]=>1
[(1,10),(2,6),(3,5),(4,9),(7,8)]=>0
[(1,10),(2,5),(3,6),(4,9),(7,8)]=>0
[(1,9),(2,5),(3,6),(4,10),(7,8)]=>1
[(1,8),(2,5),(3,6),(4,10),(7,9)]=>1
[(1,7),(2,5),(3,6),(4,10),(8,9)]=>0
[(1,6),(2,5),(3,7),(4,10),(8,9)]=>0
[(1,5),(2,6),(3,7),(4,10),(8,9)]=>0
[(1,4),(2,6),(3,7),(5,10),(8,9)]=>0
[(1,3),(2,6),(4,7),(5,10),(8,9)]=>0
[(1,2),(3,6),(4,7),(5,10),(8,9)]=>0
[(1,2),(3,5),(4,7),(6,10),(8,9)]=>0
[(1,3),(2,5),(4,7),(6,10),(8,9)]=>0
[(1,4),(2,5),(3,7),(6,10),(8,9)]=>0
[(1,5),(2,4),(3,7),(6,10),(8,9)]=>0
[(1,6),(2,4),(3,7),(5,10),(8,9)]=>0
[(1,7),(2,4),(3,6),(5,10),(8,9)]=>0
[(1,8),(2,4),(3,6),(5,10),(7,9)]=>1
[(1,9),(2,4),(3,6),(5,10),(7,8)]=>1
[(1,10),(2,4),(3,6),(5,9),(7,8)]=>0
[(1,10),(2,3),(4,6),(5,9),(7,8)]=>0
[(1,9),(2,3),(4,6),(5,10),(7,8)]=>0
[(1,8),(2,3),(4,6),(5,10),(7,9)]=>0
[(1,7),(2,3),(4,6),(5,10),(8,9)]=>0
[(1,6),(2,3),(4,7),(5,10),(8,9)]=>0
[(1,5),(2,3),(4,7),(6,10),(8,9)]=>0
[(1,4),(2,3),(5,7),(6,10),(8,9)]=>0
[(1,3),(2,4),(5,7),(6,10),(8,9)]=>0
[(1,2),(3,4),(5,7),(6,10),(8,9)]=>0
[(1,2),(3,4),(5,8),(6,10),(7,9)]=>1
[(1,3),(2,4),(5,8),(6,10),(7,9)]=>1
[(1,4),(2,3),(5,8),(6,10),(7,9)]=>0
[(1,5),(2,3),(4,8),(6,10),(7,9)]=>0
[(1,6),(2,3),(4,8),(5,10),(7,9)]=>0
[(1,7),(2,3),(4,8),(5,10),(6,9)]=>0
[(1,8),(2,3),(4,7),(5,10),(6,9)]=>0
[(1,9),(2,3),(4,7),(5,10),(6,8)]=>0
[(1,10),(2,3),(4,7),(5,9),(6,8)]=>0
[(1,10),(2,4),(3,7),(5,9),(6,8)]=>0
[(1,9),(2,4),(3,7),(5,10),(6,8)]=>1
[(1,8),(2,4),(3,7),(5,10),(6,9)]=>1
[(1,7),(2,4),(3,8),(5,10),(6,9)]=>1
[(1,6),(2,4),(3,8),(5,10),(7,9)]=>1
[(1,5),(2,4),(3,8),(6,10),(7,9)]=>1
[(1,4),(2,5),(3,8),(6,10),(7,9)]=>1
[(1,3),(2,5),(4,8),(6,10),(7,9)]=>1
[(1,2),(3,5),(4,8),(6,10),(7,9)]=>1
[(1,2),(3,6),(4,8),(5,10),(7,9)]=>1
[(1,3),(2,6),(4,8),(5,10),(7,9)]=>1
[(1,4),(2,6),(3,8),(5,10),(7,9)]=>2
[(1,5),(2,6),(3,8),(4,10),(7,9)]=>2
[(1,6),(2,5),(3,8),(4,10),(7,9)]=>1
[(1,7),(2,5),(3,8),(4,10),(6,9)]=>1
[(1,8),(2,5),(3,7),(4,10),(6,9)]=>1
[(1,9),(2,5),(3,7),(4,10),(6,8)]=>1
[(1,10),(2,5),(3,7),(4,9),(6,8)]=>0
[(1,10),(2,6),(3,7),(4,9),(5,8)]=>0
[(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)]=>3
[(1,6),(2,7),(3,8),(4,10),(5,9)]=>3
[(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)]=>1
[(1,2),(3,7),(4,8),(5,10),(6,9)]=>1
[(1,2),(3,8),(4,7),(5,10),(6,9)]=>1
[(1,3),(2,8),(4,7),(5,10),(6,9)]=>1
[(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)]=>3
[(1,7),(2,8),(3,6),(4,10),(5,9)]=>3
[(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)]=>0
[(1,10),(2,8),(3,6),(4,9),(5,7)]=>0
[(1,9),(2,8),(3,6),(4,10),(5,7)]=>1
[(1,8),(2,9),(3,6),(4,10),(5,7)]=>1
[(1,7),(2,9),(3,6),(4,10),(5,8)]=>3
[(1,6),(2,9),(3,7),(4,10),(5,8)]=>3
[(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)]=>1
[(1,2),(3,9),(4,7),(5,10),(6,8)]=>1
[(1,2),(3,10),(4,7),(5,9),(6,8)]=>0
[(1,3),(2,10),(4,7),(5,9),(6,8)]=>0
[(1,4),(2,10),(3,7),(5,9),(6,8)]=>1
[(1,5),(2,10),(3,7),(4,9),(6,8)]=>1
[(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)]=>1
[(1,9),(2,10),(3,6),(4,8),(5,7)]=>1
[(1,10),(2,9),(3,6),(4,8),(5,7)]=>0
[(1,10),(2,9),(3,7),(4,8),(5,6)]=>0
[(1,9),(2,10),(3,7),(4,8),(5,6)]=>1
[(1,8),(2,10),(3,7),(4,9),(5,6)]=>1
[(1,7),(2,10),(3,8),(4,9),(5,6)]=>1
[(1,6),(2,10),(3,8),(4,9),(5,7)]=>1
[(1,5),(2,10),(3,8),(4,9),(6,7)]=>0
[(1,4),(2,10),(3,8),(5,9),(6,7)]=>0
[(1,3),(2,10),(4,8),(5,9),(6,7)]=>0
[(1,2),(3,10),(4,8),(5,9),(6,7)]=>0
[(1,2),(3,9),(4,8),(5,10),(6,7)]=>0
[(1,3),(2,9),(4,8),(5,10),(6,7)]=>0
[(1,4),(2,9),(3,8),(5,10),(6,7)]=>0
[(1,5),(2,9),(3,8),(4,10),(6,7)]=>0
[(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)]=>1
[(1,9),(2,8),(3,7),(4,10),(5,6)]=>1
[(1,10),(2,8),(3,7),(4,9),(5,6)]=>0
[(1,10),(2,7),(3,8),(4,9),(5,6)]=>0
[(1,9),(2,7),(3,8),(4,10),(5,6)]=>1
[(1,8),(2,7),(3,9),(4,10),(5,6)]=>1
[(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)]=>0
[(1,4),(2,8),(3,9),(5,10),(6,7)]=>0
[(1,3),(2,8),(4,9),(5,10),(6,7)]=>0
[(1,2),(3,8),(4,9),(5,10),(6,7)]=>0
[(1,2),(3,7),(4,9),(5,10),(6,8)]=>1
[(1,3),(2,7),(4,9),(5,10),(6,8)]=>1
[(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)]=>3
[(1,7),(2,6),(3,9),(4,10),(5,8)]=>3
[(1,8),(2,6),(3,9),(4,10),(5,7)]=>1
[(1,9),(2,6),(3,8),(4,10),(5,7)]=>1
[(1,10),(2,6),(3,8),(4,9),(5,7)]=>0
[(1,10),(2,5),(3,8),(4,9),(6,7)]=>0
[(1,9),(2,5),(3,8),(4,10),(6,7)]=>0
[(1,8),(2,5),(3,9),(4,10),(6,7)]=>0
[(1,7),(2,5),(3,9),(4,10),(6,8)]=>1
[(1,6),(2,5),(3,9),(4,10),(7,8)]=>1
[(1,5),(2,6),(3,9),(4,10),(7,8)]=>2
[(1,4),(2,6),(3,9),(5,10),(7,8)]=>2
[(1,3),(2,6),(4,9),(5,10),(7,8)]=>1
[(1,2),(3,6),(4,9),(5,10),(7,8)]=>1
[(1,2),(3,5),(4,9),(6,10),(7,8)]=>1
[(1,3),(2,5),(4,9),(6,10),(7,8)]=>1
[(1,4),(2,5),(3,9),(6,10),(7,8)]=>1
[(1,5),(2,4),(3,9),(6,10),(7,8)]=>1
[(1,6),(2,4),(3,9),(5,10),(7,8)]=>1
[(1,7),(2,4),(3,9),(5,10),(6,8)]=>1
[(1,8),(2,4),(3,9),(5,10),(6,7)]=>0
[(1,9),(2,4),(3,8),(5,10),(6,7)]=>0
[(1,10),(2,4),(3,8),(5,9),(6,7)]=>0
[(1,10),(2,3),(4,8),(5,9),(6,7)]=>0
[(1,9),(2,3),(4,8),(5,10),(6,7)]=>0
[(1,8),(2,3),(4,9),(5,10),(6,7)]=>0
[(1,7),(2,3),(4,9),(5,10),(6,8)]=>0
[(1,6),(2,3),(4,9),(5,10),(7,8)]=>0
[(1,5),(2,3),(4,9),(6,10),(7,8)]=>0
[(1,4),(2,3),(5,9),(6,10),(7,8)]=>0
[(1,3),(2,4),(5,9),(6,10),(7,8)]=>1
[(1,2),(3,4),(5,9),(6,10),(7,8)]=>1
[(1,2),(3,4),(5,10),(6,9),(7,8)]=>0
[(1,3),(2,4),(5,10),(6,9),(7,8)]=>0
[(1,4),(2,3),(5,10),(6,9),(7,8)]=>0
[(1,5),(2,3),(4,10),(6,9),(7,8)]=>0
[(1,6),(2,3),(4,10),(5,9),(7,8)]=>0
[(1,7),(2,3),(4,10),(5,9),(6,8)]=>0
[(1,8),(2,3),(4,10),(5,9),(6,7)]=>0
[(1,9),(2,3),(4,10),(5,8),(6,7)]=>0
[(1,10),(2,3),(4,9),(5,8),(6,7)]=>0
[(1,10),(2,4),(3,9),(5,8),(6,7)]=>0
[(1,9),(2,4),(3,10),(5,8),(6,7)]=>0
[(1,8),(2,4),(3,10),(5,9),(6,7)]=>0
[(1,7),(2,4),(3,10),(5,9),(6,8)]=>1
[(1,6),(2,4),(3,10),(5,9),(7,8)]=>1
[(1,5),(2,4),(3,10),(6,9),(7,8)]=>0
[(1,4),(2,5),(3,10),(6,9),(7,8)]=>0
[(1,3),(2,5),(4,10),(6,9),(7,8)]=>0
[(1,2),(3,5),(4,10),(6,9),(7,8)]=>0
[(1,2),(3,6),(4,10),(5,9),(7,8)]=>1
[(1,3),(2,6),(4,10),(5,9),(7,8)]=>1
[(1,4),(2,6),(3,10),(5,9),(7,8)]=>1
[(1,5),(2,6),(3,10),(4,9),(7,8)]=>1
[(1,6),(2,5),(3,10),(4,9),(7,8)]=>1
[(1,7),(2,5),(3,10),(4,9),(6,8)]=>1
[(1,8),(2,5),(3,10),(4,9),(6,7)]=>0
[(1,9),(2,5),(3,10),(4,8),(6,7)]=>0
[(1,10),(2,5),(3,9),(4,8),(6,7)]=>0
[(1,10),(2,6),(3,9),(4,8),(5,7)]=>0
[(1,9),(2,6),(3,10),(4,8),(5,7)]=>1
[(1,8),(2,6),(3,10),(4,9),(5,7)]=>1
[(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)]=>1
[(1,4),(2,7),(3,10),(5,9),(6,8)]=>1
[(1,3),(2,7),(4,10),(5,9),(6,8)]=>1
[(1,2),(3,7),(4,10),(5,9),(6,8)]=>1
[(1,2),(3,8),(4,10),(5,9),(6,7)]=>0
[(1,3),(2,8),(4,10),(5,9),(6,7)]=>0
[(1,4),(2,8),(3,10),(5,9),(6,7)]=>0
[(1,5),(2,8),(3,10),(4,9),(6,7)]=>0
[(1,6),(2,8),(3,10),(4,9),(5,7)]=>1
[(1,7),(2,8),(3,10),(4,9),(5,6)]=>1
[(1,8),(2,7),(3,10),(4,9),(5,6)]=>1
[(1,9),(2,7),(3,10),(4,8),(5,6)]=>1
[(1,10),(2,7),(3,9),(4,8),(5,6)]=>0
[(1,10),(2,8),(3,9),(4,7),(5,6)]=>0
[(1,9),(2,8),(3,10),(4,7),(5,6)]=>0
[(1,8),(2,9),(3,10),(4,7),(5,6)]=>0
[(1,7),(2,9),(3,10),(4,8),(5,6)]=>1
[(1,6),(2,9),(3,10),(4,8),(5,7)]=>1
[(1,5),(2,9),(3,10),(4,8),(6,7)]=>0
[(1,4),(2,9),(3,10),(5,8),(6,7)]=>0
[(1,3),(2,9),(4,10),(5,8),(6,7)]=>0
[(1,2),(3,9),(4,10),(5,8),(6,7)]=>0
[(1,2),(3,10),(4,9),(5,8),(6,7)]=>0
[(1,3),(2,10),(4,9),(5,8),(6,7)]=>0
[(1,4),(2,10),(3,9),(5,8),(6,7)]=>0
[(1,5),(2,10),(3,9),(4,8),(6,7)]=>0
[(1,6),(2,10),(3,9),(4,8),(5,7)]=>1
[(1,7),(2,10),(3,9),(4,8),(5,6)]=>1
[(1,8),(2,10),(3,9),(4,7),(5,6)]=>0
[(1,9),(2,10),(3,8),(4,7),(5,6)]=>0
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>0
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Description
The multiplicity of the non-nesting perfect matching in the chord expansion 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 coefficient of the unique non-nesting perfect matching in the formal sum.
Computer experiments indicate that this statistic has the same distribution as StatisticsDatabase/St000383oMp00128oMp00215oMp00092.
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 coefficient of the unique non-nesting perfect matching in the formal sum.
Computer experiments indicate that this statistic has the same distribution as StatisticsDatabase/St000383oMp00128oMp00215oMp00092.
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): NN = PerfectMatching([[2*i+1,2*(i+1)] for i in range(len(M))]) return expansion(M).get(non_nesting_non_crossing(len(M)), 0)
Created
Sep 01, 2022 at 09:34 by Martin Rubey
Updated
Sep 01, 2022 at 09:34 by Martin Rubey
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