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Identifier
Values
=>
Cc0012;cc-rep
[(1,2)]=>0 [(1,2),(3,4)]=>0 [(1,3),(2,4)]=>1 [(1,4),(2,3)]=>0 [(1,2),(3,4),(5,6)]=>0 [(1,3),(2,4),(5,6)]=>1 [(1,4),(2,3),(5,6)]=>0 [(1,5),(2,3),(4,6)]=>1 [(1,6),(2,3),(4,5)]=>0 [(1,6),(2,4),(3,5)]=>1 [(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)]=>1 [(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)]=>0 [(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)]=>1 [(1,6),(2,3),(4,5),(7,8)]=>0 [(1,7),(2,3),(4,5),(6,8)]=>1 [(1,8),(2,3),(4,5),(6,7)]=>0 [(1,8),(2,4),(3,5),(6,7)]=>1 [(1,7),(2,4),(3,5),(6,8)]=>2 [(1,6),(2,4),(3,5),(7,8)]=>1 [(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)]=>1 [(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)]=>1 [(1,8),(2,5),(3,4),(6,7)]=>0 [(1,8),(2,6),(3,4),(5,7)]=>1 [(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)]=>2 [(1,3),(2,7),(4,5),(6,8)]=>1 [(1,2),(3,7),(4,5),(6,8)]=>1 [(1,2),(3,8),(4,5),(6,7)]=>0 [(1,3),(2,8),(4,5),(6,7)]=>1 [(1,4),(2,8),(3,5),(6,7)]=>1 [(1,5),(2,8),(3,4),(6,7)]=>1 [(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)]=>1 [(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)]=>1 [(1,2),(3,7),(4,6),(5,8)]=>1 [(1,3),(2,7),(4,6),(5,8)]=>2 [(1,4),(2,7),(3,6),(5,8)]=>1 [(1,5),(2,7),(3,6),(4,8)]=>1 [(1,6),(2,7),(3,5),(4,8)]=>2 [(1,7),(2,6),(3,5),(4,8)]=>1 [(1,8),(2,6),(3,5),(4,7)]=>1 [(1,8),(2,5),(3,6),(4,7)]=>1 [(1,7),(2,5),(3,6),(4,8)]=>2 [(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)]=>1 [(1,3),(2,6),(4,7),(5,8)]=>2 [(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)]=>2 [(1,4),(2,5),(3,7),(6,8)]=>2 [(1,5),(2,4),(3,7),(6,8)]=>1 [(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)]=>1 [(1,8),(2,3),(4,6),(5,7)]=>1 [(1,7),(2,3),(4,6),(5,8)]=>1 [(1,6),(2,3),(4,7),(5,8)]=>1 [(1,5),(2,3),(4,7),(6,8)]=>1 [(1,4),(2,3),(5,7),(6,8)]=>1 [(1,3),(2,4),(5,7),(6,8)]=>2 [(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)]=>1 [(1,4),(2,3),(5,8),(6,7)]=>0 [(1,5),(2,3),(4,8),(6,7)]=>1 [(1,6),(2,3),(4,8),(5,7)]=>1 [(1,7),(2,3),(4,8),(5,6)]=>1 [(1,8),(2,3),(4,7),(5,6)]=>0 [(1,8),(2,4),(3,7),(5,6)]=>1 [(1,7),(2,4),(3,8),(5,6)]=>1 [(1,6),(2,4),(3,8),(5,7)]=>2 [(1,5),(2,4),(3,8),(6,7)]=>1 [(1,4),(2,5),(3,8),(6,7)]=>1 [(1,3),(2,5),(4,8),(6,7)]=>1 [(1,2),(3,5),(4,8),(6,7)]=>1 [(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)]=>2 [(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)]=>2 [(1,8),(2,5),(3,7),(4,6)]=>1 [(1,8),(2,6),(3,7),(4,5)]=>1 [(1,7),(2,6),(3,8),(4,5)]=>1 [(1,6),(2,7),(3,8),(4,5)]=>1 [(1,5),(2,7),(3,8),(4,6)]=>2 [(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)]=>1 [(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)]=>1 [(1,7),(2,8),(3,6),(4,5)]=>1 [(1,8),(2,7),(3,6),(4,5)]=>0 [(1,2),(3,4),(5,6),(7,8),(9,10)]=>0 [(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)]=>1 [(1,6),(2,3),(4,5),(7,8),(9,10)]=>0 [(1,7),(2,3),(4,5),(6,8),(9,10)]=>1 [(1,8),(2,3),(4,5),(6,7),(9,10)]=>0 [(1,9),(2,3),(4,5),(6,7),(8,10)]=>1 [(1,10),(2,3),(4,5),(6,7),(8,9)]=>0 [(1,10),(2,4),(3,5),(6,7),(8,9)]=>1 [(1,9),(2,4),(3,5),(6,7),(8,10)]=>2 [(1,8),(2,4),(3,5),(6,7),(9,10)]=>1 [(1,7),(2,4),(3,5),(6,8),(9,10)]=>2 [(1,6),(2,4),(3,5),(7,8),(9,10)]=>1 [(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)]=>1 [(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)]=>1 [(1,8),(2,5),(3,4),(6,7),(9,10)]=>0 [(1,9),(2,5),(3,4),(6,7),(8,10)]=>1 [(1,10),(2,5),(3,4),(6,7),(8,9)]=>0 [(1,10),(2,6),(3,4),(5,7),(8,9)]=>1 [(1,9),(2,6),(3,4),(5,7),(8,10)]=>2 [(1,8),(2,6),(3,4),(5,7),(9,10)]=>1 [(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)]=>2 [(1,3),(2,7),(4,5),(6,8),(9,10)]=>1 [(1,2),(3,7),(4,5),(6,8),(9,10)]=>1 [(1,2),(3,8),(4,5),(6,7),(9,10)]=>0 [(1,3),(2,8),(4,5),(6,7),(9,10)]=>1 [(1,4),(2,8),(3,5),(6,7),(9,10)]=>1 [(1,5),(2,8),(3,4),(6,7),(9,10)]=>1 [(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)]=>1 [(1,10),(2,7),(3,4),(5,6),(8,9)]=>0 [(1,10),(2,8),(3,4),(5,6),(7,9)]=>1 [(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)]=>2 [(1,5),(2,9),(3,4),(6,7),(8,10)]=>1 [(1,4),(2,9),(3,5),(6,7),(8,10)]=>2 [(1,3),(2,9),(4,5),(6,7),(8,10)]=>1 [(1,2),(3,9),(4,5),(6,7),(8,10)]=>1 [(1,2),(3,10),(4,5),(6,7),(8,9)]=>0 [(1,3),(2,10),(4,5),(6,7),(8,9)]=>1 [(1,4),(2,10),(3,5),(6,7),(8,9)]=>1 [(1,5),(2,10),(3,4),(6,7),(8,9)]=>1 [(1,6),(2,10),(3,4),(5,7),(8,9)]=>1 [(1,7),(2,10),(3,4),(5,6),(8,9)]=>1 [(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)]=>1 [(1,9),(2,10),(3,5),(4,6),(7,8)]=>2 [(1,8),(2,10),(3,5),(4,6),(7,9)]=>2 [(1,7),(2,10),(3,5),(4,6),(8,9)]=>2 [(1,6),(2,10),(3,5),(4,7),(8,9)]=>2 [(1,5),(2,10),(3,6),(4,7),(8,9)]=>2 [(1,4),(2,10),(3,6),(5,7),(8,9)]=>2 [(1,3),(2,10),(4,6),(5,7),(8,9)]=>2 [(1,2),(3,10),(4,6),(5,7),(8,9)]=>1 [(1,2),(3,9),(4,6),(5,7),(8,10)]=>2 [(1,3),(2,9),(4,6),(5,7),(8,10)]=>2 [(1,4),(2,9),(3,6),(5,7),(8,10)]=>2 [(1,5),(2,9),(3,6),(4,7),(8,10)]=>2 [(1,6),(2,9),(3,5),(4,7),(8,10)]=>2 [(1,7),(2,9),(3,5),(4,6),(8,10)]=>2 [(1,8),(2,9),(3,5),(4,6),(7,10)]=>2 [(1,9),(2,8),(3,5),(4,6),(7,10)]=>2 [(1,10),(2,8),(3,5),(4,6),(7,9)]=>2 [(1,10),(2,7),(3,5),(4,6),(8,9)]=>1 [(1,9),(2,7),(3,5),(4,6),(8,10)]=>2 [(1,8),(2,7),(3,5),(4,6),(9,10)]=>1 [(1,7),(2,8),(3,5),(4,6),(9,10)]=>2 [(1,6),(2,8),(3,5),(4,7),(9,10)]=>2 [(1,5),(2,8),(3,6),(4,7),(9,10)]=>2 [(1,4),(2,8),(3,6),(5,7),(9,10)]=>2 [(1,3),(2,8),(4,6),(5,7),(9,10)]=>2 [(1,2),(3,8),(4,6),(5,7),(9,10)]=>1 [(1,2),(3,7),(4,6),(5,8),(9,10)]=>1 [(1,3),(2,7),(4,6),(5,8),(9,10)]=>2 [(1,4),(2,7),(3,6),(5,8),(9,10)]=>1 [(1,5),(2,7),(3,6),(4,8),(9,10)]=>1 [(1,6),(2,7),(3,5),(4,8),(9,10)]=>2 [(1,7),(2,6),(3,5),(4,8),(9,10)]=>1 [(1,8),(2,6),(3,5),(4,7),(9,10)]=>1 [(1,9),(2,6),(3,5),(4,7),(8,10)]=>2 [(1,10),(2,6),(3,5),(4,7),(8,9)]=>1 [(1,10),(2,5),(3,6),(4,7),(8,9)]=>1 [(1,9),(2,5),(3,6),(4,7),(8,10)]=>2 [(1,8),(2,5),(3,6),(4,7),(9,10)]=>1 [(1,7),(2,5),(3,6),(4,8),(9,10)]=>2 [(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)]=>1 [(1,3),(2,6),(4,7),(5,8),(9,10)]=>2 [(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)]=>2 [(1,4),(2,5),(3,7),(6,8),(9,10)]=>2 [(1,5),(2,4),(3,7),(6,8),(9,10)]=>1 [(1,6),(2,4),(3,7),(5,8),(9,10)]=>2 [(1,7),(2,4),(3,6),(5,8),(9,10)]=>2 [(1,8),(2,4),(3,6),(5,7),(9,10)]=>1 [(1,9),(2,4),(3,6),(5,7),(8,10)]=>2 [(1,10),(2,4),(3,6),(5,7),(8,9)]=>1 [(1,10),(2,3),(4,6),(5,7),(8,9)]=>1 [(1,9),(2,3),(4,6),(5,7),(8,10)]=>2 [(1,8),(2,3),(4,6),(5,7),(9,10)]=>1 [(1,7),(2,3),(4,6),(5,8),(9,10)]=>1 [(1,6),(2,3),(4,7),(5,8),(9,10)]=>1 [(1,5),(2,3),(4,7),(6,8),(9,10)]=>1 [(1,4),(2,3),(5,7),(6,8),(9,10)]=>1 [(1,3),(2,4),(5,7),(6,8),(9,10)]=>2 [(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)]=>1 [(1,4),(2,3),(5,8),(6,7),(9,10)]=>0 [(1,5),(2,3),(4,8),(6,7),(9,10)]=>1 [(1,6),(2,3),(4,8),(5,7),(9,10)]=>1 [(1,7),(2,3),(4,8),(5,6),(9,10)]=>1 [(1,8),(2,3),(4,7),(5,6),(9,10)]=>0 [(1,9),(2,3),(4,7),(5,6),(8,10)]=>1 [(1,10),(2,3),(4,7),(5,6),(8,9)]=>0 [(1,10),(2,4),(3,7),(5,6),(8,9)]=>1 [(1,9),(2,4),(3,7),(5,6),(8,10)]=>2 [(1,8),(2,4),(3,7),(5,6),(9,10)]=>1 [(1,7),(2,4),(3,8),(5,6),(9,10)]=>1 [(1,6),(2,4),(3,8),(5,7),(9,10)]=>2 [(1,5),(2,4),(3,8),(6,7),(9,10)]=>1 [(1,4),(2,5),(3,8),(6,7),(9,10)]=>1 [(1,3),(2,5),(4,8),(6,7),(9,10)]=>1 [(1,2),(3,5),(4,8),(6,7),(9,10)]=>1 [(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)]=>2 [(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)]=>2 [(1,8),(2,5),(3,7),(4,6),(9,10)]=>1 [(1,9),(2,5),(3,7),(4,6),(8,10)]=>2 [(1,10),(2,5),(3,7),(4,6),(8,9)]=>1 [(1,10),(2,6),(3,7),(4,5),(8,9)]=>1 [(1,9),(2,6),(3,7),(4,5),(8,10)]=>2 [(1,8),(2,6),(3,7),(4,5),(9,10)]=>1 [(1,7),(2,6),(3,8),(4,5),(9,10)]=>1 [(1,6),(2,7),(3,8),(4,5),(9,10)]=>1 [(1,5),(2,7),(3,8),(4,6),(9,10)]=>2 [(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)]=>1 [(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)]=>1 [(1,7),(2,8),(3,6),(4,5),(9,10)]=>1 [(1,8),(2,7),(3,6),(4,5),(9,10)]=>0 [(1,9),(2,7),(3,6),(4,5),(8,10)]=>1 [(1,10),(2,7),(3,6),(4,5),(8,9)]=>0 [(1,10),(2,8),(3,6),(4,5),(7,9)]=>1 [(1,9),(2,8),(3,6),(4,5),(7,10)]=>1 [(1,8),(2,9),(3,6),(4,5),(7,10)]=>1 [(1,7),(2,9),(3,6),(4,5),(8,10)]=>1 [(1,6),(2,9),(3,7),(4,5),(8,10)]=>2 [(1,5),(2,9),(3,7),(4,6),(8,10)]=>2 [(1,4),(2,9),(3,7),(5,6),(8,10)]=>2 [(1,3),(2,9),(4,7),(5,6),(8,10)]=>1 [(1,2),(3,9),(4,7),(5,6),(8,10)]=>1 [(1,2),(3,10),(4,7),(5,6),(8,9)]=>0 [(1,3),(2,10),(4,7),(5,6),(8,9)]=>1 [(1,4),(2,10),(3,7),(5,6),(8,9)]=>1 [(1,5),(2,10),(3,7),(4,6),(8,9)]=>1 [(1,6),(2,10),(3,7),(4,5),(8,9)]=>1 [(1,7),(2,10),(3,6),(4,5),(8,9)]=>1 [(1,8),(2,10),(3,6),(4,5),(7,9)]=>1 [(1,9),(2,10),(3,6),(4,5),(7,8)]=>1 [(1,10),(2,9),(3,6),(4,5),(7,8)]=>0 [(1,10),(2,9),(3,7),(4,5),(6,8)]=>1 [(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)]=>2 [(1,5),(2,10),(3,8),(4,6),(7,9)]=>2 [(1,4),(2,10),(3,8),(5,6),(7,9)]=>2 [(1,3),(2,10),(4,8),(5,6),(7,9)]=>2 [(1,2),(3,10),(4,8),(5,6),(7,9)]=>1 [(1,2),(3,9),(4,8),(5,6),(7,10)]=>1 [(1,3),(2,9),(4,8),(5,6),(7,10)]=>2 [(1,4),(2,9),(3,8),(5,6),(7,10)]=>1 [(1,5),(2,9),(3,8),(4,6),(7,10)]=>2 [(1,6),(2,9),(3,8),(4,5),(7,10)]=>1 [(1,7),(2,9),(3,8),(4,5),(6,10)]=>1 [(1,8),(2,9),(3,7),(4,5),(6,10)]=>2 [(1,9),(2,8),(3,7),(4,5),(6,10)]=>1 [(1,10),(2,8),(3,7),(4,5),(6,9)]=>1 [(1,10),(2,7),(3,8),(4,5),(6,9)]=>1 [(1,9),(2,7),(3,8),(4,5),(6,10)]=>2 [(1,8),(2,7),(3,9),(4,5),(6,10)]=>1 [(1,7),(2,8),(3,9),(4,5),(6,10)]=>2 [(1,6),(2,8),(3,9),(4,5),(7,10)]=>1 [(1,5),(2,8),(3,9),(4,6),(7,10)]=>2 [(1,4),(2,8),(3,9),(5,6),(7,10)]=>1 [(1,3),(2,8),(4,9),(5,6),(7,10)]=>2 [(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)]=>2 [(1,4),(2,7),(3,9),(5,6),(8,10)]=>2 [(1,5),(2,7),(3,9),(4,6),(8,10)]=>2 [(1,6),(2,7),(3,9),(4,5),(8,10)]=>2 [(1,7),(2,6),(3,9),(4,5),(8,10)]=>1 [(1,8),(2,6),(3,9),(4,5),(7,10)]=>2 [(1,9),(2,6),(3,8),(4,5),(7,10)]=>2 [(1,10),(2,6),(3,8),(4,5),(7,9)]=>1 [(1,10),(2,5),(3,8),(4,6),(7,9)]=>2 [(1,9),(2,5),(3,8),(4,6),(7,10)]=>2 [(1,8),(2,5),(3,9),(4,6),(7,10)]=>2 [(1,7),(2,5),(3,9),(4,6),(8,10)]=>2 [(1,6),(2,5),(3,9),(4,7),(8,10)]=>2 [(1,5),(2,6),(3,9),(4,7),(8,10)]=>2 [(1,4),(2,6),(3,9),(5,7),(8,10)]=>2 [(1,3),(2,6),(4,9),(5,7),(8,10)]=>2 [(1,2),(3,6),(4,9),(5,7),(8,10)]=>2 [(1,2),(3,5),(4,9),(6,7),(8,10)]=>1 [(1,3),(2,5),(4,9),(6,7),(8,10)]=>2 [(1,4),(2,5),(3,9),(6,7),(8,10)]=>2 [(1,5),(2,4),(3,9),(6,7),(8,10)]=>1 [(1,6),(2,4),(3,9),(5,7),(8,10)]=>2 [(1,7),(2,4),(3,9),(5,6),(8,10)]=>1 [(1,8),(2,4),(3,9),(5,6),(7,10)]=>2 [(1,9),(2,4),(3,8),(5,6),(7,10)]=>2 [(1,10),(2,4),(3,8),(5,6),(7,9)]=>1 [(1,10),(2,3),(4,8),(5,6),(7,9)]=>1 [(1,9),(2,3),(4,8),(5,6),(7,10)]=>1 [(1,8),(2,3),(4,9),(5,6),(7,10)]=>1 [(1,7),(2,3),(4,9),(5,6),(8,10)]=>1 [(1,6),(2,3),(4,9),(5,7),(8,10)]=>2 [(1,5),(2,3),(4,9),(6,7),(8,10)]=>1 [(1,4),(2,3),(5,9),(6,7),(8,10)]=>1 [(1,3),(2,4),(5,9),(6,7),(8,10)]=>2 [(1,2),(3,4),(5,9),(6,7),(8,10)]=>1 [(1,2),(3,4),(5,10),(6,7),(8,9)]=>0 [(1,3),(2,4),(5,10),(6,7),(8,9)]=>1 [(1,4),(2,3),(5,10),(6,7),(8,9)]=>0 [(1,5),(2,3),(4,10),(6,7),(8,9)]=>1 [(1,6),(2,3),(4,10),(5,7),(8,9)]=>1 [(1,7),(2,3),(4,10),(5,6),(8,9)]=>1 [(1,8),(2,3),(4,10),(5,6),(7,9)]=>1 [(1,9),(2,3),(4,10),(5,6),(7,8)]=>1 [(1,10),(2,3),(4,9),(5,6),(7,8)]=>0 [(1,10),(2,4),(3,9),(5,6),(7,8)]=>1 [(1,9),(2,4),(3,10),(5,6),(7,8)]=>1 [(1,8),(2,4),(3,10),(5,6),(7,9)]=>2 [(1,7),(2,4),(3,10),(5,6),(8,9)]=>1 [(1,6),(2,4),(3,10),(5,7),(8,9)]=>2 [(1,5),(2,4),(3,10),(6,7),(8,9)]=>1 [(1,4),(2,5),(3,10),(6,7),(8,9)]=>1 [(1,3),(2,5),(4,10),(6,7),(8,9)]=>1 [(1,2),(3,5),(4,10),(6,7),(8,9)]=>1 [(1,2),(3,6),(4,10),(5,7),(8,9)]=>1 [(1,3),(2,6),(4,10),(5,7),(8,9)]=>1 [(1,4),(2,6),(3,10),(5,7),(8,9)]=>2 [(1,5),(2,6),(3,10),(4,7),(8,9)]=>1 [(1,6),(2,5),(3,10),(4,7),(8,9)]=>1 [(1,7),(2,5),(3,10),(4,6),(8,9)]=>2 [(1,8),(2,5),(3,10),(4,6),(7,9)]=>2 [(1,9),(2,5),(3,10),(4,6),(7,8)]=>2 [(1,10),(2,5),(3,9),(4,6),(7,8)]=>1 [(1,10),(2,6),(3,9),(4,5),(7,8)]=>1 [(1,9),(2,6),(3,10),(4,5),(7,8)]=>1 [(1,8),(2,6),(3,10),(4,5),(7,9)]=>2 [(1,7),(2,6),(3,10),(4,5),(8,9)]=>1 [(1,6),(2,7),(3,10),(4,5),(8,9)]=>1 [(1,5),(2,7),(3,10),(4,6),(8,9)]=>2 [(1,4),(2,7),(3,10),(5,6),(8,9)]=>1 [(1,3),(2,7),(4,10),(5,6),(8,9)]=>1 [(1,2),(3,7),(4,10),(5,6),(8,9)]=>1 [(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)]=>2 [(1,5),(2,8),(3,10),(4,6),(7,9)]=>2 [(1,6),(2,8),(3,10),(4,5),(7,9)]=>2 [(1,7),(2,8),(3,10),(4,5),(6,9)]=>1 [(1,8),(2,7),(3,10),(4,5),(6,9)]=>1 [(1,9),(2,7),(3,10),(4,5),(6,8)]=>2 [(1,10),(2,7),(3,9),(4,5),(6,8)]=>1 [(1,10),(2,8),(3,9),(4,5),(6,7)]=>1 [(1,9),(2,8),(3,10),(4,5),(6,7)]=>1 [(1,8),(2,9),(3,10),(4,5),(6,7)]=>1 [(1,7),(2,9),(3,10),(4,5),(6,8)]=>2 [(1,6),(2,9),(3,10),(4,5),(7,8)]=>1 [(1,5),(2,9),(3,10),(4,6),(7,8)]=>2 [(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)]=>1 [(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)]=>1 [(1,7),(2,10),(3,9),(4,5),(6,8)]=>1 [(1,8),(2,10),(3,9),(4,5),(6,7)]=>1 [(1,9),(2,10),(3,8),(4,5),(6,7)]=>1 [(1,10),(2,9),(3,8),(4,5),(6,7)]=>0 [(1,10),(2,9),(3,8),(4,6),(5,7)]=>1 [(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)]=>1 [(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)]=>2 [(1,5),(2,6),(3,10),(4,8),(7,9)]=>2 [(1,4),(2,6),(3,10),(5,8),(7,9)]=>2 [(1,3),(2,6),(4,10),(5,8),(7,9)]=>2 [(1,2),(3,6),(4,10),(5,8),(7,9)]=>2 [(1,2),(3,5),(4,10),(6,8),(7,9)]=>2 [(1,3),(2,5),(4,10),(6,8),(7,9)]=>2 [(1,4),(2,5),(3,10),(6,8),(7,9)]=>2 [(1,5),(2,4),(3,10),(6,8),(7,9)]=>2 [(1,6),(2,4),(3,10),(5,8),(7,9)]=>2 [(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)]=>1 [(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)]=>2 [(1,5),(2,3),(4,10),(6,8),(7,9)]=>2 [(1,4),(2,3),(5,10),(6,8),(7,9)]=>1 [(1,3),(2,4),(5,10),(6,8),(7,9)]=>2 [(1,2),(3,4),(5,10),(6,8),(7,9)]=>1 [(1,2),(3,4),(5,9),(6,8),(7,10)]=>1 [(1,3),(2,4),(5,9),(6,8),(7,10)]=>2 [(1,4),(2,3),(5,9),(6,8),(7,10)]=>1 [(1,5),(2,3),(4,9),(6,8),(7,10)]=>2 [(1,6),(2,3),(4,9),(5,8),(7,10)]=>1 [(1,7),(2,3),(4,9),(5,8),(6,10)]=>1 [(1,8),(2,3),(4,9),(5,7),(6,10)]=>2 [(1,9),(2,3),(4,8),(5,7),(6,10)]=>1 [(1,10),(2,3),(4,8),(5,7),(6,9)]=>1 [(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)]=>2 [(1,5),(2,4),(3,9),(6,8),(7,10)]=>2 [(1,4),(2,5),(3,9),(6,8),(7,10)]=>2 [(1,3),(2,5),(4,9),(6,8),(7,10)]=>2 [(1,2),(3,5),(4,9),(6,8),(7,10)]=>2 [(1,2),(3,6),(4,9),(5,8),(7,10)]=>1 [(1,3),(2,6),(4,9),(5,8),(7,10)]=>2 [(1,4),(2,6),(3,9),(5,8),(7,10)]=>2 [(1,5),(2,6),(3,9),(4,8),(7,10)]=>2 [(1,6),(2,5),(3,9),(4,8),(7,10)]=>1 [(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)]=>1 [(1,10),(2,6),(3,8),(4,7),(5,9)]=>1 [(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)]=>1 [(1,6),(2,7),(3,9),(4,8),(5,10)]=>2 [(1,5),(2,7),(3,9),(4,8),(6,10)]=>1 [(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)]=>1 [(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)]=>1 [(1,9),(2,8),(3,7),(4,6),(5,10)]=>1 [(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)]=>1 [(1,5),(2,9),(3,8),(4,7),(6,10)]=>1 [(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)]=>1 [(1,2),(3,10),(4,8),(5,7),(6,9)]=>1 [(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)]=>1 [(1,10),(2,9),(3,6),(4,7),(5,8)]=>1 [(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)]=>1 [(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)]=>1 [(1,9),(2,7),(3,6),(4,8),(5,10)]=>2 [(1,8),(2,7),(3,6),(4,9),(5,10)]=>1 [(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)]=>1 [(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)]=>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)]=>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)]=>1 [(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)]=>1 [(1,5),(2,6),(3,8),(4,9),(7,10)]=>2 [(1,4),(2,6),(3,8),(5,9),(7,10)]=>2 [(1,3),(2,6),(4,8),(5,9),(7,10)]=>2 [(1,2),(3,6),(4,8),(5,9),(7,10)]=>1 [(1,2),(3,5),(4,8),(6,9),(7,10)]=>2 [(1,3),(2,5),(4,8),(6,9),(7,10)]=>2 [(1,4),(2,5),(3,8),(6,9),(7,10)]=>2 [(1,5),(2,4),(3,8),(6,9),(7,10)]=>2 [(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)]=>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)]=>1 [(1,9),(2,3),(4,7),(5,8),(6,10)]=>2 [(1,8),(2,3),(4,7),(5,9),(6,10)]=>1 [(1,7),(2,3),(4,8),(5,9),(6,10)]=>2 [(1,6),(2,3),(4,8),(5,9),(7,10)]=>1 [(1,5),(2,3),(4,8),(6,9),(7,10)]=>2 [(1,4),(2,3),(5,8),(6,9),(7,10)]=>1 [(1,3),(2,4),(5,8),(6,9),(7,10)]=>2 [(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)]=>2 [(1,4),(2,3),(5,7),(6,9),(8,10)]=>1 [(1,5),(2,3),(4,7),(6,9),(8,10)]=>2 [(1,6),(2,3),(4,7),(5,9),(8,10)]=>2 [(1,7),(2,3),(4,6),(5,9),(8,10)]=>1 [(1,8),(2,3),(4,6),(5,9),(7,10)]=>2 [(1,9),(2,3),(4,6),(5,8),(7,10)]=>2 [(1,10),(2,3),(4,6),(5,8),(7,9)]=>1 [(1,10),(2,4),(3,6),(5,8),(7,9)]=>2 [(1,9),(2,4),(3,6),(5,8),(7,10)]=>2 [(1,8),(2,4),(3,6),(5,9),(7,10)]=>2 [(1,7),(2,4),(3,6),(5,9),(8,10)]=>2 [(1,6),(2,4),(3,7),(5,9),(8,10)]=>2 [(1,5),(2,4),(3,7),(6,9),(8,10)]=>2 [(1,4),(2,5),(3,7),(6,9),(8,10)]=>2 [(1,3),(2,5),(4,7),(6,9),(8,10)]=>2 [(1,2),(3,5),(4,7),(6,9),(8,10)]=>2 [(1,2),(3,6),(4,7),(5,9),(8,10)]=>2 [(1,3),(2,6),(4,7),(5,9),(8,10)]=>2 [(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)]=>2 [(1,7),(2,5),(3,6),(4,9),(8,10)]=>2 [(1,8),(2,5),(3,6),(4,9),(7,10)]=>2 [(1,9),(2,5),(3,6),(4,8),(7,10)]=>2 [(1,10),(2,5),(3,6),(4,8),(7,9)]=>2 [(1,10),(2,6),(3,5),(4,8),(7,9)]=>1 [(1,9),(2,6),(3,5),(4,8),(7,10)]=>2 [(1,8),(2,6),(3,5),(4,9),(7,10)]=>2 [(1,7),(2,6),(3,5),(4,9),(8,10)]=>1 [(1,6),(2,7),(3,5),(4,9),(8,10)]=>2 [(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)]=>2 [(1,2),(3,7),(4,6),(5,9),(8,10)]=>1 [(1,2),(3,8),(4,6),(5,9),(7,10)]=>2 [(1,3),(2,8),(4,6),(5,9),(7,10)]=>2 [(1,4),(2,8),(3,6),(5,9),(7,10)]=>2 [(1,5),(2,8),(3,6),(4,9),(7,10)]=>2 [(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)]=>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)]=>2 [(1,5),(2,9),(3,6),(4,8),(7,10)]=>2 [(1,4),(2,9),(3,6),(5,8),(7,10)]=>2 [(1,3),(2,9),(4,6),(5,8),(7,10)]=>2 [(1,2),(3,9),(4,6),(5,8),(7,10)]=>2 [(1,2),(3,10),(4,6),(5,8),(7,9)]=>1 [(1,3),(2,10),(4,6),(5,8),(7,9)]=>2 [(1,4),(2,10),(3,6),(5,8),(7,9)]=>2 [(1,5),(2,10),(3,6),(4,8),(7,9)]=>2 [(1,6),(2,10),(3,5),(4,8),(7,9)]=>2 [(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)]=>1 [(1,10),(2,9),(3,4),(5,7),(6,8)]=>1 [(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)]=>2 [(1,5),(2,10),(3,4),(6,8),(7,9)]=>2 [(1,4),(2,10),(3,5),(6,8),(7,9)]=>2 [(1,3),(2,10),(4,5),(6,8),(7,9)]=>2 [(1,2),(3,10),(4,5),(6,8),(7,9)]=>1 [(1,2),(3,9),(4,5),(6,8),(7,10)]=>1 [(1,3),(2,9),(4,5),(6,8),(7,10)]=>2 [(1,4),(2,9),(3,5),(6,8),(7,10)]=>2 [(1,5),(2,9),(3,4),(6,8),(7,10)]=>2 [(1,6),(2,9),(3,4),(5,8),(7,10)]=>1 [(1,7),(2,9),(3,4),(5,8),(6,10)]=>1 [(1,8),(2,9),(3,4),(5,7),(6,10)]=>2 [(1,9),(2,8),(3,4),(5,7),(6,10)]=>1 [(1,10),(2,8),(3,4),(5,7),(6,9)]=>1 [(1,10),(2,7),(3,4),(5,8),(6,9)]=>1 [(1,9),(2,7),(3,4),(5,8),(6,10)]=>2 [(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)]=>1 [(1,5),(2,8),(3,4),(6,9),(7,10)]=>2 [(1,4),(2,8),(3,5),(6,9),(7,10)]=>2 [(1,3),(2,8),(4,5),(6,9),(7,10)]=>2 [(1,2),(3,8),(4,5),(6,9),(7,10)]=>1 [(1,2),(3,7),(4,5),(6,9),(8,10)]=>1 [(1,3),(2,7),(4,5),(6,9),(8,10)]=>2 [(1,4),(2,7),(3,5),(6,9),(8,10)]=>2 [(1,5),(2,7),(3,4),(6,9),(8,10)]=>2 [(1,6),(2,7),(3,4),(5,9),(8,10)]=>2 [(1,7),(2,6),(3,4),(5,9),(8,10)]=>1 [(1,8),(2,6),(3,4),(5,9),(7,10)]=>2 [(1,9),(2,6),(3,4),(5,8),(7,10)]=>2 [(1,10),(2,6),(3,4),(5,8),(7,9)]=>1 [(1,10),(2,5),(3,4),(6,8),(7,9)]=>1 [(1,9),(2,5),(3,4),(6,8),(7,10)]=>1 [(1,8),(2,5),(3,4),(6,9),(7,10)]=>1 [(1,7),(2,5),(3,4),(6,9),(8,10)]=>1 [(1,6),(2,5),(3,4),(7,9),(8,10)]=>1 [(1,5),(2,6),(3,4),(7,9),(8,10)]=>2 [(1,4),(2,6),(3,5),(7,9),(8,10)]=>2 [(1,3),(2,6),(4,5),(7,9),(8,10)]=>2 [(1,2),(3,6),(4,5),(7,9),(8,10)]=>1 [(1,2),(3,5),(4,6),(7,9),(8,10)]=>2 [(1,3),(2,5),(4,6),(7,9),(8,10)]=>2 [(1,4),(2,5),(3,6),(7,9),(8,10)]=>2 [(1,5),(2,4),(3,6),(7,9),(8,10)]=>2 [(1,6),(2,4),(3,5),(7,9),(8,10)]=>2 [(1,7),(2,4),(3,5),(6,9),(8,10)]=>2 [(1,8),(2,4),(3,5),(6,9),(7,10)]=>2 [(1,9),(2,4),(3,5),(6,8),(7,10)]=>2 [(1,10),(2,4),(3,5),(6,8),(7,9)]=>2 [(1,10),(2,3),(4,5),(6,8),(7,9)]=>1 [(1,9),(2,3),(4,5),(6,8),(7,10)]=>1 [(1,8),(2,3),(4,5),(6,9),(7,10)]=>1 [(1,7),(2,3),(4,5),(6,9),(8,10)]=>1 [(1,6),(2,3),(4,5),(7,9),(8,10)]=>1 [(1,5),(2,3),(4,6),(7,9),(8,10)]=>2 [(1,4),(2,3),(5,6),(7,9),(8,10)]=>1 [(1,3),(2,4),(5,6),(7,9),(8,10)]=>2 [(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)]=>1 [(1,4),(2,3),(5,6),(7,10),(8,9)]=>0 [(1,5),(2,3),(4,6),(7,10),(8,9)]=>1 [(1,6),(2,3),(4,5),(7,10),(8,9)]=>0 [(1,7),(2,3),(4,5),(6,10),(8,9)]=>1 [(1,8),(2,3),(4,5),(6,10),(7,9)]=>1 [(1,9),(2,3),(4,5),(6,10),(7,8)]=>1 [(1,10),(2,3),(4,5),(6,9),(7,8)]=>0 [(1,10),(2,4),(3,5),(6,9),(7,8)]=>1 [(1,9),(2,4),(3,5),(6,10),(7,8)]=>2 [(1,8),(2,4),(3,5),(6,10),(7,9)]=>2 [(1,7),(2,4),(3,5),(6,10),(8,9)]=>2 [(1,6),(2,4),(3,5),(7,10),(8,9)]=>1 [(1,5),(2,4),(3,6),(7,10),(8,9)]=>1 [(1,4),(2,5),(3,6),(7,10),(8,9)]=>1 [(1,3),(2,5),(4,6),(7,10),(8,9)]=>1 [(1,2),(3,5),(4,6),(7,10),(8,9)]=>1 [(1,2),(3,6),(4,5),(7,10),(8,9)]=>0 [(1,3),(2,6),(4,5),(7,10),(8,9)]=>1 [(1,4),(2,6),(3,5),(7,10),(8,9)]=>1 [(1,5),(2,6),(3,4),(7,10),(8,9)]=>1 [(1,6),(2,5),(3,4),(7,10),(8,9)]=>0 [(1,7),(2,5),(3,4),(6,10),(8,9)]=>1 [(1,8),(2,5),(3,4),(6,10),(7,9)]=>1 [(1,9),(2,5),(3,4),(6,10),(7,8)]=>1 [(1,10),(2,5),(3,4),(6,9),(7,8)]=>0 [(1,10),(2,6),(3,4),(5,9),(7,8)]=>1 [(1,9),(2,6),(3,4),(5,10),(7,8)]=>1 [(1,8),(2,6),(3,4),(5,10),(7,9)]=>2 [(1,7),(2,6),(3,4),(5,10),(8,9)]=>1 [(1,6),(2,7),(3,4),(5,10),(8,9)]=>1 [(1,5),(2,7),(3,4),(6,10),(8,9)]=>1 [(1,4),(2,7),(3,5),(6,10),(8,9)]=>2 [(1,3),(2,7),(4,5),(6,10),(8,9)]=>1 [(1,2),(3,7),(4,5),(6,10),(8,9)]=>1 [(1,2),(3,8),(4,5),(6,10),(7,9)]=>1 [(1,3),(2,8),(4,5),(6,10),(7,9)]=>1 [(1,4),(2,8),(3,5),(6,10),(7,9)]=>2 [(1,5),(2,8),(3,4),(6,10),(7,9)]=>1 [(1,6),(2,8),(3,4),(5,10),(7,9)]=>2 [(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)]=>2 [(1,10),(2,7),(3,4),(5,9),(6,8)]=>1 [(1,10),(2,8),(3,4),(5,9),(6,7)]=>1 [(1,9),(2,8),(3,4),(5,10),(6,7)]=>1 [(1,8),(2,9),(3,4),(5,10),(6,7)]=>1 [(1,7),(2,9),(3,4),(5,10),(6,8)]=>2 [(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)]=>2 [(1,3),(2,9),(4,5),(6,10),(7,8)]=>1 [(1,2),(3,9),(4,5),(6,10),(7,8)]=>1 [(1,2),(3,10),(4,5),(6,9),(7,8)]=>0 [(1,3),(2,10),(4,5),(6,9),(7,8)]=>1 [(1,4),(2,10),(3,5),(6,9),(7,8)]=>1 [(1,5),(2,10),(3,4),(6,9),(7,8)]=>1 [(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)]=>1 [(1,9),(2,10),(3,4),(5,8),(6,7)]=>1 [(1,10),(2,9),(3,4),(5,8),(6,7)]=>0 [(1,10),(2,9),(3,5),(4,8),(6,7)]=>1 [(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)]=>2 [(1,5),(2,10),(3,6),(4,9),(7,8)]=>2 [(1,4),(2,10),(3,6),(5,9),(7,8)]=>2 [(1,3),(2,10),(4,6),(5,9),(7,8)]=>2 [(1,2),(3,10),(4,6),(5,9),(7,8)]=>1 [(1,2),(3,9),(4,6),(5,10),(7,8)]=>1 [(1,3),(2,9),(4,6),(5,10),(7,8)]=>2 [(1,4),(2,9),(3,6),(5,10),(7,8)]=>1 [(1,5),(2,9),(3,6),(4,10),(7,8)]=>1 [(1,6),(2,9),(3,5),(4,10),(7,8)]=>2 [(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)]=>1 [(1,10),(2,8),(3,5),(4,9),(6,7)]=>1 [(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)]=>2 [(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)]=>2 [(1,2),(3,8),(4,6),(5,10),(7,9)]=>2 [(1,2),(3,7),(4,6),(5,10),(8,9)]=>1 [(1,3),(2,7),(4,6),(5,10),(8,9)]=>2 [(1,4),(2,7),(3,6),(5,10),(8,9)]=>1 [(1,5),(2,7),(3,6),(4,10),(8,9)]=>1 [(1,6),(2,7),(3,5),(4,10),(8,9)]=>2 [(1,7),(2,6),(3,5),(4,10),(8,9)]=>1 [(1,8),(2,6),(3,5),(4,10),(7,9)]=>2 [(1,9),(2,6),(3,5),(4,10),(7,8)]=>1 [(1,10),(2,6),(3,5),(4,9),(7,8)]=>1 [(1,10),(2,5),(3,6),(4,9),(7,8)]=>1 [(1,9),(2,5),(3,6),(4,10),(7,8)]=>2 [(1,8),(2,5),(3,6),(4,10),(7,9)]=>2 [(1,7),(2,5),(3,6),(4,10),(8,9)]=>2 [(1,6),(2,5),(3,7),(4,10),(8,9)]=>1 [(1,5),(2,6),(3,7),(4,10),(8,9)]=>2 [(1,4),(2,6),(3,7),(5,10),(8,9)]=>1 [(1,3),(2,6),(4,7),(5,10),(8,9)]=>2 [(1,2),(3,6),(4,7),(5,10),(8,9)]=>1 [(1,2),(3,5),(4,7),(6,10),(8,9)]=>1 [(1,3),(2,5),(4,7),(6,10),(8,9)]=>2 [(1,4),(2,5),(3,7),(6,10),(8,9)]=>2 [(1,5),(2,4),(3,7),(6,10),(8,9)]=>1 [(1,6),(2,4),(3,7),(5,10),(8,9)]=>2 [(1,7),(2,4),(3,6),(5,10),(8,9)]=>2 [(1,8),(2,4),(3,6),(5,10),(7,9)]=>2 [(1,9),(2,4),(3,6),(5,10),(7,8)]=>2 [(1,10),(2,4),(3,6),(5,9),(7,8)]=>1 [(1,10),(2,3),(4,6),(5,9),(7,8)]=>1 [(1,9),(2,3),(4,6),(5,10),(7,8)]=>1 [(1,8),(2,3),(4,6),(5,10),(7,9)]=>2 [(1,7),(2,3),(4,6),(5,10),(8,9)]=>1 [(1,6),(2,3),(4,7),(5,10),(8,9)]=>1 [(1,5),(2,3),(4,7),(6,10),(8,9)]=>1 [(1,4),(2,3),(5,7),(6,10),(8,9)]=>1 [(1,3),(2,4),(5,7),(6,10),(8,9)]=>2 [(1,2),(3,4),(5,7),(6,10),(8,9)]=>1 [(1,2),(3,4),(5,8),(6,10),(7,9)]=>1 [(1,3),(2,4),(5,8),(6,10),(7,9)]=>2 [(1,4),(2,3),(5,8),(6,10),(7,9)]=>1 [(1,5),(2,3),(4,8),(6,10),(7,9)]=>1 [(1,6),(2,3),(4,8),(5,10),(7,9)]=>2 [(1,7),(2,3),(4,8),(5,10),(6,9)]=>1 [(1,8),(2,3),(4,7),(5,10),(6,9)]=>1 [(1,9),(2,3),(4,7),(5,10),(6,8)]=>2 [(1,10),(2,3),(4,7),(5,9),(6,8)]=>1 [(1,10),(2,4),(3,7),(5,9),(6,8)]=>1 [(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)]=>2 [(1,5),(2,4),(3,8),(6,10),(7,9)]=>1 [(1,4),(2,5),(3,8),(6,10),(7,9)]=>2 [(1,3),(2,5),(4,8),(6,10),(7,9)]=>2 [(1,2),(3,5),(4,8),(6,10),(7,9)]=>1 [(1,2),(3,6),(4,8),(5,10),(7,9)]=>2 [(1,3),(2,6),(4,8),(5,10),(7,9)]=>2 [(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)]=>2 [(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)]=>1 [(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)]=>1 [(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)]=>1 [(1,3),(2,7),(4,8),(5,10),(6,9)]=>2 [(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)]=>2 [(1,4),(2,8),(3,7),(5,10),(6,9)]=>1 [(1,5),(2,8),(3,7),(4,10),(6,9)]=>2 [(1,6),(2,8),(3,7),(4,10),(5,9)]=>1 [(1,7),(2,8),(3,6),(4,10),(5,9)]=>2 [(1,8),(2,7),(3,6),(4,10),(5,9)]=>1 [(1,9),(2,7),(3,6),(4,10),(5,8)]=>2 [(1,10),(2,7),(3,6),(4,9),(5,8)]=>1 [(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)]=>1 [(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)]=>1 [(1,10),(2,9),(3,7),(4,8),(5,6)]=>1 [(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)]=>1 [(1,2),(3,9),(4,8),(5,10),(6,7)]=>1 [(1,3),(2,9),(4,8),(5,10),(6,7)]=>2 [(1,4),(2,9),(3,8),(5,10),(6,7)]=>1 [(1,5),(2,9),(3,8),(4,10),(6,7)]=>1 [(1,6),(2,9),(3,8),(4,10),(5,7)]=>2 [(1,7),(2,9),(3,8),(4,10),(5,6)]=>1 [(1,8),(2,9),(3,7),(4,10),(5,6)]=>2 [(1,9),(2,8),(3,7),(4,10),(5,6)]=>1 [(1,10),(2,8),(3,7),(4,9),(5,6)]=>1 [(1,10),(2,7),(3,8),(4,9),(5,6)]=>1 [(1,9),(2,7),(3,8),(4,10),(5,6)]=>2 [(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)]=>2 [(1,4),(2,8),(3,9),(5,10),(6,7)]=>1 [(1,3),(2,8),(4,9),(5,10),(6,7)]=>2 [(1,2),(3,8),(4,9),(5,10),(6,7)]=>1 [(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)]=>1 [(1,9),(2,5),(3,8),(4,10),(6,7)]=>2 [(1,8),(2,5),(3,9),(4,10),(6,7)]=>1 [(1,7),(2,5),(3,9),(4,10),(6,8)]=>2 [(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)]=>1 [(1,3),(2,6),(4,9),(5,10),(7,8)]=>2 [(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)]=>2 [(1,4),(2,5),(3,9),(6,10),(7,8)]=>2 [(1,5),(2,4),(3,9),(6,10),(7,8)]=>1 [(1,6),(2,4),(3,9),(5,10),(7,8)]=>2 [(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)]=>1 [(1,10),(2,3),(4,8),(5,9),(6,7)]=>1 [(1,9),(2,3),(4,8),(5,10),(6,7)]=>1 [(1,8),(2,3),(4,9),(5,10),(6,7)]=>1 [(1,7),(2,3),(4,9),(5,10),(6,8)]=>2 [(1,6),(2,3),(4,9),(5,10),(7,8)]=>1 [(1,5),(2,3),(4,9),(6,10),(7,8)]=>1 [(1,4),(2,3),(5,9),(6,10),(7,8)]=>1 [(1,3),(2,4),(5,9),(6,10),(7,8)]=>2 [(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)]=>1 [(1,4),(2,3),(5,10),(6,9),(7,8)]=>0 [(1,5),(2,3),(4,10),(6,9),(7,8)]=>1 [(1,6),(2,3),(4,10),(5,9),(7,8)]=>1 [(1,7),(2,3),(4,10),(5,9),(6,8)]=>1 [(1,8),(2,3),(4,10),(5,9),(6,7)]=>1 [(1,9),(2,3),(4,10),(5,8),(6,7)]=>1 [(1,10),(2,3),(4,9),(5,8),(6,7)]=>0 [(1,10),(2,4),(3,9),(5,8),(6,7)]=>1 [(1,9),(2,4),(3,10),(5,8),(6,7)]=>1 [(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)]=>2 [(1,5),(2,4),(3,10),(6,9),(7,8)]=>1 [(1,4),(2,5),(3,10),(6,9),(7,8)]=>1 [(1,3),(2,5),(4,10),(6,9),(7,8)]=>1 [(1,2),(3,5),(4,10),(6,9),(7,8)]=>1 [(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)]=>2 [(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)]=>2 [(1,8),(2,5),(3,10),(4,9),(6,7)]=>1 [(1,9),(2,5),(3,10),(4,8),(6,7)]=>2 [(1,10),(2,5),(3,9),(4,8),(6,7)]=>1 [(1,10),(2,6),(3,9),(4,8),(5,7)]=>1 [(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)]=>1 [(1,6),(2,7),(3,10),(4,9),(5,8)]=>1 [(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)]=>1 [(1,2),(3,7),(4,10),(5,9),(6,8)]=>1 [(1,2),(3,8),(4,10),(5,9),(6,7)]=>1 [(1,3),(2,8),(4,10),(5,9),(6,7)]=>1 [(1,4),(2,8),(3,10),(5,9),(6,7)]=>2 [(1,5),(2,8),(3,10),(4,9),(6,7)]=>1 [(1,6),(2,8),(3,10),(4,9),(5,7)]=>2 [(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)]=>2 [(1,10),(2,7),(3,9),(4,8),(5,6)]=>1 [(1,10),(2,8),(3,9),(4,7),(5,6)]=>1 [(1,9),(2,8),(3,10),(4,7),(5,6)]=>1 [(1,8),(2,9),(3,10),(4,7),(5,6)]=>1 [(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)]=>1 [(1,3),(2,9),(4,10),(5,8),(6,7)]=>1 [(1,2),(3,9),(4,10),(5,8),(6,7)]=>1 [(1,2),(3,10),(4,9),(5,8),(6,7)]=>0 [(1,3),(2,10),(4,9),(5,8),(6,7)]=>1 [(1,4),(2,10),(3,9),(5,8),(6,7)]=>1 [(1,5),(2,10),(3,9),(4,8),(6,7)]=>1 [(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)]=>1 [(1,9),(2,10),(3,8),(4,7),(5,6)]=>1 [(1,10),(2,9),(3,8),(4,7),(5,6)]=>0
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Description
The rank of the skew-symmetric form which is non-zero on crossing arcs of a perfect matching.
Two pairs $(a,b)$ and $(c,d)$ (with $a < b$ and $c < d$) in a perfect matching cross if and only if $a < c < b < d$ or $c < a < d < b$. Define a skew symmetric matrix $M$ whose rows and columns are indexed by the pairs of the matching, with
$$ M_{(a,b),(c,d)} = \begin{cases} 1 &\text{if \(a < c < b < d\)}\\ -1 &\text{if \(c < a < d < b\)}\\ 0 &\text{otherwise} \end{cases} $$
The rank of this matrix is always even. The present statistic is half of the matrix' rank.
References
[1] Helfgott, H. A. Permutations, skew-symmetric forms and degeneracy MathOverflow:336232
Code
def statistic(matching):
    def is_crossing(A, B):
        a, b = A
        c, d = B
        if a < c < b < d:
            return 1
        if c < a < d < b:
            return -1
        return 0
    arcs = sorted(matching.arcs())    
    m = matrix([[is_crossing(A, B) for A in arcs] for B in arcs])
    return m.rank()//2
Created
Jul 17, 2019 at 00:46 by Martin Rubey
Updated
Jul 17, 2019 at 00:46 by Martin Rubey