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Identifier
Values
=>
Cc0012;cc-rep
[(1,2)]=>1 [(1,2),(3,4)]=>1 [(1,3),(2,4)]=>1 [(1,4),(2,3)]=>2 [(1,2),(3,4),(5,6)]=>2 [(1,3),(2,4),(5,6)]=>2 [(1,4),(2,3),(5,6)]=>2 [(1,5),(2,3),(4,6)]=>1 [(1,6),(2,3),(4,5)]=>3 [(1,6),(2,4),(3,5)]=>3 [(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)]=>1 [(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)]=>3 [(1,2),(3,4),(5,6),(7,8)]=>2 [(1,3),(2,4),(5,6),(7,8)]=>2 [(1,4),(2,3),(5,6),(7,8)]=>2 [(1,5),(2,3),(4,6),(7,8)]=>2 [(1,6),(2,3),(4,5),(7,8)]=>2 [(1,7),(2,3),(4,5),(6,8)]=>2 [(1,8),(2,3),(4,5),(6,7)]=>4 [(1,8),(2,4),(3,5),(6,7)]=>4 [(1,7),(2,4),(3,5),(6,8)]=>2 [(1,6),(2,4),(3,5),(7,8)]=>2 [(1,5),(2,4),(3,6),(7,8)]=>2 [(1,4),(2,5),(3,6),(7,8)]=>2 [(1,3),(2,5),(4,6),(7,8)]=>2 [(1,2),(3,5),(4,6),(7,8)]=>2 [(1,2),(3,6),(4,5),(7,8)]=>2 [(1,3),(2,6),(4,5),(7,8)]=>2 [(1,4),(2,6),(3,5),(7,8)]=>2 [(1,5),(2,6),(3,4),(7,8)]=>2 [(1,6),(2,5),(3,4),(7,8)]=>2 [(1,7),(2,5),(3,4),(6,8)]=>2 [(1,8),(2,5),(3,4),(6,7)]=>4 [(1,8),(2,6),(3,4),(5,7)]=>4 [(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)]=>3 [(1,4),(2,7),(3,5),(6,8)]=>3 [(1,3),(2,7),(4,5),(6,8)]=>3 [(1,2),(3,7),(4,5),(6,8)]=>3 [(1,2),(3,8),(4,5),(6,7)]=>1 [(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)]=>4 [(1,8),(2,7),(3,5),(4,6)]=>4 [(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)]=>1 [(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)]=>1 [(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)]=>1 [(1,7),(2,6),(3,5),(4,8)]=>1 [(1,8),(2,6),(3,5),(4,7)]=>4 [(1,8),(2,5),(3,6),(4,7)]=>4 [(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)]=>1 [(1,4),(2,6),(3,7),(5,8)]=>1 [(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)]=>3 [(1,3),(2,5),(4,7),(6,8)]=>3 [(1,4),(2,5),(3,7),(6,8)]=>3 [(1,5),(2,4),(3,7),(6,8)]=>3 [(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)]=>4 [(1,8),(2,3),(4,6),(5,7)]=>4 [(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)]=>3 [(1,4),(2,3),(5,7),(6,8)]=>3 [(1,3),(2,4),(5,7),(6,8)]=>3 [(1,2),(3,4),(5,7),(6,8)]=>3 [(1,2),(3,4),(5,8),(6,7)]=>1 [(1,3),(2,4),(5,8),(6,7)]=>1 [(1,4),(2,3),(5,8),(6,7)]=>1 [(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)]=>4 [(1,8),(2,4),(3,7),(5,6)]=>4 [(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)]=>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)]=>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)]=>4 [(1,8),(2,6),(3,7),(4,5)]=>4 [(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)]=>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)]=>1 [(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)]=>4 [(1,2),(3,4),(5,6),(7,8),(9,10)]=>2 [(1,3),(2,4),(5,6),(7,8),(9,10)]=>2 [(1,4),(2,3),(5,6),(7,8),(9,10)]=>2 [(1,5),(2,3),(4,6),(7,8),(9,10)]=>2 [(1,6),(2,3),(4,5),(7,8),(9,10)]=>2 [(1,7),(2,3),(4,5),(6,8),(9,10)]=>2 [(1,8),(2,3),(4,5),(6,7),(9,10)]=>3 [(1,9),(2,3),(4,5),(6,7),(8,10)]=>2 [(1,10),(2,3),(4,5),(6,7),(8,9)]=>5 [(1,10),(2,4),(3,5),(6,7),(8,9)]=>5 [(1,9),(2,4),(3,5),(6,7),(8,10)]=>2 [(1,8),(2,4),(3,5),(6,7),(9,10)]=>3 [(1,7),(2,4),(3,5),(6,8),(9,10)]=>2 [(1,6),(2,4),(3,5),(7,8),(9,10)]=>2 [(1,5),(2,4),(3,6),(7,8),(9,10)]=>2 [(1,4),(2,5),(3,6),(7,8),(9,10)]=>2 [(1,3),(2,5),(4,6),(7,8),(9,10)]=>2 [(1,2),(3,5),(4,6),(7,8),(9,10)]=>2 [(1,2),(3,6),(4,5),(7,8),(9,10)]=>2 [(1,3),(2,6),(4,5),(7,8),(9,10)]=>2 [(1,4),(2,6),(3,5),(7,8),(9,10)]=>2 [(1,5),(2,6),(3,4),(7,8),(9,10)]=>2 [(1,6),(2,5),(3,4),(7,8),(9,10)]=>2 [(1,7),(2,5),(3,4),(6,8),(9,10)]=>2 [(1,8),(2,5),(3,4),(6,7),(9,10)]=>3 [(1,9),(2,5),(3,4),(6,7),(8,10)]=>2 [(1,10),(2,5),(3,4),(6,7),(8,9)]=>5 [(1,10),(2,6),(3,4),(5,7),(8,9)]=>5 [(1,9),(2,6),(3,4),(5,7),(8,10)]=>2 [(1,8),(2,6),(3,4),(5,7),(9,10)]=>3 [(1,7),(2,6),(3,4),(5,8),(9,10)]=>2 [(1,6),(2,7),(3,4),(5,8),(9,10)]=>2 [(1,5),(2,7),(3,4),(6,8),(9,10)]=>2 [(1,4),(2,7),(3,5),(6,8),(9,10)]=>2 [(1,3),(2,7),(4,5),(6,8),(9,10)]=>2 [(1,2),(3,7),(4,5),(6,8),(9,10)]=>2 [(1,2),(3,8),(4,5),(6,7),(9,10)]=>3 [(1,3),(2,8),(4,5),(6,7),(9,10)]=>3 [(1,4),(2,8),(3,5),(6,7),(9,10)]=>3 [(1,5),(2,8),(3,4),(6,7),(9,10)]=>3 [(1,6),(2,8),(3,4),(5,7),(9,10)]=>3 [(1,7),(2,8),(3,4),(5,6),(9,10)]=>2 [(1,8),(2,7),(3,4),(5,6),(9,10)]=>2 [(1,9),(2,7),(3,4),(5,6),(8,10)]=>3 [(1,10),(2,7),(3,4),(5,6),(8,9)]=>5 [(1,10),(2,8),(3,4),(5,6),(7,9)]=>5 [(1,9),(2,8),(3,4),(5,6),(7,10)]=>2 [(1,8),(2,9),(3,4),(5,6),(7,10)]=>2 [(1,7),(2,9),(3,4),(5,6),(8,10)]=>3 [(1,6),(2,9),(3,4),(5,7),(8,10)]=>2 [(1,5),(2,9),(3,4),(6,7),(8,10)]=>2 [(1,4),(2,9),(3,5),(6,7),(8,10)]=>2 [(1,3),(2,9),(4,5),(6,7),(8,10)]=>2 [(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)]=>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)]=>5 [(1,10),(2,9),(3,5),(4,6),(7,8)]=>5 [(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)]=>1 [(1,6),(2,10),(3,5),(4,7),(8,9)]=>1 [(1,5),(2,10),(3,6),(4,7),(8,9)]=>1 [(1,4),(2,10),(3,6),(5,7),(8,9)]=>1 [(1,3),(2,10),(4,6),(5,7),(8,9)]=>1 [(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)]=>3 [(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)]=>5 [(1,10),(2,7),(3,5),(4,6),(8,9)]=>5 [(1,9),(2,7),(3,5),(4,6),(8,10)]=>3 [(1,8),(2,7),(3,5),(4,6),(9,10)]=>2 [(1,7),(2,8),(3,5),(4,6),(9,10)]=>2 [(1,6),(2,8),(3,5),(4,7),(9,10)]=>3 [(1,5),(2,8),(3,6),(4,7),(9,10)]=>3 [(1,4),(2,8),(3,6),(5,7),(9,10)]=>3 [(1,3),(2,8),(4,6),(5,7),(9,10)]=>3 [(1,2),(3,8),(4,6),(5,7),(9,10)]=>3 [(1,2),(3,7),(4,6),(5,8),(9,10)]=>2 [(1,3),(2,7),(4,6),(5,8),(9,10)]=>2 [(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)]=>2 [(1,7),(2,6),(3,5),(4,8),(9,10)]=>2 [(1,8),(2,6),(3,5),(4,7),(9,10)]=>3 [(1,9),(2,6),(3,5),(4,7),(8,10)]=>2 [(1,10),(2,6),(3,5),(4,7),(8,9)]=>5 [(1,10),(2,5),(3,6),(4,7),(8,9)]=>5 [(1,9),(2,5),(3,6),(4,7),(8,10)]=>2 [(1,8),(2,5),(3,6),(4,7),(9,10)]=>3 [(1,7),(2,5),(3,6),(4,8),(9,10)]=>2 [(1,6),(2,5),(3,7),(4,8),(9,10)]=>3 [(1,5),(2,6),(3,7),(4,8),(9,10)]=>3 [(1,4),(2,6),(3,7),(5,8),(9,10)]=>3 [(1,3),(2,6),(4,7),(5,8),(9,10)]=>3 [(1,2),(3,6),(4,7),(5,8),(9,10)]=>3 [(1,2),(3,5),(4,7),(6,8),(9,10)]=>3 [(1,3),(2,5),(4,7),(6,8),(9,10)]=>3 [(1,4),(2,5),(3,7),(6,8),(9,10)]=>3 [(1,5),(2,4),(3,7),(6,8),(9,10)]=>3 [(1,6),(2,4),(3,7),(5,8),(9,10)]=>3 [(1,7),(2,4),(3,6),(5,8),(9,10)]=>2 [(1,8),(2,4),(3,6),(5,7),(9,10)]=>3 [(1,9),(2,4),(3,6),(5,7),(8,10)]=>2 [(1,10),(2,4),(3,6),(5,7),(8,9)]=>5 [(1,10),(2,3),(4,6),(5,7),(8,9)]=>5 [(1,9),(2,3),(4,6),(5,7),(8,10)]=>2 [(1,8),(2,3),(4,6),(5,7),(9,10)]=>3 [(1,7),(2,3),(4,6),(5,8),(9,10)]=>2 [(1,6),(2,3),(4,7),(5,8),(9,10)]=>3 [(1,5),(2,3),(4,7),(6,8),(9,10)]=>3 [(1,4),(2,3),(5,7),(6,8),(9,10)]=>3 [(1,3),(2,4),(5,7),(6,8),(9,10)]=>3 [(1,2),(3,4),(5,7),(6,8),(9,10)]=>3 [(1,2),(3,4),(5,8),(6,7),(9,10)]=>3 [(1,3),(2,4),(5,8),(6,7),(9,10)]=>3 [(1,4),(2,3),(5,8),(6,7),(9,10)]=>3 [(1,5),(2,3),(4,8),(6,7),(9,10)]=>3 [(1,6),(2,3),(4,8),(5,7),(9,10)]=>3 [(1,7),(2,3),(4,8),(5,6),(9,10)]=>2 [(1,8),(2,3),(4,7),(5,6),(9,10)]=>2 [(1,9),(2,3),(4,7),(5,6),(8,10)]=>3 [(1,10),(2,3),(4,7),(5,6),(8,9)]=>5 [(1,10),(2,4),(3,7),(5,6),(8,9)]=>5 [(1,9),(2,4),(3,7),(5,6),(8,10)]=>3 [(1,8),(2,4),(3,7),(5,6),(9,10)]=>2 [(1,7),(2,4),(3,8),(5,6),(9,10)]=>2 [(1,6),(2,4),(3,8),(5,7),(9,10)]=>3 [(1,5),(2,4),(3,8),(6,7),(9,10)]=>3 [(1,4),(2,5),(3,8),(6,7),(9,10)]=>3 [(1,3),(2,5),(4,8),(6,7),(9,10)]=>3 [(1,2),(3,5),(4,8),(6,7),(9,10)]=>3 [(1,2),(3,6),(4,8),(5,7),(9,10)]=>3 [(1,3),(2,6),(4,8),(5,7),(9,10)]=>3 [(1,4),(2,6),(3,8),(5,7),(9,10)]=>3 [(1,5),(2,6),(3,8),(4,7),(9,10)]=>3 [(1,6),(2,5),(3,8),(4,7),(9,10)]=>3 [(1,7),(2,5),(3,8),(4,6),(9,10)]=>2 [(1,8),(2,5),(3,7),(4,6),(9,10)]=>2 [(1,9),(2,5),(3,7),(4,6),(8,10)]=>3 [(1,10),(2,5),(3,7),(4,6),(8,9)]=>5 [(1,10),(2,6),(3,7),(4,5),(8,9)]=>5 [(1,9),(2,6),(3,7),(4,5),(8,10)]=>3 [(1,8),(2,6),(3,7),(4,5),(9,10)]=>2 [(1,7),(2,6),(3,8),(4,5),(9,10)]=>2 [(1,6),(2,7),(3,8),(4,5),(9,10)]=>2 [(1,5),(2,7),(3,8),(4,6),(9,10)]=>2 [(1,4),(2,7),(3,8),(5,6),(9,10)]=>2 [(1,3),(2,7),(4,8),(5,6),(9,10)]=>2 [(1,2),(3,7),(4,8),(5,6),(9,10)]=>2 [(1,2),(3,8),(4,7),(5,6),(9,10)]=>2 [(1,3),(2,8),(4,7),(5,6),(9,10)]=>2 [(1,4),(2,8),(3,7),(5,6),(9,10)]=>2 [(1,5),(2,8),(3,7),(4,6),(9,10)]=>2 [(1,6),(2,8),(3,7),(4,5),(9,10)]=>2 [(1,7),(2,8),(3,6),(4,5),(9,10)]=>2 [(1,8),(2,7),(3,6),(4,5),(9,10)]=>2 [(1,9),(2,7),(3,6),(4,5),(8,10)]=>3 [(1,10),(2,7),(3,6),(4,5),(8,9)]=>5 [(1,10),(2,8),(3,6),(4,5),(7,9)]=>5 [(1,9),(2,8),(3,6),(4,5),(7,10)]=>2 [(1,8),(2,9),(3,6),(4,5),(7,10)]=>2 [(1,7),(2,9),(3,6),(4,5),(8,10)]=>3 [(1,6),(2,9),(3,7),(4,5),(8,10)]=>3 [(1,5),(2,9),(3,7),(4,6),(8,10)]=>3 [(1,4),(2,9),(3,7),(5,6),(8,10)]=>3 [(1,3),(2,9),(4,7),(5,6),(8,10)]=>3 [(1,2),(3,9),(4,7),(5,6),(8,10)]=>3 [(1,2),(3,10),(4,7),(5,6),(8,9)]=>1 [(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)]=>5 [(1,10),(2,9),(3,7),(4,5),(6,8)]=>5 [(1,9),(2,10),(3,7),(4,5),(6,8)]=>1 [(1,8),(2,10),(3,7),(4,5),(6,9)]=>1 [(1,7),(2,10),(3,8),(4,5),(6,9)]=>1 [(1,6),(2,10),(3,8),(4,5),(7,9)]=>1 [(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)]=>1 [(1,2),(3,10),(4,8),(5,6),(7,9)]=>1 [(1,2),(3,9),(4,8),(5,6),(7,10)]=>4 [(1,3),(2,9),(4,8),(5,6),(7,10)]=>4 [(1,4),(2,9),(3,8),(5,6),(7,10)]=>4 [(1,5),(2,9),(3,8),(4,6),(7,10)]=>4 [(1,6),(2,9),(3,8),(4,5),(7,10)]=>4 [(1,7),(2,9),(3,8),(4,5),(6,10)]=>1 [(1,8),(2,9),(3,7),(4,5),(6,10)]=>1 [(1,9),(2,8),(3,7),(4,5),(6,10)]=>1 [(1,10),(2,8),(3,7),(4,5),(6,9)]=>5 [(1,10),(2,7),(3,8),(4,5),(6,9)]=>5 [(1,9),(2,7),(3,8),(4,5),(6,10)]=>1 [(1,8),(2,7),(3,9),(4,5),(6,10)]=>1 [(1,7),(2,8),(3,9),(4,5),(6,10)]=>1 [(1,6),(2,8),(3,9),(4,5),(7,10)]=>4 [(1,5),(2,8),(3,9),(4,6),(7,10)]=>4 [(1,4),(2,8),(3,9),(5,6),(7,10)]=>4 [(1,3),(2,8),(4,9),(5,6),(7,10)]=>4 [(1,2),(3,8),(4,9),(5,6),(7,10)]=>4 [(1,2),(3,7),(4,9),(5,6),(8,10)]=>3 [(1,3),(2,7),(4,9),(5,6),(8,10)]=>3 [(1,4),(2,7),(3,9),(5,6),(8,10)]=>3 [(1,5),(2,7),(3,9),(4,6),(8,10)]=>3 [(1,6),(2,7),(3,9),(4,5),(8,10)]=>3 [(1,7),(2,6),(3,9),(4,5),(8,10)]=>3 [(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)]=>5 [(1,10),(2,5),(3,8),(4,6),(7,9)]=>5 [(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)]=>3 [(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)]=>2 [(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)]=>2 [(1,6),(2,4),(3,9),(5,7),(8,10)]=>2 [(1,7),(2,4),(3,9),(5,6),(8,10)]=>3 [(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)]=>5 [(1,10),(2,3),(4,8),(5,6),(7,9)]=>5 [(1,9),(2,3),(4,8),(5,6),(7,10)]=>2 [(1,8),(2,3),(4,9),(5,6),(7,10)]=>2 [(1,7),(2,3),(4,9),(5,6),(8,10)]=>3 [(1,6),(2,3),(4,9),(5,7),(8,10)]=>2 [(1,5),(2,3),(4,9),(6,7),(8,10)]=>2 [(1,4),(2,3),(5,9),(6,7),(8,10)]=>2 [(1,3),(2,4),(5,9),(6,7),(8,10)]=>2 [(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)]=>1 [(1,4),(2,3),(5,10),(6,7),(8,9)]=>1 [(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)]=>5 [(1,10),(2,4),(3,9),(5,6),(7,8)]=>5 [(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)]=>1 [(1,6),(2,4),(3,10),(5,7),(8,9)]=>1 [(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)]=>1 [(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)]=>1 [(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)]=>5 [(1,10),(2,6),(3,9),(4,5),(7,8)]=>5 [(1,9),(2,6),(3,10),(4,5),(7,8)]=>1 [(1,8),(2,6),(3,10),(4,5),(7,9)]=>1 [(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)]=>1 [(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)]=>1 [(1,5),(2,8),(3,10),(4,6),(7,9)]=>1 [(1,6),(2,8),(3,10),(4,5),(7,9)]=>1 [(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)]=>1 [(1,10),(2,7),(3,9),(4,5),(6,8)]=>5 [(1,10),(2,8),(3,9),(4,5),(6,7)]=>5 [(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)]=>1 [(1,6),(2,9),(3,10),(4,5),(7,8)]=>1 [(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)]=>1 [(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)]=>5 [(1,10),(2,9),(3,8),(4,6),(5,7)]=>5 [(1,9),(2,10),(3,8),(4,6),(5,7)]=>1 [(1,8),(2,10),(3,9),(4,6),(5,7)]=>1 [(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)]=>1 [(1,2),(3,10),(4,9),(5,7),(6,8)]=>1 [(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)]=>1 [(1,9),(2,8),(3,10),(4,6),(5,7)]=>1 [(1,10),(2,8),(3,9),(4,6),(5,7)]=>5 [(1,10),(2,7),(3,9),(4,6),(5,8)]=>5 [(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)]=>1 [(1,7),(2,6),(3,10),(4,8),(5,9)]=>1 [(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)]=>5 [(1,10),(2,5),(3,9),(4,7),(6,8)]=>5 [(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)]=>1 [(1,3),(2,5),(4,10),(6,8),(7,9)]=>1 [(1,4),(2,5),(3,10),(6,8),(7,9)]=>1 [(1,5),(2,4),(3,10),(6,8),(7,9)]=>1 [(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)]=>5 [(1,10),(2,3),(4,9),(5,7),(6,8)]=>5 [(1,9),(2,3),(4,10),(5,7),(6,8)]=>1 [(1,8),(2,3),(4,10),(5,7),(6,9)]=>1 [(1,7),(2,3),(4,10),(5,8),(6,9)]=>1 [(1,6),(2,3),(4,10),(5,8),(7,9)]=>1 [(1,5),(2,3),(4,10),(6,8),(7,9)]=>1 [(1,4),(2,3),(5,10),(6,8),(7,9)]=>1 [(1,3),(2,4),(5,10),(6,8),(7,9)]=>1 [(1,2),(3,4),(5,10),(6,8),(7,9)]=>1 [(1,2),(3,4),(5,9),(6,8),(7,10)]=>4 [(1,3),(2,4),(5,9),(6,8),(7,10)]=>4 [(1,4),(2,3),(5,9),(6,8),(7,10)]=>4 [(1,5),(2,3),(4,9),(6,8),(7,10)]=>4 [(1,6),(2,3),(4,9),(5,8),(7,10)]=>4 [(1,7),(2,3),(4,9),(5,8),(6,10)]=>1 [(1,8),(2,3),(4,9),(5,7),(6,10)]=>1 [(1,9),(2,3),(4,8),(5,7),(6,10)]=>1 [(1,10),(2,3),(4,8),(5,7),(6,9)]=>5 [(1,10),(2,4),(3,8),(5,7),(6,9)]=>5 [(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)]=>1 [(1,6),(2,4),(3,9),(5,8),(7,10)]=>4 [(1,5),(2,4),(3,9),(6,8),(7,10)]=>4 [(1,4),(2,5),(3,9),(6,8),(7,10)]=>4 [(1,3),(2,5),(4,9),(6,8),(7,10)]=>4 [(1,2),(3,5),(4,9),(6,8),(7,10)]=>4 [(1,2),(3,6),(4,9),(5,8),(7,10)]=>4 [(1,3),(2,6),(4,9),(5,8),(7,10)]=>4 [(1,4),(2,6),(3,9),(5,8),(7,10)]=>4 [(1,5),(2,6),(3,9),(4,8),(7,10)]=>4 [(1,6),(2,5),(3,9),(4,8),(7,10)]=>4 [(1,7),(2,5),(3,9),(4,8),(6,10)]=>1 [(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)]=>5 [(1,10),(2,6),(3,8),(4,7),(5,9)]=>5 [(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)]=>1 [(1,6),(2,7),(3,9),(4,8),(5,10)]=>1 [(1,5),(2,7),(3,9),(4,8),(6,10)]=>1 [(1,4),(2,7),(3,9),(5,8),(6,10)]=>1 [(1,3),(2,7),(4,9),(5,8),(6,10)]=>1 [(1,2),(3,7),(4,9),(5,8),(6,10)]=>1 [(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)]=>1 [(1,5),(2,8),(3,9),(4,7),(6,10)]=>1 [(1,6),(2,8),(3,9),(4,7),(5,10)]=>1 [(1,7),(2,8),(3,9),(4,6),(5,10)]=>1 [(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)]=>5 [(1,10),(2,8),(3,7),(4,6),(5,9)]=>5 [(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)]=>1 [(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)]=>1 [(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)]=>1 [(1,3),(2,10),(4,8),(5,7),(6,9)]=>1 [(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)]=>5 [(1,10),(2,9),(3,6),(4,7),(5,8)]=>5 [(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)]=>1 [(1,6),(2,10),(3,7),(4,8),(5,9)]=>1 [(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)]=>1 [(1,2),(3,10),(4,7),(5,8),(6,9)]=>1 [(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)]=>1 [(1,5),(2,9),(3,7),(4,8),(6,10)]=>1 [(1,6),(2,9),(3,7),(4,8),(5,10)]=>1 [(1,7),(2,9),(3,6),(4,8),(5,10)]=>1 [(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)]=>5 [(1,10),(2,7),(3,6),(4,8),(5,9)]=>5 [(1,9),(2,7),(3,6),(4,8),(5,10)]=>1 [(1,8),(2,7),(3,6),(4,9),(5,10)]=>1 [(1,7),(2,8),(3,6),(4,9),(5,10)]=>1 [(1,6),(2,8),(3,7),(4,9),(5,10)]=>1 [(1,5),(2,8),(3,7),(4,9),(6,10)]=>1 [(1,4),(2,8),(3,7),(5,9),(6,10)]=>1 [(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)]=>1 [(1,3),(2,7),(4,8),(5,9),(6,10)]=>1 [(1,4),(2,7),(3,8),(5,9),(6,10)]=>1 [(1,5),(2,7),(3,8),(4,9),(6,10)]=>1 [(1,6),(2,7),(3,8),(4,9),(5,10)]=>1 [(1,7),(2,6),(3,8),(4,9),(5,10)]=>1 [(1,8),(2,6),(3,7),(4,9),(5,10)]=>1 [(1,9),(2,6),(3,7),(4,8),(5,10)]=>1 [(1,10),(2,6),(3,7),(4,8),(5,9)]=>5 [(1,10),(2,5),(3,7),(4,8),(6,9)]=>5 [(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)]=>1 [(1,6),(2,5),(3,8),(4,9),(7,10)]=>4 [(1,5),(2,6),(3,8),(4,9),(7,10)]=>4 [(1,4),(2,6),(3,8),(5,9),(7,10)]=>4 [(1,3),(2,6),(4,8),(5,9),(7,10)]=>4 [(1,2),(3,6),(4,8),(5,9),(7,10)]=>4 [(1,2),(3,5),(4,8),(6,9),(7,10)]=>4 [(1,3),(2,5),(4,8),(6,9),(7,10)]=>4 [(1,4),(2,5),(3,8),(6,9),(7,10)]=>4 [(1,5),(2,4),(3,8),(6,9),(7,10)]=>4 [(1,6),(2,4),(3,8),(5,9),(7,10)]=>4 [(1,7),(2,4),(3,8),(5,9),(6,10)]=>1 [(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)]=>5 [(1,10),(2,3),(4,7),(5,8),(6,9)]=>5 [(1,9),(2,3),(4,7),(5,8),(6,10)]=>1 [(1,8),(2,3),(4,7),(5,9),(6,10)]=>1 [(1,7),(2,3),(4,8),(5,9),(6,10)]=>1 [(1,6),(2,3),(4,8),(5,9),(7,10)]=>4 [(1,5),(2,3),(4,8),(6,9),(7,10)]=>4 [(1,4),(2,3),(5,8),(6,9),(7,10)]=>4 [(1,3),(2,4),(5,8),(6,9),(7,10)]=>4 [(1,2),(3,4),(5,8),(6,9),(7,10)]=>4 [(1,2),(3,4),(5,7),(6,9),(8,10)]=>2 [(1,3),(2,4),(5,7),(6,9),(8,10)]=>2 [(1,4),(2,3),(5,7),(6,9),(8,10)]=>2 [(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)]=>3 [(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)]=>5 [(1,10),(2,4),(3,6),(5,8),(7,9)]=>5 [(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)]=>3 [(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)]=>3 [(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)]=>5 [(1,10),(2,6),(3,5),(4,8),(7,9)]=>5 [(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)]=>3 [(1,6),(2,7),(3,5),(4,9),(8,10)]=>3 [(1,5),(2,7),(3,6),(4,9),(8,10)]=>3 [(1,4),(2,7),(3,6),(5,9),(8,10)]=>3 [(1,3),(2,7),(4,6),(5,9),(8,10)]=>3 [(1,2),(3,7),(4,6),(5,9),(8,10)]=>3 [(1,2),(3,8),(4,6),(5,9),(7,10)]=>4 [(1,3),(2,8),(4,6),(5,9),(7,10)]=>4 [(1,4),(2,8),(3,6),(5,9),(7,10)]=>4 [(1,5),(2,8),(3,6),(4,9),(7,10)]=>4 [(1,6),(2,8),(3,5),(4,9),(7,10)]=>4 [(1,7),(2,8),(3,5),(4,9),(6,10)]=>1 [(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)]=>5 [(1,10),(2,8),(3,5),(4,7),(6,9)]=>5 [(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)]=>1 [(1,6),(2,9),(3,5),(4,8),(7,10)]=>4 [(1,5),(2,9),(3,6),(4,8),(7,10)]=>4 [(1,4),(2,9),(3,6),(5,8),(7,10)]=>4 [(1,3),(2,9),(4,6),(5,8),(7,10)]=>4 [(1,2),(3,9),(4,6),(5,8),(7,10)]=>4 [(1,2),(3,10),(4,6),(5,8),(7,9)]=>1 [(1,3),(2,10),(4,6),(5,8),(7,9)]=>1 [(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)]=>5 [(1,10),(2,9),(3,4),(5,7),(6,8)]=>5 [(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)]=>1 [(1,4),(2,10),(3,5),(6,8),(7,9)]=>1 [(1,3),(2,10),(4,5),(6,8),(7,9)]=>1 [(1,2),(3,10),(4,5),(6,8),(7,9)]=>1 [(1,2),(3,9),(4,5),(6,8),(7,10)]=>4 [(1,3),(2,9),(4,5),(6,8),(7,10)]=>4 [(1,4),(2,9),(3,5),(6,8),(7,10)]=>4 [(1,5),(2,9),(3,4),(6,8),(7,10)]=>4 [(1,6),(2,9),(3,4),(5,8),(7,10)]=>4 [(1,7),(2,9),(3,4),(5,8),(6,10)]=>1 [(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)]=>5 [(1,10),(2,7),(3,4),(5,8),(6,9)]=>5 [(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)]=>1 [(1,6),(2,8),(3,4),(5,9),(7,10)]=>4 [(1,5),(2,8),(3,4),(6,9),(7,10)]=>4 [(1,4),(2,8),(3,5),(6,9),(7,10)]=>4 [(1,3),(2,8),(4,5),(6,9),(7,10)]=>4 [(1,2),(3,8),(4,5),(6,9),(7,10)]=>4 [(1,2),(3,7),(4,5),(6,9),(8,10)]=>3 [(1,3),(2,7),(4,5),(6,9),(8,10)]=>3 [(1,4),(2,7),(3,5),(6,9),(8,10)]=>3 [(1,5),(2,7),(3,4),(6,9),(8,10)]=>3 [(1,6),(2,7),(3,4),(5,9),(8,10)]=>3 [(1,7),(2,6),(3,4),(5,9),(8,10)]=>3 [(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)]=>5 [(1,10),(2,5),(3,4),(6,8),(7,9)]=>5 [(1,9),(2,5),(3,4),(6,8),(7,10)]=>2 [(1,8),(2,5),(3,4),(6,9),(7,10)]=>2 [(1,7),(2,5),(3,4),(6,9),(8,10)]=>3 [(1,6),(2,5),(3,4),(7,9),(8,10)]=>2 [(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)]=>2 [(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)]=>3 [(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)]=>5 [(1,10),(2,3),(4,5),(6,8),(7,9)]=>5 [(1,9),(2,3),(4,5),(6,8),(7,10)]=>2 [(1,8),(2,3),(4,5),(6,9),(7,10)]=>2 [(1,7),(2,3),(4,5),(6,9),(8,10)]=>3 [(1,6),(2,3),(4,5),(7,9),(8,10)]=>2 [(1,5),(2,3),(4,6),(7,9),(8,10)]=>2 [(1,4),(2,3),(5,6),(7,9),(8,10)]=>2 [(1,3),(2,4),(5,6),(7,9),(8,10)]=>2 [(1,2),(3,4),(5,6),(7,9),(8,10)]=>2 [(1,2),(3,4),(5,6),(7,10),(8,9)]=>4 [(1,3),(2,4),(5,6),(7,10),(8,9)]=>4 [(1,4),(2,3),(5,6),(7,10),(8,9)]=>4 [(1,5),(2,3),(4,6),(7,10),(8,9)]=>4 [(1,6),(2,3),(4,5),(7,10),(8,9)]=>4 [(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)]=>5 [(1,10),(2,4),(3,5),(6,9),(7,8)]=>5 [(1,9),(2,4),(3,5),(6,10),(7,8)]=>1 [(1,8),(2,4),(3,5),(6,10),(7,9)]=>1 [(1,7),(2,4),(3,5),(6,10),(8,9)]=>1 [(1,6),(2,4),(3,5),(7,10),(8,9)]=>4 [(1,5),(2,4),(3,6),(7,10),(8,9)]=>4 [(1,4),(2,5),(3,6),(7,10),(8,9)]=>4 [(1,3),(2,5),(4,6),(7,10),(8,9)]=>4 [(1,2),(3,5),(4,6),(7,10),(8,9)]=>4 [(1,2),(3,6),(4,5),(7,10),(8,9)]=>4 [(1,3),(2,6),(4,5),(7,10),(8,9)]=>4 [(1,4),(2,6),(3,5),(7,10),(8,9)]=>4 [(1,5),(2,6),(3,4),(7,10),(8,9)]=>4 [(1,6),(2,5),(3,4),(7,10),(8,9)]=>4 [(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)]=>5 [(1,10),(2,6),(3,4),(5,9),(7,8)]=>5 [(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)]=>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)]=>1 [(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)]=>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)]=>5 [(1,10),(2,8),(3,4),(5,9),(6,7)]=>5 [(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)]=>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)]=>1 [(1,2),(3,9),(4,5),(6,10),(7,8)]=>1 [(1,2),(3,10),(4,5),(6,9),(7,8)]=>1 [(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)]=>5 [(1,10),(2,9),(3,5),(4,8),(6,7)]=>5 [(1,9),(2,10),(3,5),(4,8),(6,7)]=>1 [(1,8),(2,10),(3,5),(4,9),(6,7)]=>1 [(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)]=>1 [(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)]=>1 [(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)]=>1 [(1,7),(2,9),(3,5),(4,10),(6,8)]=>1 [(1,8),(2,9),(3,5),(4,10),(6,7)]=>1 [(1,9),(2,8),(3,5),(4,10),(6,7)]=>1 [(1,10),(2,8),(3,5),(4,9),(6,7)]=>5 [(1,10),(2,7),(3,5),(4,9),(6,8)]=>5 [(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)]=>1 [(1,4),(2,8),(3,6),(5,10),(7,9)]=>1 [(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)]=>1 [(1,3),(2,7),(4,6),(5,10),(8,9)]=>1 [(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)]=>1 [(1,7),(2,6),(3,5),(4,10),(8,9)]=>1 [(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)]=>5 [(1,10),(2,5),(3,6),(4,9),(7,8)]=>5 [(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)]=>1 [(1,6),(2,5),(3,7),(4,10),(8,9)]=>1 [(1,5),(2,6),(3,7),(4,10),(8,9)]=>1 [(1,4),(2,6),(3,7),(5,10),(8,9)]=>1 [(1,3),(2,6),(4,7),(5,10),(8,9)]=>1 [(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)]=>1 [(1,4),(2,5),(3,7),(6,10),(8,9)]=>1 [(1,5),(2,4),(3,7),(6,10),(8,9)]=>1 [(1,6),(2,4),(3,7),(5,10),(8,9)]=>1 [(1,7),(2,4),(3,6),(5,10),(8,9)]=>1 [(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)]=>5 [(1,10),(2,3),(4,6),(5,9),(7,8)]=>5 [(1,9),(2,3),(4,6),(5,10),(7,8)]=>1 [(1,8),(2,3),(4,6),(5,10),(7,9)]=>1 [(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)]=>1 [(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)]=>1 [(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)]=>1 [(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)]=>1 [(1,10),(2,3),(4,7),(5,9),(6,8)]=>5 [(1,10),(2,4),(3,7),(5,9),(6,8)]=>5 [(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)]=>1 [(1,5),(2,6),(3,8),(4,10),(7,9)]=>1 [(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)]=>5 [(1,10),(2,6),(3,7),(4,9),(5,8)]=>5 [(1,9),(2,6),(3,7),(4,10),(5,8)]=>1 [(1,8),(2,6),(3,7),(4,10),(5,9)]=>1 [(1,7),(2,6),(3,8),(4,10),(5,9)]=>1 [(1,6),(2,7),(3,8),(4,10),(5,9)]=>1 [(1,5),(2,7),(3,8),(4,10),(6,9)]=>1 [(1,4),(2,7),(3,8),(5,10),(6,9)]=>1 [(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)]=>1 [(1,5),(2,8),(3,7),(4,10),(6,9)]=>1 [(1,6),(2,8),(3,7),(4,10),(5,9)]=>1 [(1,7),(2,8),(3,6),(4,10),(5,9)]=>1 [(1,8),(2,7),(3,6),(4,10),(5,9)]=>1 [(1,9),(2,7),(3,6),(4,10),(5,8)]=>1 [(1,10),(2,7),(3,6),(4,9),(5,8)]=>5 [(1,10),(2,8),(3,6),(4,9),(5,7)]=>5 [(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)]=>1 [(1,6),(2,9),(3,7),(4,10),(5,8)]=>1 [(1,5),(2,9),(3,7),(4,10),(6,8)]=>1 [(1,4),(2,9),(3,7),(5,10),(6,8)]=>1 [(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)]=>1 [(1,3),(2,10),(4,7),(5,9),(6,8)]=>1 [(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)]=>1 [(1,7),(2,10),(3,6),(4,9),(5,8)]=>1 [(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)]=>5 [(1,10),(2,9),(3,7),(4,8),(5,6)]=>5 [(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)]=>1 [(1,4),(2,10),(3,8),(5,9),(6,7)]=>1 [(1,3),(2,10),(4,8),(5,9),(6,7)]=>1 [(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)]=>1 [(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)]=>1 [(1,7),(2,9),(3,8),(4,10),(5,6)]=>1 [(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)]=>5 [(1,10),(2,7),(3,8),(4,9),(5,6)]=>5 [(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)]=>1 [(1,6),(2,8),(3,9),(4,10),(5,7)]=>1 [(1,5),(2,8),(3,9),(4,10),(6,7)]=>1 [(1,4),(2,8),(3,9),(5,10),(6,7)]=>1 [(1,3),(2,8),(4,9),(5,10),(6,7)]=>1 [(1,2),(3,8),(4,9),(5,10),(6,7)]=>1 [(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)]=>1 [(1,5),(2,7),(3,9),(4,10),(6,8)]=>1 [(1,6),(2,7),(3,9),(4,10),(5,8)]=>1 [(1,7),(2,6),(3,9),(4,10),(5,8)]=>1 [(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)]=>5 [(1,10),(2,5),(3,8),(4,9),(6,7)]=>5 [(1,9),(2,5),(3,8),(4,10),(6,7)]=>1 [(1,8),(2,5),(3,9),(4,10),(6,7)]=>1 [(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)]=>1 [(1,4),(2,6),(3,9),(5,10),(7,8)]=>1 [(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)]=>1 [(1,9),(2,4),(3,8),(5,10),(6,7)]=>1 [(1,10),(2,4),(3,8),(5,9),(6,7)]=>5 [(1,10),(2,3),(4,8),(5,9),(6,7)]=>5 [(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)]=>1 [(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)]=>1 [(1,2),(3,4),(5,9),(6,10),(7,8)]=>1 [(1,2),(3,4),(5,10),(6,9),(7,8)]=>1 [(1,3),(2,4),(5,10),(6,9),(7,8)]=>1 [(1,4),(2,3),(5,10),(6,9),(7,8)]=>1 [(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)]=>5 [(1,10),(2,4),(3,9),(5,8),(6,7)]=>5 [(1,9),(2,4),(3,10),(5,8),(6,7)]=>1 [(1,8),(2,4),(3,10),(5,9),(6,7)]=>1 [(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)]=>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)]=>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)]=>1 [(1,9),(2,5),(3,10),(4,8),(6,7)]=>1 [(1,10),(2,5),(3,9),(4,8),(6,7)]=>5 [(1,10),(2,6),(3,9),(4,8),(5,7)]=>5 [(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)]=>1 [(1,6),(2,7),(3,10),(4,9),(5,8)]=>1 [(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)]=>1 [(1,3),(2,8),(4,10),(5,9),(6,7)]=>1 [(1,4),(2,8),(3,10),(5,9),(6,7)]=>1 [(1,5),(2,8),(3,10),(4,9),(6,7)]=>1 [(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)]=>5 [(1,10),(2,8),(3,9),(4,7),(5,6)]=>5 [(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)]=>1 [(1,6),(2,9),(3,10),(4,8),(5,7)]=>1 [(1,5),(2,9),(3,10),(4,8),(6,7)]=>1 [(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)]=>1 [(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)]=>5 [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>2 [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>2 [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>3 [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>1 [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>1 [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>4 [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>2 [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>4 [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>1 [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>1 [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>3 [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>1 [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>1 [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>1 [(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)]=>2 [(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]=>3 [(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)]=>2 [(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)]=>2 [(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)]=>4 [(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)]=>2 [(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)]=>3 [(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)]=>2 [(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)]=>2 [(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)]=>3 [(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)]=>4 [(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)]=>2 [(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)]=>5 [(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)]=>4 [(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)]=>2 [(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)]=>3 [(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)]=>2 [(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)]=>2 [(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)]=>4 [(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)]=>2 [(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)]=>3 [(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)]=>2 [(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)]=>2 [(1,2),(3,4),(5,6),(7,9),(8,12),(10,11)]=>5 [(1,2),(3,4),(5,6),(7,10),(8,12),(9,11)]=>5 [(1,2),(3,4),(5,6),(7,11),(8,9),(10,12)]=>2 [(1,2),(3,4),(5,6),(7,11),(8,10),(9,12)]=>2 [(1,2),(3,4),(5,6),(7,11),(8,12),(9,10)]=>5 [(1,2),(3,4),(5,6),(7,12),(8,10),(9,11)]=>1 [(1,2),(3,4),(5,7),(6,8),(9,12),(10,11)]=>2 [(1,2),(3,4),(5,7),(6,9),(8,12),(10,11)]=>5 [(1,2),(3,4),(5,7),(6,10),(8,9),(11,12)]=>3 [(1,2),(3,4),(5,7),(6,10),(8,12),(9,11)]=>5 [(1,2),(3,4),(5,7),(6,11),(8,9),(10,12)]=>2 [(1,2),(3,4),(5,7),(6,11),(8,10),(9,12)]=>2 [(1,2),(3,4),(5,7),(6,11),(8,12),(9,10)]=>5 [(1,2),(3,4),(5,7),(6,12),(8,9),(10,11)]=>1 [(1,2),(3,4),(5,7),(6,12),(8,10),(9,11)]=>1 [(1,2),(3,4),(5,7),(6,12),(8,11),(9,10)]=>1 [(1,2),(3,4),(5,8),(6,7),(9,11),(10,12)]=>4 [(1,2),(3,4),(5,8),(6,9),(7,12),(10,11)]=>1 [(1,2),(3,4),(5,8),(6,10),(7,12),(9,11)]=>1 [(1,2),(3,4),(5,8),(6,10),(7,9),(11,12)]=>3 [(1,2),(3,4),(5,8),(6,11),(7,12),(9,10)]=>1 [(1,2),(3,4),(5,8),(6,11),(7,10),(9,12)]=>2 [(1,2),(3,4),(5,8),(6,11),(7,9),(10,12)]=>4 [(1,2),(3,4),(5,8),(6,12),(7,11),(9,10)]=>1 [(1,2),(3,4),(5,8),(6,12),(7,10),(9,11)]=>1 [(1,2),(3,4),(5,8),(6,12),(7,9),(10,11)]=>1 [(1,2),(3,4),(5,9),(6,7),(8,10),(11,12)]=>2 [(1,2),(3,4),(5,9),(6,7),(8,11),(10,12)]=>3 [(1,2),(3,4),(5,9),(6,7),(8,12),(10,11)]=>5 [(1,2),(3,4),(5,9),(6,8),(7,12),(10,11)]=>1 [(1,2),(3,4),(5,9),(6,8),(7,11),(10,12)]=>3 [(1,2),(3,4),(5,9),(6,8),(7,10),(11,12)]=>4 [(1,2),(3,4),(5,9),(6,10),(7,12),(8,11)]=>1 [(1,2),(3,4),(5,9),(6,10),(7,8),(11,12)]=>4 [(1,2),(3,4),(5,9),(6,11),(7,12),(8,10)]=>1 [(1,2),(3,4),(5,9),(6,11),(7,10),(8,12)]=>5 [(1,2),(3,4),(5,9),(6,11),(7,8),(10,12)]=>3 [(1,2),(3,4),(5,9),(6,12),(7,11),(8,10)]=>1 [(1,2),(3,4),(5,9),(6,12),(7,10),(8,11)]=>1 [(1,2),(3,4),(5,9),(6,12),(7,8),(10,11)]=>1 [(1,2),(3,4),(5,10),(6,7),(8,11),(9,12)]=>2 [(1,2),(3,4),(5,10),(6,7),(8,12),(9,11)]=>5 [(1,2),(3,4),(5,10),(6,8),(7,12),(9,11)]=>1 [(1,2),(3,4),(5,10),(6,8),(7,11),(9,12)]=>2 [(1,2),(3,4),(5,10),(6,8),(7,9),(11,12)]=>3 [(1,2),(3,4),(5,10),(6,9),(7,12),(8,11)]=>1 [(1,2),(3,4),(5,10),(6,9),(7,11),(8,12)]=>5 [(1,2),(3,4),(5,10),(6,11),(7,12),(8,9)]=>1 [(1,2),(3,4),(5,10),(6,11),(7,9),(8,12)]=>5 [(1,2),(3,4),(5,10),(6,11),(7,8),(9,12)]=>2 [(1,2),(3,4),(5,10),(6,12),(7,11),(8,9)]=>1 [(1,2),(3,4),(5,10),(6,12),(7,9),(8,11)]=>1 [(1,2),(3,4),(5,10),(6,12),(7,8),(9,11)]=>1 [(1,2),(3,4),(5,11),(6,7),(8,9),(10,12)]=>2 [(1,2),(3,4),(5,11),(6,7),(8,10),(9,12)]=>2 [(1,2),(3,4),(5,11),(6,7),(8,12),(9,10)]=>5 [(1,2),(3,4),(5,11),(6,8),(7,12),(9,10)]=>1 [(1,2),(3,4),(5,11),(6,8),(7,10),(9,12)]=>2 [(1,2),(3,4),(5,11),(6,8),(7,9),(10,12)]=>4 [(1,2),(3,4),(5,11),(6,9),(7,12),(8,10)]=>1 [(1,2),(3,4),(5,11),(6,9),(7,10),(8,12)]=>5 [(1,2),(3,4),(5,11),(6,9),(7,8),(10,12)]=>3 [(1,2),(3,4),(5,11),(6,10),(7,12),(8,9)]=>1 [(1,2),(3,4),(5,11),(6,10),(7,9),(8,12)]=>5 [(1,2),(3,4),(5,11),(6,10),(7,8),(9,12)]=>2 [(1,2),(3,4),(5,11),(6,12),(7,10),(8,9)]=>1 [(1,2),(3,4),(5,11),(6,12),(7,9),(8,10)]=>1 [(1,2),(3,4),(5,11),(6,12),(7,8),(9,10)]=>1 [(1,2),(3,4),(5,12),(6,7),(8,10),(9,11)]=>1 [(1,2),(3,4),(5,12),(6,8),(7,11),(9,10)]=>1 [(1,2),(3,4),(5,12),(6,8),(7,10),(9,11)]=>1 [(1,2),(3,4),(5,12),(6,8),(7,9),(10,11)]=>1 [(1,2),(3,4),(5,12),(6,9),(7,11),(8,10)]=>1 [(1,2),(3,4),(5,12),(6,9),(7,10),(8,11)]=>1 [(1,2),(3,4),(5,12),(6,10),(7,11),(8,9)]=>1 [(1,2),(3,4),(5,12),(6,10),(7,9),(8,11)]=>1 [(1,2),(3,4),(5,12),(6,10),(7,8),(9,11)]=>1 [(1,2),(3,4),(5,12),(6,11),(7,9),(8,10)]=>1 [(1,2),(3,5),(4,6),(7,8),(9,12),(10,11)]=>2 [(1,2),(3,5),(4,6),(7,9),(8,12),(10,11)]=>5 [(1,2),(3,5),(4,6),(7,10),(8,9),(11,12)]=>3 [(1,2),(3,5),(4,6),(7,10),(8,12),(9,11)]=>5 [(1,2),(3,5),(4,6),(7,11),(8,9),(10,12)]=>2 [(1,2),(3,5),(4,6),(7,11),(8,10),(9,12)]=>2 [(1,2),(3,5),(4,6),(7,11),(8,12),(9,10)]=>5 [(1,2),(3,5),(4,6),(7,12),(8,9),(10,11)]=>1 [(1,2),(3,5),(4,6),(7,12),(8,10),(9,11)]=>1 [(1,2),(3,5),(4,6),(7,12),(8,11),(9,10)]=>1 [(1,2),(3,5),(4,7),(6,8),(9,12),(10,11)]=>2 [(1,2),(3,5),(4,7),(6,9),(8,12),(10,11)]=>5 [(1,2),(3,5),(4,7),(6,10),(8,9),(11,12)]=>3 [(1,2),(3,5),(4,7),(6,10),(8,12),(9,11)]=>5 [(1,2),(3,5),(4,7),(6,11),(8,9),(10,12)]=>2 [(1,2),(3,5),(4,7),(6,11),(8,10),(9,12)]=>2
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Description
The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching.
The bijection between perfect matchings of $\{1,\dots,2n\}$ and trees with $n+1$ leaves is described in Example 5.2.6 of [1].
The number of trees having precisely $j$ leaves in the subtree not containing $1$, computed in [2], is
$$ \binom{n}{j}(2j-3)!!(2n-2j-1)!! $$
References
[1] Stanley, R. P. Enumerative combinatorics. Vol. 2 MathSciNet:1676282
[2] Dale, M. R. T., Moon, J. W. The permuted analogues of three Catalan sets MathSciNet:1209991
Code
def statistic(m):
    T = matching_to_tree(m)
    if 1 in T[0].leaf_labels():
        return len(T[1].leaf_labels())
    return len(T[0].leaf_labels())

def matching_to_tree(m):
    """
    INPUT:

    - m, a PerfectMatching on {1,...,2n}.

    OUTPUT:

    a decreasingly labelled, unordered full binary tree with n+1 leaves.

    EXAMPLES::

        sage: m = PerfectMatching([(1,4),(2,9),(3,10),(5,7),(6,8),(11,12)])
        sage: ascii_art(matching_to_tree(m))
    """
    # the children of the smallest label are the largest remaining
    # element and its partner
    trees = [LabelledRootedTree([LabelledRootedTree([], label=i),
                                 LabelledRootedTree([], label=j)]) for i, j in m]
    max_label = m.size()//2+1 # last labelled node

    while len(trees) > 1:
        max_label += 1
        # find tree with smallest child and both children smaller than max_label
        A = sorted([T for T in trees if max(T[0].label(), T[1].label()) < max_label],
                   key = lambda T: min(T[0].label(), T[1].label()))[0]
        trees.remove(A)
        # give it's root node the new label
        A = LabelledRootedTree(A, label=max_label)
        # find tree with child having label max_label
        B = (T for T in trees
             if T[0].label() == max_label or T[1].label() == max_label).next()
        trees.remove(B)
        # replace B with [B[0], A] or [B[1], A]
        if B[0].label() == max_label:
            C = LabelledRootedTree([A, B[1]])
        else:
            C = LabelledRootedTree([A, B[0]])

        trees.append(C)

    return trees[0]
Created
Nov 09, 2017 at 21:36 by Martin Rubey
Updated
Nov 09, 2017 at 21:36 by Martin Rubey