Identifier
- St000042: Perfect matchings ⟶ ℤ
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)]=>2
[(1,4),(2,5),(3,6)]=>3
[(1,3),(2,5),(4,6)]=>2
[(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)]=>2
[(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)]=>2
[(1,4),(2,5),(3,6),(7,8)]=>3
[(1,3),(2,5),(4,6),(7,8)]=>2
[(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)]=>2
[(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)]=>2
[(1,6),(2,7),(3,4),(5,8)]=>3
[(1,5),(2,7),(3,4),(6,8)]=>2
[(1,4),(2,7),(3,5),(6,8)]=>3
[(1,3),(2,7),(4,5),(6,8)]=>2
[(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)]=>2
[(1,5),(2,8),(3,4),(6,7)]=>1
[(1,6),(2,8),(3,4),(5,7)]=>2
[(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)]=>3
[(1,5),(2,8),(3,6),(4,7)]=>4
[(1,4),(2,8),(3,6),(5,7)]=>3
[(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)]=>2
[(1,3),(2,7),(4,6),(5,8)]=>3
[(1,4),(2,7),(3,6),(5,8)]=>4
[(1,5),(2,7),(3,6),(4,8)]=>5
[(1,6),(2,7),(3,5),(4,8)]=>4
[(1,7),(2,6),(3,5),(4,8)]=>3
[(1,8),(2,6),(3,5),(4,7)]=>2
[(1,8),(2,5),(3,6),(4,7)]=>3
[(1,7),(2,5),(3,6),(4,8)]=>4
[(1,6),(2,5),(3,7),(4,8)]=>5
[(1,5),(2,6),(3,7),(4,8)]=>6
[(1,4),(2,6),(3,7),(5,8)]=>5
[(1,3),(2,6),(4,7),(5,8)]=>4
[(1,2),(3,6),(4,7),(5,8)]=>3
[(1,2),(3,5),(4,7),(6,8)]=>2
[(1,3),(2,5),(4,7),(6,8)]=>3
[(1,4),(2,5),(3,7),(6,8)]=>4
[(1,5),(2,4),(3,7),(6,8)]=>3
[(1,6),(2,4),(3,7),(5,8)]=>4
[(1,7),(2,4),(3,6),(5,8)]=>3
[(1,8),(2,4),(3,6),(5,7)]=>2
[(1,8),(2,3),(4,6),(5,7)]=>1
[(1,7),(2,3),(4,6),(5,8)]=>2
[(1,6),(2,3),(4,7),(5,8)]=>3
[(1,5),(2,3),(4,7),(6,8)]=>2
[(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)]=>2
[(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)]=>2
[(1,6),(2,4),(3,8),(5,7)]=>3
[(1,5),(2,4),(3,8),(6,7)]=>2
[(1,4),(2,5),(3,8),(6,7)]=>3
[(1,3),(2,5),(4,8),(6,7)]=>2
[(1,2),(3,5),(4,8),(6,7)]=>1
[(1,2),(3,6),(4,8),(5,7)]=>2
[(1,3),(2,6),(4,8),(5,7)]=>3
[(1,4),(2,6),(3,8),(5,7)]=>4
[(1,5),(2,6),(3,8),(4,7)]=>5
[(1,6),(2,5),(3,8),(4,7)]=>4
[(1,7),(2,5),(3,8),(4,6)]=>3
[(1,8),(2,5),(3,7),(4,6)]=>2
[(1,8),(2,6),(3,7),(4,5)]=>1
[(1,7),(2,6),(3,8),(4,5)]=>2
[(1,6),(2,7),(3,8),(4,5)]=>3
[(1,5),(2,7),(3,8),(4,6)]=>4
[(1,4),(2,7),(3,8),(5,6)]=>3
[(1,3),(2,7),(4,8),(5,6)]=>2
[(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)]=>2
[(1,5),(2,8),(3,7),(4,6)]=>3
[(1,6),(2,8),(3,7),(4,5)]=>2
[(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)]=>2
[(1,4),(2,5),(3,6),(7,8),(9,10)]=>3
[(1,3),(2,5),(4,6),(7,8),(9,10)]=>2
[(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)]=>2
[(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)]=>2
[(1,6),(2,7),(3,4),(5,8),(9,10)]=>3
[(1,5),(2,7),(3,4),(6,8),(9,10)]=>2
[(1,4),(2,7),(3,5),(6,8),(9,10)]=>3
[(1,3),(2,7),(4,5),(6,8),(9,10)]=>2
[(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)]=>2
[(1,5),(2,8),(3,4),(6,7),(9,10)]=>1
[(1,6),(2,8),(3,4),(5,7),(9,10)]=>2
[(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)]=>2
[(1,8),(2,9),(3,4),(5,6),(7,10)]=>3
[(1,7),(2,9),(3,4),(5,6),(8,10)]=>2
[(1,6),(2,9),(3,4),(5,7),(8,10)]=>3
[(1,5),(2,9),(3,4),(6,7),(8,10)]=>2
[(1,4),(2,9),(3,5),(6,7),(8,10)]=>3
[(1,3),(2,9),(4,5),(6,7),(8,10)]=>2
[(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)]=>2
[(1,5),(2,10),(3,4),(6,7),(8,9)]=>1
[(1,6),(2,10),(3,4),(5,7),(8,9)]=>2
[(1,7),(2,10),(3,4),(5,6),(8,9)]=>1
[(1,8),(2,10),(3,4),(5,6),(7,9)]=>2
[(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)]=>3
[(1,7),(2,10),(3,5),(4,6),(8,9)]=>2
[(1,6),(2,10),(3,5),(4,7),(8,9)]=>3
[(1,5),(2,10),(3,6),(4,7),(8,9)]=>4
[(1,4),(2,10),(3,6),(5,7),(8,9)]=>3
[(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)]=>3
[(1,4),(2,9),(3,6),(5,7),(8,10)]=>4
[(1,5),(2,9),(3,6),(4,7),(8,10)]=>5
[(1,6),(2,9),(3,5),(4,7),(8,10)]=>4
[(1,7),(2,9),(3,5),(4,6),(8,10)]=>3
[(1,8),(2,9),(3,5),(4,6),(7,10)]=>4
[(1,9),(2,8),(3,5),(4,6),(7,10)]=>3
[(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)]=>3
[(1,5),(2,8),(3,6),(4,7),(9,10)]=>4
[(1,4),(2,8),(3,6),(5,7),(9,10)]=>3
[(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)]=>2
[(1,3),(2,7),(4,6),(5,8),(9,10)]=>3
[(1,4),(2,7),(3,6),(5,8),(9,10)]=>4
[(1,5),(2,7),(3,6),(4,8),(9,10)]=>5
[(1,6),(2,7),(3,5),(4,8),(9,10)]=>4
[(1,7),(2,6),(3,5),(4,8),(9,10)]=>3
[(1,8),(2,6),(3,5),(4,7),(9,10)]=>2
[(1,9),(2,6),(3,5),(4,7),(8,10)]=>3
[(1,10),(2,6),(3,5),(4,7),(8,9)]=>2
[(1,10),(2,5),(3,6),(4,7),(8,9)]=>3
[(1,9),(2,5),(3,6),(4,7),(8,10)]=>4
[(1,8),(2,5),(3,6),(4,7),(9,10)]=>3
[(1,7),(2,5),(3,6),(4,8),(9,10)]=>4
[(1,6),(2,5),(3,7),(4,8),(9,10)]=>5
[(1,5),(2,6),(3,7),(4,8),(9,10)]=>6
[(1,4),(2,6),(3,7),(5,8),(9,10)]=>5
[(1,3),(2,6),(4,7),(5,8),(9,10)]=>4
[(1,2),(3,6),(4,7),(5,8),(9,10)]=>3
[(1,2),(3,5),(4,7),(6,8),(9,10)]=>2
[(1,3),(2,5),(4,7),(6,8),(9,10)]=>3
[(1,4),(2,5),(3,7),(6,8),(9,10)]=>4
[(1,5),(2,4),(3,7),(6,8),(9,10)]=>3
[(1,6),(2,4),(3,7),(5,8),(9,10)]=>4
[(1,7),(2,4),(3,6),(5,8),(9,10)]=>3
[(1,8),(2,4),(3,6),(5,7),(9,10)]=>2
[(1,9),(2,4),(3,6),(5,7),(8,10)]=>3
[(1,10),(2,4),(3,6),(5,7),(8,9)]=>2
[(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)]=>2
[(1,6),(2,3),(4,7),(5,8),(9,10)]=>3
[(1,5),(2,3),(4,7),(6,8),(9,10)]=>2
[(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)]=>2
[(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)]=>2
[(1,6),(2,4),(3,8),(5,7),(9,10)]=>3
[(1,5),(2,4),(3,8),(6,7),(9,10)]=>2
[(1,4),(2,5),(3,8),(6,7),(9,10)]=>3
[(1,3),(2,5),(4,8),(6,7),(9,10)]=>2
[(1,2),(3,5),(4,8),(6,7),(9,10)]=>1
[(1,2),(3,6),(4,8),(5,7),(9,10)]=>2
[(1,3),(2,6),(4,8),(5,7),(9,10)]=>3
[(1,4),(2,6),(3,8),(5,7),(9,10)]=>4
[(1,5),(2,6),(3,8),(4,7),(9,10)]=>5
[(1,6),(2,5),(3,8),(4,7),(9,10)]=>4
[(1,7),(2,5),(3,8),(4,6),(9,10)]=>3
[(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)]=>2
[(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)]=>2
[(1,6),(2,7),(3,8),(4,5),(9,10)]=>3
[(1,5),(2,7),(3,8),(4,6),(9,10)]=>4
[(1,4),(2,7),(3,8),(5,6),(9,10)]=>3
[(1,3),(2,7),(4,8),(5,6),(9,10)]=>2
[(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)]=>2
[(1,5),(2,8),(3,7),(4,6),(9,10)]=>3
[(1,6),(2,8),(3,7),(4,5),(9,10)]=>2
[(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)]=>2
[(1,8),(2,9),(3,6),(4,5),(7,10)]=>3
[(1,7),(2,9),(3,6),(4,5),(8,10)]=>2
[(1,6),(2,9),(3,7),(4,5),(8,10)]=>3
[(1,5),(2,9),(3,7),(4,6),(8,10)]=>4
[(1,4),(2,9),(3,7),(5,6),(8,10)]=>3
[(1,3),(2,9),(4,7),(5,6),(8,10)]=>2
[(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)]=>2
[(1,5),(2,10),(3,7),(4,6),(8,9)]=>3
[(1,6),(2,10),(3,7),(4,5),(8,9)]=>2
[(1,7),(2,10),(3,6),(4,5),(8,9)]=>1
[(1,8),(2,10),(3,6),(4,5),(7,9)]=>2
[(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)]=>3
[(1,7),(2,10),(3,8),(4,5),(6,9)]=>4
[(1,6),(2,10),(3,8),(4,5),(7,9)]=>3
[(1,5),(2,10),(3,8),(4,6),(7,9)]=>4
[(1,4),(2,10),(3,8),(5,6),(7,9)]=>3
[(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)]=>2
[(1,3),(2,9),(4,8),(5,6),(7,10)]=>3
[(1,4),(2,9),(3,8),(5,6),(7,10)]=>4
[(1,5),(2,9),(3,8),(4,6),(7,10)]=>5
[(1,6),(2,9),(3,8),(4,5),(7,10)]=>4
[(1,7),(2,9),(3,8),(4,5),(6,10)]=>5
[(1,8),(2,9),(3,7),(4,5),(6,10)]=>4
[(1,9),(2,8),(3,7),(4,5),(6,10)]=>3
[(1,10),(2,8),(3,7),(4,5),(6,9)]=>2
[(1,10),(2,7),(3,8),(4,5),(6,9)]=>3
[(1,9),(2,7),(3,8),(4,5),(6,10)]=>4
[(1,8),(2,7),(3,9),(4,5),(6,10)]=>5
[(1,7),(2,8),(3,9),(4,5),(6,10)]=>6
[(1,6),(2,8),(3,9),(4,5),(7,10)]=>5
[(1,5),(2,8),(3,9),(4,6),(7,10)]=>6
[(1,4),(2,8),(3,9),(5,6),(7,10)]=>5
[(1,3),(2,8),(4,9),(5,6),(7,10)]=>4
[(1,2),(3,8),(4,9),(5,6),(7,10)]=>3
[(1,2),(3,7),(4,9),(5,6),(8,10)]=>2
[(1,3),(2,7),(4,9),(5,6),(8,10)]=>3
[(1,4),(2,7),(3,9),(5,6),(8,10)]=>4
[(1,5),(2,7),(3,9),(4,6),(8,10)]=>5
[(1,6),(2,7),(3,9),(4,5),(8,10)]=>4
[(1,7),(2,6),(3,9),(4,5),(8,10)]=>3
[(1,8),(2,6),(3,9),(4,5),(7,10)]=>4
[(1,9),(2,6),(3,8),(4,5),(7,10)]=>3
[(1,10),(2,6),(3,8),(4,5),(7,9)]=>2
[(1,10),(2,5),(3,8),(4,6),(7,9)]=>3
[(1,9),(2,5),(3,8),(4,6),(7,10)]=>4
[(1,8),(2,5),(3,9),(4,6),(7,10)]=>5
[(1,7),(2,5),(3,9),(4,6),(8,10)]=>4
[(1,6),(2,5),(3,9),(4,7),(8,10)]=>5
[(1,5),(2,6),(3,9),(4,7),(8,10)]=>6
[(1,4),(2,6),(3,9),(5,7),(8,10)]=>5
[(1,3),(2,6),(4,9),(5,7),(8,10)]=>4
[(1,2),(3,6),(4,9),(5,7),(8,10)]=>3
[(1,2),(3,5),(4,9),(6,7),(8,10)]=>2
[(1,3),(2,5),(4,9),(6,7),(8,10)]=>3
[(1,4),(2,5),(3,9),(6,7),(8,10)]=>4
[(1,5),(2,4),(3,9),(6,7),(8,10)]=>3
[(1,6),(2,4),(3,9),(5,7),(8,10)]=>4
[(1,7),(2,4),(3,9),(5,6),(8,10)]=>3
[(1,8),(2,4),(3,9),(5,6),(7,10)]=>4
[(1,9),(2,4),(3,8),(5,6),(7,10)]=>3
[(1,10),(2,4),(3,8),(5,6),(7,9)]=>2
[(1,10),(2,3),(4,8),(5,6),(7,9)]=>1
[(1,9),(2,3),(4,8),(5,6),(7,10)]=>2
[(1,8),(2,3),(4,9),(5,6),(7,10)]=>3
[(1,7),(2,3),(4,9),(5,6),(8,10)]=>2
[(1,6),(2,3),(4,9),(5,7),(8,10)]=>3
[(1,5),(2,3),(4,9),(6,7),(8,10)]=>2
[(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)]=>2
[(1,7),(2,3),(4,10),(5,6),(8,9)]=>1
[(1,8),(2,3),(4,10),(5,6),(7,9)]=>2
[(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)]=>2
[(1,8),(2,4),(3,10),(5,6),(7,9)]=>3
[(1,7),(2,4),(3,10),(5,6),(8,9)]=>2
[(1,6),(2,4),(3,10),(5,7),(8,9)]=>3
[(1,5),(2,4),(3,10),(6,7),(8,9)]=>2
[(1,4),(2,5),(3,10),(6,7),(8,9)]=>3
[(1,3),(2,5),(4,10),(6,7),(8,9)]=>2
[(1,2),(3,5),(4,10),(6,7),(8,9)]=>1
[(1,2),(3,6),(4,10),(5,7),(8,9)]=>2
[(1,3),(2,6),(4,10),(5,7),(8,9)]=>3
[(1,4),(2,6),(3,10),(5,7),(8,9)]=>4
[(1,5),(2,6),(3,10),(4,7),(8,9)]=>5
[(1,6),(2,5),(3,10),(4,7),(8,9)]=>4
[(1,7),(2,5),(3,10),(4,6),(8,9)]=>3
[(1,8),(2,5),(3,10),(4,6),(7,9)]=>4
[(1,9),(2,5),(3,10),(4,6),(7,8)]=>3
[(1,10),(2,5),(3,9),(4,6),(7,8)]=>2
[(1,10),(2,6),(3,9),(4,5),(7,8)]=>1
[(1,9),(2,6),(3,10),(4,5),(7,8)]=>2
[(1,8),(2,6),(3,10),(4,5),(7,9)]=>3
[(1,7),(2,6),(3,10),(4,5),(8,9)]=>2
[(1,6),(2,7),(3,10),(4,5),(8,9)]=>3
[(1,5),(2,7),(3,10),(4,6),(8,9)]=>4
[(1,4),(2,7),(3,10),(5,6),(8,9)]=>3
[(1,3),(2,7),(4,10),(5,6),(8,9)]=>2
[(1,2),(3,7),(4,10),(5,6),(8,9)]=>1
[(1,2),(3,8),(4,10),(5,6),(7,9)]=>2
[(1,3),(2,8),(4,10),(5,6),(7,9)]=>3
[(1,4),(2,8),(3,10),(5,6),(7,9)]=>4
[(1,5),(2,8),(3,10),(4,6),(7,9)]=>5
[(1,6),(2,8),(3,10),(4,5),(7,9)]=>4
[(1,7),(2,8),(3,10),(4,5),(6,9)]=>5
[(1,8),(2,7),(3,10),(4,5),(6,9)]=>4
[(1,9),(2,7),(3,10),(4,5),(6,8)]=>3
[(1,10),(2,7),(3,9),(4,5),(6,8)]=>2
[(1,10),(2,8),(3,9),(4,5),(6,7)]=>1
[(1,9),(2,8),(3,10),(4,5),(6,7)]=>2
[(1,8),(2,9),(3,10),(4,5),(6,7)]=>3
[(1,7),(2,9),(3,10),(4,5),(6,8)]=>4
[(1,6),(2,9),(3,10),(4,5),(7,8)]=>3
[(1,5),(2,9),(3,10),(4,6),(7,8)]=>4
[(1,4),(2,9),(3,10),(5,6),(7,8)]=>3
[(1,3),(2,9),(4,10),(5,6),(7,8)]=>2
[(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)]=>2
[(1,5),(2,10),(3,9),(4,6),(7,8)]=>3
[(1,6),(2,10),(3,9),(4,5),(7,8)]=>2
[(1,7),(2,10),(3,9),(4,5),(6,8)]=>3
[(1,8),(2,10),(3,9),(4,5),(6,7)]=>2
[(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)]=>3
[(1,7),(2,10),(3,9),(4,6),(5,8)]=>4
[(1,6),(2,10),(3,9),(4,7),(5,8)]=>5
[(1,5),(2,10),(3,9),(4,7),(6,8)]=>4
[(1,4),(2,10),(3,9),(5,7),(6,8)]=>3
[(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)]=>3
[(1,4),(2,9),(3,10),(5,7),(6,8)]=>4
[(1,5),(2,9),(3,10),(4,7),(6,8)]=>5
[(1,6),(2,9),(3,10),(4,7),(5,8)]=>6
[(1,7),(2,9),(3,10),(4,6),(5,8)]=>5
[(1,8),(2,9),(3,10),(4,6),(5,7)]=>4
[(1,9),(2,8),(3,10),(4,6),(5,7)]=>3
[(1,10),(2,8),(3,9),(4,6),(5,7)]=>2
[(1,10),(2,7),(3,9),(4,6),(5,8)]=>3
[(1,9),(2,7),(3,10),(4,6),(5,8)]=>4
[(1,8),(2,7),(3,10),(4,6),(5,9)]=>5
[(1,7),(2,8),(3,10),(4,6),(5,9)]=>6
[(1,6),(2,8),(3,10),(4,7),(5,9)]=>7
[(1,5),(2,8),(3,10),(4,7),(6,9)]=>6
[(1,4),(2,8),(3,10),(5,7),(6,9)]=>5
[(1,3),(2,8),(4,10),(5,7),(6,9)]=>4
[(1,2),(3,8),(4,10),(5,7),(6,9)]=>3
[(1,2),(3,7),(4,10),(5,8),(6,9)]=>4
[(1,3),(2,7),(4,10),(5,8),(6,9)]=>5
[(1,4),(2,7),(3,10),(5,8),(6,9)]=>6
[(1,5),(2,7),(3,10),(4,8),(6,9)]=>7
[(1,6),(2,7),(3,10),(4,8),(5,9)]=>8
[(1,7),(2,6),(3,10),(4,8),(5,9)]=>7
[(1,8),(2,6),(3,10),(4,7),(5,9)]=>6
[(1,9),(2,6),(3,10),(4,7),(5,8)]=>5
[(1,10),(2,6),(3,9),(4,7),(5,8)]=>4
[(1,10),(2,5),(3,9),(4,7),(6,8)]=>3
[(1,9),(2,5),(3,10),(4,7),(6,8)]=>4
[(1,8),(2,5),(3,10),(4,7),(6,9)]=>5
[(1,7),(2,5),(3,10),(4,8),(6,9)]=>6
[(1,6),(2,5),(3,10),(4,8),(7,9)]=>5
[(1,5),(2,6),(3,10),(4,8),(7,9)]=>6
[(1,4),(2,6),(3,10),(5,8),(7,9)]=>5
[(1,3),(2,6),(4,10),(5,8),(7,9)]=>4
[(1,2),(3,6),(4,10),(5,8),(7,9)]=>3
[(1,2),(3,5),(4,10),(6,8),(7,9)]=>2
[(1,3),(2,5),(4,10),(6,8),(7,9)]=>3
[(1,4),(2,5),(3,10),(6,8),(7,9)]=>4
[(1,5),(2,4),(3,10),(6,8),(7,9)]=>3
[(1,6),(2,4),(3,10),(5,8),(7,9)]=>4
[(1,7),(2,4),(3,10),(5,8),(6,9)]=>5
[(1,8),(2,4),(3,10),(5,7),(6,9)]=>4
[(1,9),(2,4),(3,10),(5,7),(6,8)]=>3
[(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)]=>3
[(1,7),(2,3),(4,10),(5,8),(6,9)]=>4
[(1,6),(2,3),(4,10),(5,8),(7,9)]=>3
[(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)]=>2
[(1,3),(2,4),(5,9),(6,8),(7,10)]=>3
[(1,4),(2,3),(5,9),(6,8),(7,10)]=>2
[(1,5),(2,3),(4,9),(6,8),(7,10)]=>3
[(1,6),(2,3),(4,9),(5,8),(7,10)]=>4
[(1,7),(2,3),(4,9),(5,8),(6,10)]=>5
[(1,8),(2,3),(4,9),(5,7),(6,10)]=>4
[(1,9),(2,3),(4,8),(5,7),(6,10)]=>3
[(1,10),(2,3),(4,8),(5,7),(6,9)]=>2
[(1,10),(2,4),(3,8),(5,7),(6,9)]=>3
[(1,9),(2,4),(3,8),(5,7),(6,10)]=>4
[(1,8),(2,4),(3,9),(5,7),(6,10)]=>5
[(1,7),(2,4),(3,9),(5,8),(6,10)]=>6
[(1,6),(2,4),(3,9),(5,8),(7,10)]=>5
[(1,5),(2,4),(3,9),(6,8),(7,10)]=>4
[(1,4),(2,5),(3,9),(6,8),(7,10)]=>5
[(1,3),(2,5),(4,9),(6,8),(7,10)]=>4
[(1,2),(3,5),(4,9),(6,8),(7,10)]=>3
[(1,2),(3,6),(4,9),(5,8),(7,10)]=>4
[(1,3),(2,6),(4,9),(5,8),(7,10)]=>5
[(1,4),(2,6),(3,9),(5,8),(7,10)]=>6
[(1,5),(2,6),(3,9),(4,8),(7,10)]=>7
[(1,6),(2,5),(3,9),(4,8),(7,10)]=>6
[(1,7),(2,5),(3,9),(4,8),(6,10)]=>7
[(1,8),(2,5),(3,9),(4,7),(6,10)]=>6
[(1,9),(2,5),(3,8),(4,7),(6,10)]=>5
[(1,10),(2,5),(3,8),(4,7),(6,9)]=>4
[(1,10),(2,6),(3,8),(4,7),(5,9)]=>5
[(1,9),(2,6),(3,8),(4,7),(5,10)]=>6
[(1,8),(2,6),(3,9),(4,7),(5,10)]=>7
[(1,7),(2,6),(3,9),(4,8),(5,10)]=>8
[(1,6),(2,7),(3,9),(4,8),(5,10)]=>9
[(1,5),(2,7),(3,9),(4,8),(6,10)]=>8
[(1,4),(2,7),(3,9),(5,8),(6,10)]=>7
[(1,3),(2,7),(4,9),(5,8),(6,10)]=>6
[(1,2),(3,7),(4,9),(5,8),(6,10)]=>5
[(1,2),(3,8),(4,9),(5,7),(6,10)]=>4
[(1,3),(2,8),(4,9),(5,7),(6,10)]=>5
[(1,4),(2,8),(3,9),(5,7),(6,10)]=>6
[(1,5),(2,8),(3,9),(4,7),(6,10)]=>7
[(1,6),(2,8),(3,9),(4,7),(5,10)]=>8
[(1,7),(2,8),(3,9),(4,6),(5,10)]=>7
[(1,8),(2,7),(3,9),(4,6),(5,10)]=>6
[(1,9),(2,7),(3,8),(4,6),(5,10)]=>5
[(1,10),(2,7),(3,8),(4,6),(5,9)]=>4
[(1,10),(2,8),(3,7),(4,6),(5,9)]=>3
[(1,9),(2,8),(3,7),(4,6),(5,10)]=>4
[(1,8),(2,9),(3,7),(4,6),(5,10)]=>5
[(1,7),(2,9),(3,8),(4,6),(5,10)]=>6
[(1,6),(2,9),(3,8),(4,7),(5,10)]=>7
[(1,5),(2,9),(3,8),(4,7),(6,10)]=>6
[(1,4),(2,9),(3,8),(5,7),(6,10)]=>5
[(1,3),(2,9),(4,8),(5,7),(6,10)]=>4
[(1,2),(3,9),(4,8),(5,7),(6,10)]=>3
[(1,2),(3,10),(4,8),(5,7),(6,9)]=>2
[(1,3),(2,10),(4,8),(5,7),(6,9)]=>3
[(1,4),(2,10),(3,8),(5,7),(6,9)]=>4
[(1,5),(2,10),(3,8),(4,7),(6,9)]=>5
[(1,6),(2,10),(3,8),(4,7),(5,9)]=>6
[(1,7),(2,10),(3,8),(4,6),(5,9)]=>5
[(1,8),(2,10),(3,7),(4,6),(5,9)]=>4
[(1,9),(2,10),(3,7),(4,6),(5,8)]=>3
[(1,10),(2,9),(3,7),(4,6),(5,8)]=>2
[(1,10),(2,9),(3,6),(4,7),(5,8)]=>3
[(1,9),(2,10),(3,6),(4,7),(5,8)]=>4
[(1,8),(2,10),(3,6),(4,7),(5,9)]=>5
[(1,7),(2,10),(3,6),(4,8),(5,9)]=>6
[(1,6),(2,10),(3,7),(4,8),(5,9)]=>7
[(1,5),(2,10),(3,7),(4,8),(6,9)]=>6
[(1,4),(2,10),(3,7),(5,8),(6,9)]=>5
[(1,3),(2,10),(4,7),(5,8),(6,9)]=>4
[(1,2),(3,10),(4,7),(5,8),(6,9)]=>3
[(1,2),(3,9),(4,7),(5,8),(6,10)]=>4
[(1,3),(2,9),(4,7),(5,8),(6,10)]=>5
[(1,4),(2,9),(3,7),(5,8),(6,10)]=>6
[(1,5),(2,9),(3,7),(4,8),(6,10)]=>7
[(1,6),(2,9),(3,7),(4,8),(5,10)]=>8
[(1,7),(2,9),(3,6),(4,8),(5,10)]=>7
[(1,8),(2,9),(3,6),(4,7),(5,10)]=>6
[(1,9),(2,8),(3,6),(4,7),(5,10)]=>5
[(1,10),(2,8),(3,6),(4,7),(5,9)]=>4
[(1,10),(2,7),(3,6),(4,8),(5,9)]=>5
[(1,9),(2,7),(3,6),(4,8),(5,10)]=>6
[(1,8),(2,7),(3,6),(4,9),(5,10)]=>7
[(1,7),(2,8),(3,6),(4,9),(5,10)]=>8
[(1,6),(2,8),(3,7),(4,9),(5,10)]=>9
[(1,5),(2,8),(3,7),(4,9),(6,10)]=>8
[(1,4),(2,8),(3,7),(5,9),(6,10)]=>7
[(1,3),(2,8),(4,7),(5,9),(6,10)]=>6
[(1,2),(3,8),(4,7),(5,9),(6,10)]=>5
[(1,2),(3,7),(4,8),(5,9),(6,10)]=>6
[(1,3),(2,7),(4,8),(5,9),(6,10)]=>7
[(1,4),(2,7),(3,8),(5,9),(6,10)]=>8
[(1,5),(2,7),(3,8),(4,9),(6,10)]=>9
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>10
[(1,7),(2,6),(3,8),(4,9),(5,10)]=>9
[(1,8),(2,6),(3,7),(4,9),(5,10)]=>8
[(1,9),(2,6),(3,7),(4,8),(5,10)]=>7
[(1,10),(2,6),(3,7),(4,8),(5,9)]=>6
[(1,10),(2,5),(3,7),(4,8),(6,9)]=>5
[(1,9),(2,5),(3,7),(4,8),(6,10)]=>6
[(1,8),(2,5),(3,7),(4,9),(6,10)]=>7
[(1,7),(2,5),(3,8),(4,9),(6,10)]=>8
[(1,6),(2,5),(3,8),(4,9),(7,10)]=>7
[(1,5),(2,6),(3,8),(4,9),(7,10)]=>8
[(1,4),(2,6),(3,8),(5,9),(7,10)]=>7
[(1,3),(2,6),(4,8),(5,9),(7,10)]=>6
[(1,2),(3,6),(4,8),(5,9),(7,10)]=>5
[(1,2),(3,5),(4,8),(6,9),(7,10)]=>4
[(1,3),(2,5),(4,8),(6,9),(7,10)]=>5
[(1,4),(2,5),(3,8),(6,9),(7,10)]=>6
[(1,5),(2,4),(3,8),(6,9),(7,10)]=>5
[(1,6),(2,4),(3,8),(5,9),(7,10)]=>6
[(1,7),(2,4),(3,8),(5,9),(6,10)]=>7
[(1,8),(2,4),(3,7),(5,9),(6,10)]=>6
[(1,9),(2,4),(3,7),(5,8),(6,10)]=>5
[(1,10),(2,4),(3,7),(5,8),(6,9)]=>4
[(1,10),(2,3),(4,7),(5,8),(6,9)]=>3
[(1,9),(2,3),(4,7),(5,8),(6,10)]=>4
[(1,8),(2,3),(4,7),(5,9),(6,10)]=>5
[(1,7),(2,3),(4,8),(5,9),(6,10)]=>6
[(1,6),(2,3),(4,8),(5,9),(7,10)]=>5
[(1,5),(2,3),(4,8),(6,9),(7,10)]=>4
[(1,4),(2,3),(5,8),(6,9),(7,10)]=>3
[(1,3),(2,4),(5,8),(6,9),(7,10)]=>4
[(1,2),(3,4),(5,8),(6,9),(7,10)]=>3
[(1,2),(3,4),(5,7),(6,9),(8,10)]=>2
[(1,3),(2,4),(5,7),(6,9),(8,10)]=>3
[(1,4),(2,3),(5,7),(6,9),(8,10)]=>2
[(1,5),(2,3),(4,7),(6,9),(8,10)]=>3
[(1,6),(2,3),(4,7),(5,9),(8,10)]=>4
[(1,7),(2,3),(4,6),(5,9),(8,10)]=>3
[(1,8),(2,3),(4,6),(5,9),(7,10)]=>4
[(1,9),(2,3),(4,6),(5,8),(7,10)]=>3
[(1,10),(2,3),(4,6),(5,8),(7,9)]=>2
[(1,10),(2,4),(3,6),(5,8),(7,9)]=>3
[(1,9),(2,4),(3,6),(5,8),(7,10)]=>4
[(1,8),(2,4),(3,6),(5,9),(7,10)]=>5
[(1,7),(2,4),(3,6),(5,9),(8,10)]=>4
[(1,6),(2,4),(3,7),(5,9),(8,10)]=>5
[(1,5),(2,4),(3,7),(6,9),(8,10)]=>4
[(1,4),(2,5),(3,7),(6,9),(8,10)]=>5
[(1,3),(2,5),(4,7),(6,9),(8,10)]=>4
[(1,2),(3,5),(4,7),(6,9),(8,10)]=>3
[(1,2),(3,6),(4,7),(5,9),(8,10)]=>4
[(1,3),(2,6),(4,7),(5,9),(8,10)]=>5
[(1,4),(2,6),(3,7),(5,9),(8,10)]=>6
[(1,5),(2,6),(3,7),(4,9),(8,10)]=>7
[(1,6),(2,5),(3,7),(4,9),(8,10)]=>6
[(1,7),(2,5),(3,6),(4,9),(8,10)]=>5
[(1,8),(2,5),(3,6),(4,9),(7,10)]=>6
[(1,9),(2,5),(3,6),(4,8),(7,10)]=>5
[(1,10),(2,5),(3,6),(4,8),(7,9)]=>4
[(1,10),(2,6),(3,5),(4,8),(7,9)]=>3
[(1,9),(2,6),(3,5),(4,8),(7,10)]=>4
[(1,8),(2,6),(3,5),(4,9),(7,10)]=>5
[(1,7),(2,6),(3,5),(4,9),(8,10)]=>4
[(1,6),(2,7),(3,5),(4,9),(8,10)]=>5
[(1,5),(2,7),(3,6),(4,9),(8,10)]=>6
[(1,4),(2,7),(3,6),(5,9),(8,10)]=>5
[(1,3),(2,7),(4,6),(5,9),(8,10)]=>4
[(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)]=>5
[(1,4),(2,8),(3,6),(5,9),(7,10)]=>6
[(1,5),(2,8),(3,6),(4,9),(7,10)]=>7
[(1,6),(2,8),(3,5),(4,9),(7,10)]=>6
[(1,7),(2,8),(3,5),(4,9),(6,10)]=>7
[(1,8),(2,7),(3,5),(4,9),(6,10)]=>6
[(1,9),(2,7),(3,5),(4,8),(6,10)]=>5
[(1,10),(2,7),(3,5),(4,8),(6,9)]=>4
[(1,10),(2,8),(3,5),(4,7),(6,9)]=>3
[(1,9),(2,8),(3,5),(4,7),(6,10)]=>4
[(1,8),(2,9),(3,5),(4,7),(6,10)]=>5
[(1,7),(2,9),(3,5),(4,8),(6,10)]=>6
[(1,6),(2,9),(3,5),(4,8),(7,10)]=>5
[(1,5),(2,9),(3,6),(4,8),(7,10)]=>6
[(1,4),(2,9),(3,6),(5,8),(7,10)]=>5
[(1,3),(2,9),(4,6),(5,8),(7,10)]=>4
[(1,2),(3,9),(4,6),(5,8),(7,10)]=>3
[(1,2),(3,10),(4,6),(5,8),(7,9)]=>2
[(1,3),(2,10),(4,6),(5,8),(7,9)]=>3
[(1,4),(2,10),(3,6),(5,8),(7,9)]=>4
[(1,5),(2,10),(3,6),(4,8),(7,9)]=>5
[(1,6),(2,10),(3,5),(4,8),(7,9)]=>4
[(1,7),(2,10),(3,5),(4,8),(6,9)]=>5
[(1,8),(2,10),(3,5),(4,7),(6,9)]=>4
[(1,9),(2,10),(3,5),(4,7),(6,8)]=>3
[(1,10),(2,9),(3,5),(4,7),(6,8)]=>2
[(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)]=>3
[(1,7),(2,10),(3,4),(5,8),(6,9)]=>4
[(1,6),(2,10),(3,4),(5,8),(7,9)]=>3
[(1,5),(2,10),(3,4),(6,8),(7,9)]=>2
[(1,4),(2,10),(3,5),(6,8),(7,9)]=>3
[(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)]=>2
[(1,3),(2,9),(4,5),(6,8),(7,10)]=>3
[(1,4),(2,9),(3,5),(6,8),(7,10)]=>4
[(1,5),(2,9),(3,4),(6,8),(7,10)]=>3
[(1,6),(2,9),(3,4),(5,8),(7,10)]=>4
[(1,7),(2,9),(3,4),(5,8),(6,10)]=>5
[(1,8),(2,9),(3,4),(5,7),(6,10)]=>4
[(1,9),(2,8),(3,4),(5,7),(6,10)]=>3
[(1,10),(2,8),(3,4),(5,7),(6,9)]=>2
[(1,10),(2,7),(3,4),(5,8),(6,9)]=>3
[(1,9),(2,7),(3,4),(5,8),(6,10)]=>4
[(1,8),(2,7),(3,4),(5,9),(6,10)]=>5
[(1,7),(2,8),(3,4),(5,9),(6,10)]=>6
[(1,6),(2,8),(3,4),(5,9),(7,10)]=>5
[(1,5),(2,8),(3,4),(6,9),(7,10)]=>4
[(1,4),(2,8),(3,5),(6,9),(7,10)]=>5
[(1,3),(2,8),(4,5),(6,9),(7,10)]=>4
[(1,2),(3,8),(4,5),(6,9),(7,10)]=>3
[(1,2),(3,7),(4,5),(6,9),(8,10)]=>2
[(1,3),(2,7),(4,5),(6,9),(8,10)]=>3
[(1,4),(2,7),(3,5),(6,9),(8,10)]=>4
[(1,5),(2,7),(3,4),(6,9),(8,10)]=>3
[(1,6),(2,7),(3,4),(5,9),(8,10)]=>4
[(1,7),(2,6),(3,4),(5,9),(8,10)]=>3
[(1,8),(2,6),(3,4),(5,9),(7,10)]=>4
[(1,9),(2,6),(3,4),(5,8),(7,10)]=>3
[(1,10),(2,6),(3,4),(5,8),(7,9)]=>2
[(1,10),(2,5),(3,4),(6,8),(7,9)]=>1
[(1,9),(2,5),(3,4),(6,8),(7,10)]=>2
[(1,8),(2,5),(3,4),(6,9),(7,10)]=>3
[(1,7),(2,5),(3,4),(6,9),(8,10)]=>2
[(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)]=>3
[(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)]=>3
[(1,4),(2,5),(3,6),(7,9),(8,10)]=>4
[(1,5),(2,4),(3,6),(7,9),(8,10)]=>3
[(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)]=>4
[(1,9),(2,4),(3,5),(6,8),(7,10)]=>3
[(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)]=>2
[(1,8),(2,3),(4,5),(6,9),(7,10)]=>3
[(1,7),(2,3),(4,5),(6,9),(8,10)]=>2
[(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)]=>2
[(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)]=>3
[(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)]=>2
[(1,4),(2,5),(3,6),(7,10),(8,9)]=>3
[(1,3),(2,5),(4,6),(7,10),(8,9)]=>2
[(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)]=>2
[(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)]=>2
[(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)]=>2
[(1,8),(2,6),(3,4),(5,10),(7,9)]=>3
[(1,7),(2,6),(3,4),(5,10),(8,9)]=>2
[(1,6),(2,7),(3,4),(5,10),(8,9)]=>3
[(1,5),(2,7),(3,4),(6,10),(8,9)]=>2
[(1,4),(2,7),(3,5),(6,10),(8,9)]=>3
[(1,3),(2,7),(4,5),(6,10),(8,9)]=>2
[(1,2),(3,7),(4,5),(6,10),(8,9)]=>1
[(1,2),(3,8),(4,5),(6,10),(7,9)]=>2
[(1,3),(2,8),(4,5),(6,10),(7,9)]=>3
[(1,4),(2,8),(3,5),(6,10),(7,9)]=>4
[(1,5),(2,8),(3,4),(6,10),(7,9)]=>3
[(1,6),(2,8),(3,4),(5,10),(7,9)]=>4
[(1,7),(2,8),(3,4),(5,10),(6,9)]=>5
[(1,8),(2,7),(3,4),(5,10),(6,9)]=>4
[(1,9),(2,7),(3,4),(5,10),(6,8)]=>3
[(1,10),(2,7),(3,4),(5,9),(6,8)]=>2
[(1,10),(2,8),(3,4),(5,9),(6,7)]=>1
[(1,9),(2,8),(3,4),(5,10),(6,7)]=>2
[(1,8),(2,9),(3,4),(5,10),(6,7)]=>3
[(1,7),(2,9),(3,4),(5,10),(6,8)]=>4
[(1,6),(2,9),(3,4),(5,10),(7,8)]=>3
[(1,5),(2,9),(3,4),(6,10),(7,8)]=>2
[(1,4),(2,9),(3,5),(6,10),(7,8)]=>3
[(1,3),(2,9),(4,5),(6,10),(7,8)]=>2
[(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)]=>2
[(1,5),(2,10),(3,4),(6,9),(7,8)]=>1
[(1,6),(2,10),(3,4),(5,9),(7,8)]=>2
[(1,7),(2,10),(3,4),(5,9),(6,8)]=>3
[(1,8),(2,10),(3,4),(5,9),(6,7)]=>2
[(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)]=>3
[(1,7),(2,10),(3,5),(4,9),(6,8)]=>4
[(1,6),(2,10),(3,5),(4,9),(7,8)]=>3
[(1,5),(2,10),(3,6),(4,9),(7,8)]=>4
[(1,4),(2,10),(3,6),(5,9),(7,8)]=>3
[(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)]=>2
[(1,3),(2,9),(4,6),(5,10),(7,8)]=>3
[(1,4),(2,9),(3,6),(5,10),(7,8)]=>4
[(1,5),(2,9),(3,6),(4,10),(7,8)]=>5
[(1,6),(2,9),(3,5),(4,10),(7,8)]=>4
[(1,7),(2,9),(3,5),(4,10),(6,8)]=>5
[(1,8),(2,9),(3,5),(4,10),(6,7)]=>4
[(1,9),(2,8),(3,5),(4,10),(6,7)]=>3
[(1,10),(2,8),(3,5),(4,9),(6,7)]=>2
[(1,10),(2,7),(3,5),(4,9),(6,8)]=>3
[(1,9),(2,7),(3,5),(4,10),(6,8)]=>4
[(1,8),(2,7),(3,5),(4,10),(6,9)]=>5
[(1,7),(2,8),(3,5),(4,10),(6,9)]=>6
[(1,6),(2,8),(3,5),(4,10),(7,9)]=>5
[(1,5),(2,8),(3,6),(4,10),(7,9)]=>6
[(1,4),(2,8),(3,6),(5,10),(7,9)]=>5
[(1,3),(2,8),(4,6),(5,10),(7,9)]=>4
[(1,2),(3,8),(4,6),(5,10),(7,9)]=>3
[(1,2),(3,7),(4,6),(5,10),(8,9)]=>2
[(1,3),(2,7),(4,6),(5,10),(8,9)]=>3
[(1,4),(2,7),(3,6),(5,10),(8,9)]=>4
[(1,5),(2,7),(3,6),(4,10),(8,9)]=>5
[(1,6),(2,7),(3,5),(4,10),(8,9)]=>4
[(1,7),(2,6),(3,5),(4,10),(8,9)]=>3
[(1,8),(2,6),(3,5),(4,10),(7,9)]=>4
[(1,9),(2,6),(3,5),(4,10),(7,8)]=>3
[(1,10),(2,6),(3,5),(4,9),(7,8)]=>2
[(1,10),(2,5),(3,6),(4,9),(7,8)]=>3
[(1,9),(2,5),(3,6),(4,10),(7,8)]=>4
[(1,8),(2,5),(3,6),(4,10),(7,9)]=>5
[(1,7),(2,5),(3,6),(4,10),(8,9)]=>4
[(1,6),(2,5),(3,7),(4,10),(8,9)]=>5
[(1,5),(2,6),(3,7),(4,10),(8,9)]=>6
[(1,4),(2,6),(3,7),(5,10),(8,9)]=>5
[(1,3),(2,6),(4,7),(5,10),(8,9)]=>4
[(1,2),(3,6),(4,7),(5,10),(8,9)]=>3
[(1,2),(3,5),(4,7),(6,10),(8,9)]=>2
[(1,3),(2,5),(4,7),(6,10),(8,9)]=>3
[(1,4),(2,5),(3,7),(6,10),(8,9)]=>4
[(1,5),(2,4),(3,7),(6,10),(8,9)]=>3
[(1,6),(2,4),(3,7),(5,10),(8,9)]=>4
[(1,7),(2,4),(3,6),(5,10),(8,9)]=>3
[(1,8),(2,4),(3,6),(5,10),(7,9)]=>4
[(1,9),(2,4),(3,6),(5,10),(7,8)]=>3
[(1,10),(2,4),(3,6),(5,9),(7,8)]=>2
[(1,10),(2,3),(4,6),(5,9),(7,8)]=>1
[(1,9),(2,3),(4,6),(5,10),(7,8)]=>2
[(1,8),(2,3),(4,6),(5,10),(7,9)]=>3
[(1,7),(2,3),(4,6),(5,10),(8,9)]=>2
[(1,6),(2,3),(4,7),(5,10),(8,9)]=>3
[(1,5),(2,3),(4,7),(6,10),(8,9)]=>2
[(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)]=>2
[(1,3),(2,4),(5,8),(6,10),(7,9)]=>3
[(1,4),(2,3),(5,8),(6,10),(7,9)]=>2
[(1,5),(2,3),(4,8),(6,10),(7,9)]=>3
[(1,6),(2,3),(4,8),(5,10),(7,9)]=>4
[(1,7),(2,3),(4,8),(5,10),(6,9)]=>5
[(1,8),(2,3),(4,7),(5,10),(6,9)]=>4
[(1,9),(2,3),(4,7),(5,10),(6,8)]=>3
[(1,10),(2,3),(4,7),(5,9),(6,8)]=>2
[(1,10),(2,4),(3,7),(5,9),(6,8)]=>3
[(1,9),(2,4),(3,7),(5,10),(6,8)]=>4
[(1,8),(2,4),(3,7),(5,10),(6,9)]=>5
[(1,7),(2,4),(3,8),(5,10),(6,9)]=>6
[(1,6),(2,4),(3,8),(5,10),(7,9)]=>5
[(1,5),(2,4),(3,8),(6,10),(7,9)]=>4
[(1,4),(2,5),(3,8),(6,10),(7,9)]=>5
[(1,3),(2,5),(4,8),(6,10),(7,9)]=>4
[(1,2),(3,5),(4,8),(6,10),(7,9)]=>3
[(1,2),(3,6),(4,8),(5,10),(7,9)]=>4
[(1,3),(2,6),(4,8),(5,10),(7,9)]=>5
[(1,4),(2,6),(3,8),(5,10),(7,9)]=>6
[(1,5),(2,6),(3,8),(4,10),(7,9)]=>7
[(1,6),(2,5),(3,8),(4,10),(7,9)]=>6
[(1,7),(2,5),(3,8),(4,10),(6,9)]=>7
[(1,8),(2,5),(3,7),(4,10),(6,9)]=>6
[(1,9),(2,5),(3,7),(4,10),(6,8)]=>5
[(1,10),(2,5),(3,7),(4,9),(6,8)]=>4
[(1,10),(2,6),(3,7),(4,9),(5,8)]=>5
[(1,9),(2,6),(3,7),(4,10),(5,8)]=>6
[(1,8),(2,6),(3,7),(4,10),(5,9)]=>7
[(1,7),(2,6),(3,8),(4,10),(5,9)]=>8
[(1,6),(2,7),(3,8),(4,10),(5,9)]=>9
[(1,5),(2,7),(3,8),(4,10),(6,9)]=>8
[(1,4),(2,7),(3,8),(5,10),(6,9)]=>7
[(1,3),(2,7),(4,8),(5,10),(6,9)]=>6
[(1,2),(3,7),(4,8),(5,10),(6,9)]=>5
[(1,2),(3,8),(4,7),(5,10),(6,9)]=>4
[(1,3),(2,8),(4,7),(5,10),(6,9)]=>5
[(1,4),(2,8),(3,7),(5,10),(6,9)]=>6
[(1,5),(2,8),(3,7),(4,10),(6,9)]=>7
[(1,6),(2,8),(3,7),(4,10),(5,9)]=>8
[(1,7),(2,8),(3,6),(4,10),(5,9)]=>7
[(1,8),(2,7),(3,6),(4,10),(5,9)]=>6
[(1,9),(2,7),(3,6),(4,10),(5,8)]=>5
[(1,10),(2,7),(3,6),(4,9),(5,8)]=>4
[(1,10),(2,8),(3,6),(4,9),(5,7)]=>3
[(1,9),(2,8),(3,6),(4,10),(5,7)]=>4
[(1,8),(2,9),(3,6),(4,10),(5,7)]=>5
[(1,7),(2,9),(3,6),(4,10),(5,8)]=>6
[(1,6),(2,9),(3,7),(4,10),(5,8)]=>7
[(1,5),(2,9),(3,7),(4,10),(6,8)]=>6
[(1,4),(2,9),(3,7),(5,10),(6,8)]=>5
[(1,3),(2,9),(4,7),(5,10),(6,8)]=>4
[(1,2),(3,9),(4,7),(5,10),(6,8)]=>3
[(1,2),(3,10),(4,7),(5,9),(6,8)]=>2
[(1,3),(2,10),(4,7),(5,9),(6,8)]=>3
[(1,4),(2,10),(3,7),(5,9),(6,8)]=>4
[(1,5),(2,10),(3,7),(4,9),(6,8)]=>5
[(1,6),(2,10),(3,7),(4,9),(5,8)]=>6
[(1,7),(2,10),(3,6),(4,9),(5,8)]=>5
[(1,8),(2,10),(3,6),(4,9),(5,7)]=>4
[(1,9),(2,10),(3,6),(4,8),(5,7)]=>3
[(1,10),(2,9),(3,6),(4,8),(5,7)]=>2
[(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)]=>3
[(1,7),(2,10),(3,8),(4,9),(5,6)]=>4
[(1,6),(2,10),(3,8),(4,9),(5,7)]=>5
[(1,5),(2,10),(3,8),(4,9),(6,7)]=>4
[(1,4),(2,10),(3,8),(5,9),(6,7)]=>3
[(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)]=>2
[(1,3),(2,9),(4,8),(5,10),(6,7)]=>3
[(1,4),(2,9),(3,8),(5,10),(6,7)]=>4
[(1,5),(2,9),(3,8),(4,10),(6,7)]=>5
[(1,6),(2,9),(3,8),(4,10),(5,7)]=>6
[(1,7),(2,9),(3,8),(4,10),(5,6)]=>5
[(1,8),(2,9),(3,7),(4,10),(5,6)]=>4
[(1,9),(2,8),(3,7),(4,10),(5,6)]=>3
[(1,10),(2,8),(3,7),(4,9),(5,6)]=>2
[(1,10),(2,7),(3,8),(4,9),(5,6)]=>3
[(1,9),(2,7),(3,8),(4,10),(5,6)]=>4
[(1,8),(2,7),(3,9),(4,10),(5,6)]=>5
[(1,7),(2,8),(3,9),(4,10),(5,6)]=>6
[(1,6),(2,8),(3,9),(4,10),(5,7)]=>7
[(1,5),(2,8),(3,9),(4,10),(6,7)]=>6
[(1,4),(2,8),(3,9),(5,10),(6,7)]=>5
[(1,3),(2,8),(4,9),(5,10),(6,7)]=>4
[(1,2),(3,8),(4,9),(5,10),(6,7)]=>3
[(1,2),(3,7),(4,9),(5,10),(6,8)]=>4
[(1,3),(2,7),(4,9),(5,10),(6,8)]=>5
[(1,4),(2,7),(3,9),(5,10),(6,8)]=>6
[(1,5),(2,7),(3,9),(4,10),(6,8)]=>7
[(1,6),(2,7),(3,9),(4,10),(5,8)]=>8
[(1,7),(2,6),(3,9),(4,10),(5,8)]=>7
[(1,8),(2,6),(3,9),(4,10),(5,7)]=>6
[(1,9),(2,6),(3,8),(4,10),(5,7)]=>5
[(1,10),(2,6),(3,8),(4,9),(5,7)]=>4
[(1,10),(2,5),(3,8),(4,9),(6,7)]=>3
[(1,9),(2,5),(3,8),(4,10),(6,7)]=>4
[(1,8),(2,5),(3,9),(4,10),(6,7)]=>5
[(1,7),(2,5),(3,9),(4,10),(6,8)]=>6
[(1,6),(2,5),(3,9),(4,10),(7,8)]=>5
[(1,5),(2,6),(3,9),(4,10),(7,8)]=>6
[(1,4),(2,6),(3,9),(5,10),(7,8)]=>5
[(1,3),(2,6),(4,9),(5,10),(7,8)]=>4
[(1,2),(3,6),(4,9),(5,10),(7,8)]=>3
[(1,2),(3,5),(4,9),(6,10),(7,8)]=>2
[(1,3),(2,5),(4,9),(6,10),(7,8)]=>3
[(1,4),(2,5),(3,9),(6,10),(7,8)]=>4
[(1,5),(2,4),(3,9),(6,10),(7,8)]=>3
[(1,6),(2,4),(3,9),(5,10),(7,8)]=>4
[(1,7),(2,4),(3,9),(5,10),(6,8)]=>5
[(1,8),(2,4),(3,9),(5,10),(6,7)]=>4
[(1,9),(2,4),(3,8),(5,10),(6,7)]=>3
[(1,10),(2,4),(3,8),(5,9),(6,7)]=>2
[(1,10),(2,3),(4,8),(5,9),(6,7)]=>1
[(1,9),(2,3),(4,8),(5,10),(6,7)]=>2
[(1,8),(2,3),(4,9),(5,10),(6,7)]=>3
[(1,7),(2,3),(4,9),(5,10),(6,8)]=>4
[(1,6),(2,3),(4,9),(5,10),(7,8)]=>3
[(1,5),(2,3),(4,9),(6,10),(7,8)]=>2
[(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)]=>2
[(1,7),(2,3),(4,10),(5,9),(6,8)]=>3
[(1,8),(2,3),(4,10),(5,9),(6,7)]=>2
[(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)]=>2
[(1,8),(2,4),(3,10),(5,9),(6,7)]=>3
[(1,7),(2,4),(3,10),(5,9),(6,8)]=>4
[(1,6),(2,4),(3,10),(5,9),(7,8)]=>3
[(1,5),(2,4),(3,10),(6,9),(7,8)]=>2
[(1,4),(2,5),(3,10),(6,9),(7,8)]=>3
[(1,3),(2,5),(4,10),(6,9),(7,8)]=>2
[(1,2),(3,5),(4,10),(6,9),(7,8)]=>1
[(1,2),(3,6),(4,10),(5,9),(7,8)]=>2
[(1,3),(2,6),(4,10),(5,9),(7,8)]=>3
[(1,4),(2,6),(3,10),(5,9),(7,8)]=>4
[(1,5),(2,6),(3,10),(4,9),(7,8)]=>5
[(1,6),(2,5),(3,10),(4,9),(7,8)]=>4
[(1,7),(2,5),(3,10),(4,9),(6,8)]=>5
[(1,8),(2,5),(3,10),(4,9),(6,7)]=>4
[(1,9),(2,5),(3,10),(4,8),(6,7)]=>3
[(1,10),(2,5),(3,9),(4,8),(6,7)]=>2
[(1,10),(2,6),(3,9),(4,8),(5,7)]=>3
[(1,9),(2,6),(3,10),(4,8),(5,7)]=>4
[(1,8),(2,6),(3,10),(4,9),(5,7)]=>5
[(1,7),(2,6),(3,10),(4,9),(5,8)]=>6
[(1,6),(2,7),(3,10),(4,9),(5,8)]=>7
[(1,5),(2,7),(3,10),(4,9),(6,8)]=>6
[(1,4),(2,7),(3,10),(5,9),(6,8)]=>5
[(1,3),(2,7),(4,10),(5,9),(6,8)]=>4
[(1,2),(3,7),(4,10),(5,9),(6,8)]=>3
[(1,2),(3,8),(4,10),(5,9),(6,7)]=>2
[(1,3),(2,8),(4,10),(5,9),(6,7)]=>3
[(1,4),(2,8),(3,10),(5,9),(6,7)]=>4
[(1,5),(2,8),(3,10),(4,9),(6,7)]=>5
[(1,6),(2,8),(3,10),(4,9),(5,7)]=>6
[(1,7),(2,8),(3,10),(4,9),(5,6)]=>5
[(1,8),(2,7),(3,10),(4,9),(5,6)]=>4
[(1,9),(2,7),(3,10),(4,8),(5,6)]=>3
[(1,10),(2,7),(3,9),(4,8),(5,6)]=>2
[(1,10),(2,8),(3,9),(4,7),(5,6)]=>1
[(1,9),(2,8),(3,10),(4,7),(5,6)]=>2
[(1,8),(2,9),(3,10),(4,7),(5,6)]=>3
[(1,7),(2,9),(3,10),(4,8),(5,6)]=>4
[(1,6),(2,9),(3,10),(4,8),(5,7)]=>5
[(1,5),(2,9),(3,10),(4,8),(6,7)]=>4
[(1,4),(2,9),(3,10),(5,8),(6,7)]=>3
[(1,3),(2,9),(4,10),(5,8),(6,7)]=>2
[(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)]=>2
[(1,5),(2,10),(3,9),(4,8),(6,7)]=>3
[(1,6),(2,10),(3,9),(4,8),(5,7)]=>4
[(1,7),(2,10),(3,9),(4,8),(5,6)]=>3
[(1,8),(2,10),(3,9),(4,7),(5,6)]=>2
[(1,9),(2,10),(3,8),(4,7),(5,6)]=>1
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>0
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>0
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]=>0
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)]=>0
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]=>0
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)]=>0
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)]=>0
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]=>0
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)]=>0
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]=>0
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)]=>0
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]=>0
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)]=>0
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)]=>0
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]=>0
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)]=>0
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)]=>0
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]=>0
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]=>0
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)]=>0
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]=>0
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)]=>0
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)]=>0
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)]=>0
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]=>0
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)]=>0
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]=>0
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)]=>0
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)]=>0
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)]=>0
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]=>0
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)]=>0
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)]=>0
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)]=>0
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]=>0
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)]=>0
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]=>0
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)]=>0
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]=>0
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]=>0
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)]=>0
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]=>0
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)]=>0
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)]=>0
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]=>0
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)]=>0
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)]=>0
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]=>0
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)]=>0
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)]=>0
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]=>0
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)]=>0
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)]=>0
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)]=>0
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]=>0
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)]=>0
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]=>0
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)]=>0
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)]=>0
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)]=>0
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]=>0
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)]=>0
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)]=>0
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)]=>0
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]=>0
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)]=>0
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]=>0
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)]=>0
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)]=>0
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]=>0
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)]=>0
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]=>0
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]=>0
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)]=>0
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]=>0
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)]=>0
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]=>0
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)]=>0
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]=>0
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)]=>0
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]=>0
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)]=>0
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)]=>0
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]=>0
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)]=>0
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)]=>0
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)]=>0
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]=>0
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)]=>0
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]=>0
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)]=>0
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)]=>0
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]=>0
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)]=>0
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]=>0
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)]=>0
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)]=>0
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]=>0
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)]=>0
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)]=>0
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)]=>0
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]=>0
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)]=>0
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)]=>0
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)]=>0
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)]=>0
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]=>0
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)]=>0
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)]=>0
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)]=>0
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)]=>0
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)]=>1
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]=>1
[(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)]=>3
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)]=>1
[(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)]=>2
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)]=>3
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)]=>4
[(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)]=>5
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)]=>6
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)]=>1
[(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)]=>2
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)]=>3
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)]=>4
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)]=>2
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)]=>3
[(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)]=>4
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)]=>5
[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)]=>4
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)]=>5
[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)]=>6
[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)]=>7
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)]=>3
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)]=>4
[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)]=>4
[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)]=>5
[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)]=>6
[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)]=>5
[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)]=>6
[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)]=>7
[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)]=>8
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)]=>6
[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)]=>7
[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)]=>8
[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)]=>9
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)]=>10
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)]=>1
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)]=>2
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)]=>2
[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)]=>3
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)]=>4
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)]=>2
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)]=>3
[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)]=>3
[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)]=>4
[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)]=>5
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)]=>4
[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)]=>5
[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)]=>6
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)]=>7
[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)]=>2
[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)]=>3
[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)]=>3
[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)]=>4
[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)]=>5
[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)]=>3
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)]=>4
[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)]=>4
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)]=>5
[(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)]=>6
[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)]=>5
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)]=>6
[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)]=>7
[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)]=>8
[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)]=>4
[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)]=>5
[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)]=>5
[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)]=>6
[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)]=>7
[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)]=>6
[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)]=>7
[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)]=>8
[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)]=>9
[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)]=>7
[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)]=>8
[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)]=>9
[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)]=>10
[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)]=>11
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)]=>3
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)]=>4
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)]=>4
[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)]=>5
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)]=>6
[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)]=>4
[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)]=>5
[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)]=>5
[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)]=>6
[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)]=>7
[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)]=>6
[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)]=>7
[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)]=>8
[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)]=>9
[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)]=>5
[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)]=>6
[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)]=>6
[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)]=>7
[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)]=>8
[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)]=>7
[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)]=>8
[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)]=>9
[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)]=>10
[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)]=>8
[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)]=>9
[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)]=>10
[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)]=>11
[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)]=>12
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)]=>6
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)]=>7
[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)]=>7
[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)]=>8
[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)]=>9
[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)]=>8
[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)]=>9
[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)]=>10
[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)]=>11
[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)]=>9
[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)]=>10
[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)]=>11
[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)]=>12
[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)]=>13
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)]=>10
[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)]=>11
[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)]=>12
[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)]=>13
[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)]=>14
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>15
[(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)]=>0
[(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)]=>0
[(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)]=>0
[(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)]=>0
[(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)]=>0
[(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)]=>0
[(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)]=>0
[(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)]=>0
[(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)]=>0
[(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)]=>0
[(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)]=>0
[(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)]=>0
[(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)]=>0
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)]=>0
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)]=>0
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)]=>0
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)]=>0
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)]=>0
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)]=>0
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)]=>0
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)]=>0
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)]=>0
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)]=>0
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)]=>0
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)]=>0
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)]=>0
[(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)]=>0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)]=>0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)]=>0
[(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)]=>0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)]=>0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)]=>0
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)]=>0
[(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)]=>0
[(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)]=>0
[(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)]=>0
[(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)]=>0
[(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)]=>0
[(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)]=>0
[(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)]=>0
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)]=>0
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)]=>0
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10),(17,18)]=>0
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)]=>0
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11),(17,18)]=>0
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10),(17,18)]=>0
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)]=>0
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)]=>0
[(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10),(19,20)]=>0
[(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)]=>0
[(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11),(19,20)]=>0
[(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)]=>0
[(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,22)]=>0
[(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)]=>0
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Description
The number of crossings of a perfect matching.
This is the number of pairs of edges $((a,b),(c,d))$ such that $a\le c\le b\le d$, i.e., the edges $(a,b)$ and $(c,d)$ cross when drawing the perfect matching as a chord diagram.
The generating function for perfect matchings $M$ of $\{1,\dots,2n\}$ according to the number of crossings $\textrm{cr}(M)$ is given by the Touchard-Riordan formula ([2], [4], a bijective proof is given in [7]):
$$ \sum_{M} q^{\textrm{cr}(M)} = \frac{1}{(1-q)^n} \sum_{k=0}^n\left(\binom{2n}{n-k}-\binom{2n}{n-k-1}\right)(-1)^k q^{\binom{k+1}{2}} $$
This is the number of pairs of edges $((a,b),(c,d))$ such that $a\le c\le b\le d$, i.e., the edges $(a,b)$ and $(c,d)$ cross when drawing the perfect matching as a chord diagram.
The generating function for perfect matchings $M$ of $\{1,\dots,2n\}$ according to the number of crossings $\textrm{cr}(M)$ is given by the Touchard-Riordan formula ([2], [4], a bijective proof is given in [7]):
$$ \sum_{M} q^{\textrm{cr}(M)} = \frac{1}{(1-q)^n} \sum_{k=0}^n\left(\binom{2n}{n-k}-\binom{2n}{n-k-1}\right)(-1)^k q^{\binom{k+1}{2}} $$
References
[1] de Médicis, A., Viennot, X. G. Moments des $q$-polynômes de Laguerre et la bijection de Foata-Zeilberger MathSciNet:1288802
[2] Riordan, J. The distribution of crossings of chords joining pairs of $2n$ points on a circle MathSciNet:0366686
[3] Simion, R., Stanton, D. Octabasic Laguerre polynomials and permutation statistics MathSciNet:1418763
[4] Touchard, J. Sur un problème de configurations et sur les fractions continues MathSciNet:0046325
[5] Josuat-Vergès, M., Rubey, M. Crossings, Motzkin paths and moments MathSciNet:2819649
[6] Triangle read by rows: T(n,k) gives number of ways of arranging n chords on a circle with k simple intersections (i.e. no intersections with 3 or more chords) - positive values only. OEIS:A067311
[7] Penaud, J.-G. Une preuve bijective d'une formule de Touchard-Riordan MathSciNet:1336847
[2] Riordan, J. The distribution of crossings of chords joining pairs of $2n$ points on a circle MathSciNet:0366686
[3] Simion, R., Stanton, D. Octabasic Laguerre polynomials and permutation statistics MathSciNet:1418763
[4] Touchard, J. Sur un problème de configurations et sur les fractions continues MathSciNet:0046325
[5] Josuat-Vergès, M., Rubey, M. Crossings, Motzkin paths and moments MathSciNet:2819649
[6] Triangle read by rows: T(n,k) gives number of ways of arranging n chords on a circle with k simple intersections (i.e. no intersections with 3 or more chords) - positive values only. OEIS:A067311
[7] Penaud, J.-G. Une preuve bijective d'une formule de Touchard-Riordan MathSciNet:1336847
Code
def statistic(x): return len(x.crossings())
Created
Mar 01, 2013 at 02:53 by Alejandro Morales
Updated
Dec 25, 2017 at 17:42 by Martin Rubey
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