Identifier
-
Mp00116:
Perfect matchings
—Kasraoui-Zeng⟶
Perfect matchings
St000042: Perfect matchings ⟶ ℤ
Values
[(1,2)] => [(1,2)] => 0
[(1,2),(3,4)] => [(1,2),(3,4)] => 0
[(1,3),(2,4)] => [(1,4),(2,3)] => 0
[(1,4),(2,3)] => [(1,3),(2,4)] => 1
[(1,2),(3,4),(5,6)] => [(1,2),(3,4),(5,6)] => 0
[(1,3),(2,4),(5,6)] => [(1,4),(2,3),(5,6)] => 0
[(1,4),(2,3),(5,6)] => [(1,3),(2,4),(5,6)] => 1
[(1,5),(2,3),(4,6)] => [(1,3),(2,6),(4,5)] => 1
[(1,6),(2,3),(4,5)] => [(1,3),(2,5),(4,6)] => 2
[(1,6),(2,4),(3,5)] => [(1,5),(2,4),(3,6)] => 2
[(1,5),(2,4),(3,6)] => [(1,6),(2,4),(3,5)] => 1
[(1,4),(2,5),(3,6)] => [(1,6),(2,5),(3,4)] => 0
[(1,3),(2,5),(4,6)] => [(1,6),(2,3),(4,5)] => 0
[(1,2),(3,5),(4,6)] => [(1,2),(3,6),(4,5)] => 0
[(1,2),(3,6),(4,5)] => [(1,2),(3,5),(4,6)] => 1
[(1,3),(2,6),(4,5)] => [(1,5),(2,3),(4,6)] => 1
[(1,4),(2,6),(3,5)] => [(1,5),(2,6),(3,4)] => 1
[(1,5),(2,6),(3,4)] => [(1,4),(2,6),(3,5)] => 2
[(1,6),(2,5),(3,4)] => [(1,4),(2,5),(3,6)] => 3
[(1,2),(3,4),(5,6),(7,8)] => [(1,2),(3,4),(5,6),(7,8)] => 0
[(1,3),(2,4),(5,6),(7,8)] => [(1,4),(2,3),(5,6),(7,8)] => 0
[(1,4),(2,3),(5,6),(7,8)] => [(1,3),(2,4),(5,6),(7,8)] => 1
[(1,5),(2,3),(4,6),(7,8)] => [(1,3),(2,6),(4,5),(7,8)] => 1
[(1,6),(2,3),(4,5),(7,8)] => [(1,3),(2,5),(4,6),(7,8)] => 2
[(1,7),(2,3),(4,5),(6,8)] => [(1,3),(2,5),(4,8),(6,7)] => 2
[(1,8),(2,3),(4,5),(6,7)] => [(1,3),(2,5),(4,7),(6,8)] => 3
[(1,8),(2,4),(3,5),(6,7)] => [(1,5),(2,4),(3,7),(6,8)] => 3
[(1,7),(2,4),(3,5),(6,8)] => [(1,5),(2,4),(3,8),(6,7)] => 2
[(1,6),(2,4),(3,5),(7,8)] => [(1,5),(2,4),(3,6),(7,8)] => 2
[(1,5),(2,4),(3,6),(7,8)] => [(1,6),(2,4),(3,5),(7,8)] => 1
[(1,4),(2,5),(3,6),(7,8)] => [(1,6),(2,5),(3,4),(7,8)] => 0
[(1,3),(2,5),(4,6),(7,8)] => [(1,6),(2,3),(4,5),(7,8)] => 0
[(1,2),(3,5),(4,6),(7,8)] => [(1,2),(3,6),(4,5),(7,8)] => 0
[(1,2),(3,6),(4,5),(7,8)] => [(1,2),(3,5),(4,6),(7,8)] => 1
[(1,3),(2,6),(4,5),(7,8)] => [(1,5),(2,3),(4,6),(7,8)] => 1
[(1,4),(2,6),(3,5),(7,8)] => [(1,5),(2,6),(3,4),(7,8)] => 1
[(1,5),(2,6),(3,4),(7,8)] => [(1,4),(2,6),(3,5),(7,8)] => 2
[(1,6),(2,5),(3,4),(7,8)] => [(1,4),(2,5),(3,6),(7,8)] => 3
[(1,7),(2,5),(3,4),(6,8)] => [(1,4),(2,5),(3,8),(6,7)] => 3
[(1,8),(2,5),(3,4),(6,7)] => [(1,4),(2,5),(3,7),(6,8)] => 4
[(1,8),(2,6),(3,4),(5,7)] => [(1,4),(2,7),(3,6),(5,8)] => 4
[(1,7),(2,6),(3,4),(5,8)] => [(1,4),(2,8),(3,6),(5,7)] => 3
[(1,6),(2,7),(3,4),(5,8)] => [(1,4),(2,8),(3,7),(5,6)] => 2
[(1,5),(2,7),(3,4),(6,8)] => [(1,4),(2,8),(3,5),(6,7)] => 2
[(1,4),(2,7),(3,5),(6,8)] => [(1,5),(2,8),(3,4),(6,7)] => 1
[(1,3),(2,7),(4,5),(6,8)] => [(1,5),(2,3),(4,8),(6,7)] => 1
[(1,2),(3,7),(4,5),(6,8)] => [(1,2),(3,5),(4,8),(6,7)] => 1
[(1,2),(3,8),(4,5),(6,7)] => [(1,2),(3,5),(4,7),(6,8)] => 2
[(1,3),(2,8),(4,5),(6,7)] => [(1,5),(2,3),(4,7),(6,8)] => 2
[(1,4),(2,8),(3,5),(6,7)] => [(1,5),(2,7),(3,4),(6,8)] => 2
[(1,5),(2,8),(3,4),(6,7)] => [(1,4),(2,7),(3,5),(6,8)] => 3
[(1,6),(2,8),(3,4),(5,7)] => [(1,4),(2,7),(3,8),(5,6)] => 3
[(1,7),(2,8),(3,4),(5,6)] => [(1,4),(2,6),(3,8),(5,7)] => 4
[(1,8),(2,7),(3,4),(5,6)] => [(1,4),(2,6),(3,7),(5,8)] => 5
[(1,8),(2,7),(3,5),(4,6)] => [(1,6),(2,5),(3,7),(4,8)] => 5
[(1,7),(2,8),(3,5),(4,6)] => [(1,6),(2,5),(3,8),(4,7)] => 4
[(1,6),(2,8),(3,5),(4,7)] => [(1,7),(2,5),(3,8),(4,6)] => 3
[(1,5),(2,8),(3,6),(4,7)] => [(1,7),(2,6),(3,8),(4,5)] => 2
[(1,4),(2,8),(3,6),(5,7)] => [(1,7),(2,6),(3,4),(5,8)] => 2
[(1,3),(2,8),(4,6),(5,7)] => [(1,7),(2,3),(4,6),(5,8)] => 2
[(1,2),(3,8),(4,6),(5,7)] => [(1,2),(3,7),(4,6),(5,8)] => 2
[(1,2),(3,7),(4,6),(5,8)] => [(1,2),(3,8),(4,6),(5,7)] => 1
[(1,3),(2,7),(4,6),(5,8)] => [(1,8),(2,3),(4,6),(5,7)] => 1
[(1,4),(2,7),(3,6),(5,8)] => [(1,8),(2,6),(3,4),(5,7)] => 1
[(1,5),(2,7),(3,6),(4,8)] => [(1,8),(2,6),(3,7),(4,5)] => 1
[(1,6),(2,7),(3,5),(4,8)] => [(1,8),(2,5),(3,7),(4,6)] => 2
[(1,7),(2,6),(3,5),(4,8)] => [(1,8),(2,5),(3,6),(4,7)] => 3
[(1,8),(2,6),(3,5),(4,7)] => [(1,7),(2,5),(3,6),(4,8)] => 4
[(1,8),(2,5),(3,6),(4,7)] => [(1,7),(2,6),(3,5),(4,8)] => 3
[(1,7),(2,5),(3,6),(4,8)] => [(1,8),(2,6),(3,5),(4,7)] => 2
[(1,6),(2,5),(3,7),(4,8)] => [(1,8),(2,7),(3,5),(4,6)] => 1
[(1,5),(2,6),(3,7),(4,8)] => [(1,8),(2,7),(3,6),(4,5)] => 0
[(1,4),(2,6),(3,7),(5,8)] => [(1,8),(2,7),(3,4),(5,6)] => 0
[(1,3),(2,6),(4,7),(5,8)] => [(1,8),(2,3),(4,7),(5,6)] => 0
[(1,2),(3,6),(4,7),(5,8)] => [(1,2),(3,8),(4,7),(5,6)] => 0
[(1,2),(3,5),(4,7),(6,8)] => [(1,2),(3,8),(4,5),(6,7)] => 0
[(1,3),(2,5),(4,7),(6,8)] => [(1,8),(2,3),(4,5),(6,7)] => 0
[(1,4),(2,5),(3,7),(6,8)] => [(1,8),(2,5),(3,4),(6,7)] => 0
[(1,5),(2,4),(3,7),(6,8)] => [(1,8),(2,4),(3,5),(6,7)] => 1
[(1,6),(2,4),(3,7),(5,8)] => [(1,8),(2,4),(3,7),(5,6)] => 1
[(1,7),(2,4),(3,6),(5,8)] => [(1,8),(2,4),(3,6),(5,7)] => 2
[(1,8),(2,4),(3,6),(5,7)] => [(1,7),(2,4),(3,6),(5,8)] => 3
[(1,8),(2,3),(4,6),(5,7)] => [(1,3),(2,7),(4,6),(5,8)] => 3
[(1,7),(2,3),(4,6),(5,8)] => [(1,3),(2,8),(4,6),(5,7)] => 2
[(1,6),(2,3),(4,7),(5,8)] => [(1,3),(2,8),(4,7),(5,6)] => 1
[(1,5),(2,3),(4,7),(6,8)] => [(1,3),(2,8),(4,5),(6,7)] => 1
[(1,4),(2,3),(5,7),(6,8)] => [(1,3),(2,4),(5,8),(6,7)] => 1
[(1,3),(2,4),(5,7),(6,8)] => [(1,4),(2,3),(5,8),(6,7)] => 0
[(1,2),(3,4),(5,7),(6,8)] => [(1,2),(3,4),(5,8),(6,7)] => 0
[(1,2),(3,4),(5,8),(6,7)] => [(1,2),(3,4),(5,7),(6,8)] => 1
[(1,3),(2,4),(5,8),(6,7)] => [(1,4),(2,3),(5,7),(6,8)] => 1
[(1,4),(2,3),(5,8),(6,7)] => [(1,3),(2,4),(5,7),(6,8)] => 2
[(1,5),(2,3),(4,8),(6,7)] => [(1,3),(2,7),(4,5),(6,8)] => 2
[(1,6),(2,3),(4,8),(5,7)] => [(1,3),(2,7),(4,8),(5,6)] => 2
[(1,7),(2,3),(4,8),(5,6)] => [(1,3),(2,6),(4,8),(5,7)] => 3
[(1,8),(2,3),(4,7),(5,6)] => [(1,3),(2,6),(4,7),(5,8)] => 4
[(1,8),(2,4),(3,7),(5,6)] => [(1,6),(2,4),(3,7),(5,8)] => 4
[(1,7),(2,4),(3,8),(5,6)] => [(1,6),(2,4),(3,8),(5,7)] => 3
[(1,6),(2,4),(3,8),(5,7)] => [(1,7),(2,4),(3,8),(5,6)] => 2
[(1,5),(2,4),(3,8),(6,7)] => [(1,7),(2,4),(3,5),(6,8)] => 2
[(1,4),(2,5),(3,8),(6,7)] => [(1,7),(2,5),(3,4),(6,8)] => 1
>>> Load all 1202 entries. <<<[(1,3),(2,5),(4,8),(6,7)] => [(1,7),(2,3),(4,5),(6,8)] => 1
[(1,2),(3,5),(4,8),(6,7)] => [(1,2),(3,7),(4,5),(6,8)] => 1
[(1,2),(3,6),(4,8),(5,7)] => [(1,2),(3,7),(4,8),(5,6)] => 1
[(1,3),(2,6),(4,8),(5,7)] => [(1,7),(2,3),(4,8),(5,6)] => 1
[(1,4),(2,6),(3,8),(5,7)] => [(1,7),(2,8),(3,4),(5,6)] => 1
[(1,5),(2,6),(3,8),(4,7)] => [(1,7),(2,8),(3,6),(4,5)] => 1
[(1,6),(2,5),(3,8),(4,7)] => [(1,7),(2,8),(3,5),(4,6)] => 2
[(1,7),(2,5),(3,8),(4,6)] => [(1,6),(2,8),(3,5),(4,7)] => 3
[(1,8),(2,5),(3,7),(4,6)] => [(1,6),(2,7),(3,5),(4,8)] => 4
[(1,8),(2,6),(3,7),(4,5)] => [(1,5),(2,7),(3,6),(4,8)] => 5
[(1,7),(2,6),(3,8),(4,5)] => [(1,5),(2,8),(3,6),(4,7)] => 4
[(1,6),(2,7),(3,8),(4,5)] => [(1,5),(2,8),(3,7),(4,6)] => 3
[(1,5),(2,7),(3,8),(4,6)] => [(1,6),(2,8),(3,7),(4,5)] => 2
[(1,4),(2,7),(3,8),(5,6)] => [(1,6),(2,8),(3,4),(5,7)] => 2
[(1,3),(2,7),(4,8),(5,6)] => [(1,6),(2,3),(4,8),(5,7)] => 2
[(1,2),(3,7),(4,8),(5,6)] => [(1,2),(3,6),(4,8),(5,7)] => 2
[(1,2),(3,8),(4,7),(5,6)] => [(1,2),(3,6),(4,7),(5,8)] => 3
[(1,3),(2,8),(4,7),(5,6)] => [(1,6),(2,3),(4,7),(5,8)] => 3
[(1,4),(2,8),(3,7),(5,6)] => [(1,6),(2,7),(3,4),(5,8)] => 3
[(1,5),(2,8),(3,7),(4,6)] => [(1,6),(2,7),(3,8),(4,5)] => 3
[(1,6),(2,8),(3,7),(4,5)] => [(1,5),(2,7),(3,8),(4,6)] => 4
[(1,7),(2,8),(3,6),(4,5)] => [(1,5),(2,6),(3,8),(4,7)] => 5
[(1,8),(2,7),(3,6),(4,5)] => [(1,5),(2,6),(3,7),(4,8)] => 6
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 0
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 0
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [(1,3),(2,4),(5,6),(7,8),(9,10)] => 1
[(1,5),(2,3),(4,6),(7,8),(9,10)] => [(1,3),(2,6),(4,5),(7,8),(9,10)] => 1
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [(1,3),(2,5),(4,6),(7,8),(9,10)] => 2
[(1,7),(2,3),(4,5),(6,8),(9,10)] => [(1,3),(2,5),(4,8),(6,7),(9,10)] => 2
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [(1,3),(2,5),(4,7),(6,8),(9,10)] => 3
[(1,9),(2,3),(4,5),(6,7),(8,10)] => [(1,3),(2,5),(4,7),(6,10),(8,9)] => 3
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [(1,3),(2,5),(4,7),(6,9),(8,10)] => 4
[(1,10),(2,4),(3,5),(6,7),(8,9)] => [(1,5),(2,4),(3,7),(6,9),(8,10)] => 4
[(1,9),(2,4),(3,5),(6,7),(8,10)] => [(1,5),(2,4),(3,7),(6,10),(8,9)] => 3
[(1,8),(2,4),(3,5),(6,7),(9,10)] => [(1,5),(2,4),(3,7),(6,8),(9,10)] => 3
[(1,7),(2,4),(3,5),(6,8),(9,10)] => [(1,5),(2,4),(3,8),(6,7),(9,10)] => 2
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [(1,5),(2,4),(3,6),(7,8),(9,10)] => 2
[(1,5),(2,4),(3,6),(7,8),(9,10)] => [(1,6),(2,4),(3,5),(7,8),(9,10)] => 1
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 0
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [(1,2),(3,5),(4,6),(7,8),(9,10)] => 1
[(1,3),(2,6),(4,5),(7,8),(9,10)] => [(1,5),(2,3),(4,6),(7,8),(9,10)] => 1
[(1,4),(2,6),(3,5),(7,8),(9,10)] => [(1,5),(2,6),(3,4),(7,8),(9,10)] => 1
[(1,5),(2,6),(3,4),(7,8),(9,10)] => [(1,4),(2,6),(3,5),(7,8),(9,10)] => 2
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [(1,4),(2,5),(3,6),(7,8),(9,10)] => 3
[(1,7),(2,5),(3,4),(6,8),(9,10)] => [(1,4),(2,5),(3,8),(6,7),(9,10)] => 3
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [(1,4),(2,5),(3,7),(6,8),(9,10)] => 4
[(1,9),(2,5),(3,4),(6,7),(8,10)] => [(1,4),(2,5),(3,7),(6,10),(8,9)] => 4
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [(1,4),(2,5),(3,7),(6,9),(8,10)] => 5
[(1,10),(2,6),(3,4),(5,7),(8,9)] => [(1,4),(2,7),(3,6),(5,9),(8,10)] => 5
[(1,9),(2,6),(3,4),(5,7),(8,10)] => [(1,4),(2,7),(3,6),(5,10),(8,9)] => 4
[(1,8),(2,6),(3,4),(5,7),(9,10)] => [(1,4),(2,7),(3,6),(5,8),(9,10)] => 4
[(1,7),(2,6),(3,4),(5,8),(9,10)] => [(1,4),(2,8),(3,6),(5,7),(9,10)] => 3
[(1,6),(2,7),(3,4),(5,8),(9,10)] => [(1,4),(2,8),(3,7),(5,6),(9,10)] => 2
[(1,5),(2,7),(3,4),(6,8),(9,10)] => [(1,4),(2,8),(3,5),(6,7),(9,10)] => 2
[(1,4),(2,7),(3,5),(6,8),(9,10)] => [(1,5),(2,8),(3,4),(6,7),(9,10)] => 1
[(1,3),(2,7),(4,5),(6,8),(9,10)] => [(1,5),(2,3),(4,8),(6,7),(9,10)] => 1
[(1,2),(3,7),(4,5),(6,8),(9,10)] => [(1,2),(3,5),(4,8),(6,7),(9,10)] => 1
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [(1,2),(3,5),(4,7),(6,8),(9,10)] => 2
[(1,3),(2,8),(4,5),(6,7),(9,10)] => [(1,5),(2,3),(4,7),(6,8),(9,10)] => 2
[(1,4),(2,8),(3,5),(6,7),(9,10)] => [(1,5),(2,7),(3,4),(6,8),(9,10)] => 2
[(1,5),(2,8),(3,4),(6,7),(9,10)] => [(1,4),(2,7),(3,5),(6,8),(9,10)] => 3
[(1,6),(2,8),(3,4),(5,7),(9,10)] => [(1,4),(2,7),(3,8),(5,6),(9,10)] => 3
[(1,7),(2,8),(3,4),(5,6),(9,10)] => [(1,4),(2,6),(3,8),(5,7),(9,10)] => 4
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [(1,4),(2,6),(3,7),(5,8),(9,10)] => 5
[(1,9),(2,7),(3,4),(5,6),(8,10)] => [(1,4),(2,6),(3,7),(5,10),(8,9)] => 5
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [(1,4),(2,6),(3,7),(5,9),(8,10)] => 6
[(1,10),(2,8),(3,4),(5,6),(7,9)] => [(1,4),(2,6),(3,9),(5,8),(7,10)] => 6
[(1,9),(2,8),(3,4),(5,6),(7,10)] => [(1,4),(2,6),(3,10),(5,8),(7,9)] => 5
[(1,8),(2,9),(3,4),(5,6),(7,10)] => [(1,4),(2,6),(3,10),(5,9),(7,8)] => 4
[(1,7),(2,9),(3,4),(5,6),(8,10)] => [(1,4),(2,6),(3,10),(5,7),(8,9)] => 4
[(1,6),(2,9),(3,4),(5,7),(8,10)] => [(1,4),(2,7),(3,10),(5,6),(8,9)] => 3
[(1,5),(2,9),(3,4),(6,7),(8,10)] => [(1,4),(2,7),(3,5),(6,10),(8,9)] => 3
[(1,4),(2,9),(3,5),(6,7),(8,10)] => [(1,5),(2,7),(3,4),(6,10),(8,9)] => 2
[(1,3),(2,9),(4,5),(6,7),(8,10)] => [(1,5),(2,3),(4,7),(6,10),(8,9)] => 2
[(1,2),(3,9),(4,5),(6,7),(8,10)] => [(1,2),(3,5),(4,7),(6,10),(8,9)] => 2
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [(1,2),(3,5),(4,7),(6,9),(8,10)] => 3
[(1,3),(2,10),(4,5),(6,7),(8,9)] => [(1,5),(2,3),(4,7),(6,9),(8,10)] => 3
[(1,4),(2,10),(3,5),(6,7),(8,9)] => [(1,5),(2,7),(3,4),(6,9),(8,10)] => 3
[(1,5),(2,10),(3,4),(6,7),(8,9)] => [(1,4),(2,7),(3,5),(6,9),(8,10)] => 4
[(1,6),(2,10),(3,4),(5,7),(8,9)] => [(1,4),(2,7),(3,9),(5,6),(8,10)] => 4
[(1,7),(2,10),(3,4),(5,6),(8,9)] => [(1,4),(2,6),(3,9),(5,7),(8,10)] => 5
[(1,8),(2,10),(3,4),(5,6),(7,9)] => [(1,4),(2,6),(3,9),(5,10),(7,8)] => 5
[(1,9),(2,10),(3,4),(5,6),(7,8)] => [(1,4),(2,6),(3,8),(5,10),(7,9)] => 6
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [(1,4),(2,6),(3,8),(5,9),(7,10)] => 7
[(1,10),(2,9),(3,5),(4,6),(7,8)] => [(1,6),(2,5),(3,8),(4,9),(7,10)] => 7
[(1,9),(2,10),(3,5),(4,6),(7,8)] => [(1,6),(2,5),(3,8),(4,10),(7,9)] => 6
[(1,8),(2,10),(3,5),(4,6),(7,9)] => [(1,6),(2,5),(3,9),(4,10),(7,8)] => 5
[(1,7),(2,10),(3,5),(4,6),(8,9)] => [(1,6),(2,5),(3,9),(4,7),(8,10)] => 5
[(1,6),(2,10),(3,5),(4,7),(8,9)] => [(1,7),(2,5),(3,9),(4,6),(8,10)] => 4
[(1,5),(2,10),(3,6),(4,7),(8,9)] => [(1,7),(2,6),(3,9),(4,5),(8,10)] => 3
[(1,4),(2,10),(3,6),(5,7),(8,9)] => [(1,7),(2,6),(3,4),(5,9),(8,10)] => 3
[(1,3),(2,10),(4,6),(5,7),(8,9)] => [(1,7),(2,3),(4,6),(5,9),(8,10)] => 3
[(1,2),(3,10),(4,6),(5,7),(8,9)] => [(1,2),(3,7),(4,6),(5,9),(8,10)] => 3
[(1,2),(3,9),(4,6),(5,7),(8,10)] => [(1,2),(3,7),(4,6),(5,10),(8,9)] => 2
[(1,3),(2,9),(4,6),(5,7),(8,10)] => [(1,7),(2,3),(4,6),(5,10),(8,9)] => 2
[(1,4),(2,9),(3,6),(5,7),(8,10)] => [(1,7),(2,6),(3,4),(5,10),(8,9)] => 2
[(1,5),(2,9),(3,6),(4,7),(8,10)] => [(1,7),(2,6),(3,10),(4,5),(8,9)] => 2
[(1,6),(2,9),(3,5),(4,7),(8,10)] => [(1,7),(2,5),(3,10),(4,6),(8,9)] => 3
[(1,7),(2,9),(3,5),(4,6),(8,10)] => [(1,6),(2,5),(3,10),(4,7),(8,9)] => 4
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [(1,6),(2,5),(3,10),(4,9),(7,8)] => 4
[(1,9),(2,8),(3,5),(4,6),(7,10)] => [(1,6),(2,5),(3,10),(4,8),(7,9)] => 5
[(1,10),(2,8),(3,5),(4,6),(7,9)] => [(1,6),(2,5),(3,9),(4,8),(7,10)] => 6
[(1,10),(2,7),(3,5),(4,6),(8,9)] => [(1,6),(2,5),(3,7),(4,9),(8,10)] => 6
[(1,9),(2,7),(3,5),(4,6),(8,10)] => [(1,6),(2,5),(3,7),(4,10),(8,9)] => 5
[(1,8),(2,7),(3,5),(4,6),(9,10)] => [(1,6),(2,5),(3,7),(4,8),(9,10)] => 5
[(1,7),(2,8),(3,5),(4,6),(9,10)] => [(1,6),(2,5),(3,8),(4,7),(9,10)] => 4
[(1,6),(2,8),(3,5),(4,7),(9,10)] => [(1,7),(2,5),(3,8),(4,6),(9,10)] => 3
[(1,5),(2,8),(3,6),(4,7),(9,10)] => [(1,7),(2,6),(3,8),(4,5),(9,10)] => 2
[(1,4),(2,8),(3,6),(5,7),(9,10)] => [(1,7),(2,6),(3,4),(5,8),(9,10)] => 2
[(1,3),(2,8),(4,6),(5,7),(9,10)] => [(1,7),(2,3),(4,6),(5,8),(9,10)] => 2
[(1,2),(3,8),(4,6),(5,7),(9,10)] => [(1,2),(3,7),(4,6),(5,8),(9,10)] => 2
[(1,2),(3,7),(4,6),(5,8),(9,10)] => [(1,2),(3,8),(4,6),(5,7),(9,10)] => 1
[(1,3),(2,7),(4,6),(5,8),(9,10)] => [(1,8),(2,3),(4,6),(5,7),(9,10)] => 1
[(1,4),(2,7),(3,6),(5,8),(9,10)] => [(1,8),(2,6),(3,4),(5,7),(9,10)] => 1
[(1,5),(2,7),(3,6),(4,8),(9,10)] => [(1,8),(2,6),(3,7),(4,5),(9,10)] => 1
[(1,6),(2,7),(3,5),(4,8),(9,10)] => [(1,8),(2,5),(3,7),(4,6),(9,10)] => 2
[(1,7),(2,6),(3,5),(4,8),(9,10)] => [(1,8),(2,5),(3,6),(4,7),(9,10)] => 3
[(1,8),(2,6),(3,5),(4,7),(9,10)] => [(1,7),(2,5),(3,6),(4,8),(9,10)] => 4
[(1,9),(2,6),(3,5),(4,7),(8,10)] => [(1,7),(2,5),(3,6),(4,10),(8,9)] => 4
[(1,10),(2,6),(3,5),(4,7),(8,9)] => [(1,7),(2,5),(3,6),(4,9),(8,10)] => 5
[(1,10),(2,5),(3,6),(4,7),(8,9)] => [(1,7),(2,6),(3,5),(4,9),(8,10)] => 4
[(1,9),(2,5),(3,6),(4,7),(8,10)] => [(1,7),(2,6),(3,5),(4,10),(8,9)] => 3
[(1,8),(2,5),(3,6),(4,7),(9,10)] => [(1,7),(2,6),(3,5),(4,8),(9,10)] => 3
[(1,7),(2,5),(3,6),(4,8),(9,10)] => [(1,8),(2,6),(3,5),(4,7),(9,10)] => 2
[(1,6),(2,5),(3,7),(4,8),(9,10)] => [(1,8),(2,7),(3,5),(4,6),(9,10)] => 1
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[(1,5),(2,4),(3,7),(6,8),(9,10)] => [(1,8),(2,4),(3,5),(6,7),(9,10)] => 1
[(1,6),(2,4),(3,7),(5,8),(9,10)] => [(1,8),(2,4),(3,7),(5,6),(9,10)] => 1
[(1,7),(2,4),(3,6),(5,8),(9,10)] => [(1,8),(2,4),(3,6),(5,7),(9,10)] => 2
[(1,8),(2,4),(3,6),(5,7),(9,10)] => [(1,7),(2,4),(3,6),(5,8),(9,10)] => 3
[(1,9),(2,4),(3,6),(5,7),(8,10)] => [(1,7),(2,4),(3,6),(5,10),(8,9)] => 3
[(1,10),(2,4),(3,6),(5,7),(8,9)] => [(1,7),(2,4),(3,6),(5,9),(8,10)] => 4
[(1,10),(2,3),(4,6),(5,7),(8,9)] => [(1,3),(2,7),(4,6),(5,9),(8,10)] => 4
[(1,9),(2,3),(4,6),(5,7),(8,10)] => [(1,3),(2,7),(4,6),(5,10),(8,9)] => 3
[(1,8),(2,3),(4,6),(5,7),(9,10)] => [(1,3),(2,7),(4,6),(5,8),(9,10)] => 3
[(1,7),(2,3),(4,6),(5,8),(9,10)] => [(1,3),(2,8),(4,6),(5,7),(9,10)] => 2
[(1,6),(2,3),(4,7),(5,8),(9,10)] => [(1,3),(2,8),(4,7),(5,6),(9,10)] => 1
[(1,5),(2,3),(4,7),(6,8),(9,10)] => [(1,3),(2,8),(4,5),(6,7),(9,10)] => 1
[(1,4),(2,3),(5,7),(6,8),(9,10)] => [(1,3),(2,4),(5,8),(6,7),(9,10)] => 1
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 0
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [(1,2),(3,4),(5,7),(6,8),(9,10)] => 1
[(1,3),(2,4),(5,8),(6,7),(9,10)] => [(1,4),(2,3),(5,7),(6,8),(9,10)] => 1
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [(1,3),(2,4),(5,7),(6,8),(9,10)] => 2
[(1,5),(2,3),(4,8),(6,7),(9,10)] => [(1,3),(2,7),(4,5),(6,8),(9,10)] => 2
[(1,6),(2,3),(4,8),(5,7),(9,10)] => [(1,3),(2,7),(4,8),(5,6),(9,10)] => 2
[(1,7),(2,3),(4,8),(5,6),(9,10)] => [(1,3),(2,6),(4,8),(5,7),(9,10)] => 3
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [(1,3),(2,6),(4,7),(5,8),(9,10)] => 4
[(1,9),(2,3),(4,7),(5,6),(8,10)] => [(1,3),(2,6),(4,7),(5,10),(8,9)] => 4
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [(1,3),(2,6),(4,7),(5,9),(8,10)] => 5
[(1,10),(2,4),(3,7),(5,6),(8,9)] => [(1,6),(2,4),(3,7),(5,9),(8,10)] => 5
[(1,9),(2,4),(3,7),(5,6),(8,10)] => [(1,6),(2,4),(3,7),(5,10),(8,9)] => 4
[(1,8),(2,4),(3,7),(5,6),(9,10)] => [(1,6),(2,4),(3,7),(5,8),(9,10)] => 4
[(1,7),(2,4),(3,8),(5,6),(9,10)] => [(1,6),(2,4),(3,8),(5,7),(9,10)] => 3
[(1,6),(2,4),(3,8),(5,7),(9,10)] => [(1,7),(2,4),(3,8),(5,6),(9,10)] => 2
[(1,5),(2,4),(3,8),(6,7),(9,10)] => [(1,7),(2,4),(3,5),(6,8),(9,10)] => 2
[(1,4),(2,5),(3,8),(6,7),(9,10)] => [(1,7),(2,5),(3,4),(6,8),(9,10)] => 1
[(1,3),(2,5),(4,8),(6,7),(9,10)] => [(1,7),(2,3),(4,5),(6,8),(9,10)] => 1
[(1,2),(3,5),(4,8),(6,7),(9,10)] => [(1,2),(3,7),(4,5),(6,8),(9,10)] => 1
[(1,2),(3,6),(4,8),(5,7),(9,10)] => [(1,2),(3,7),(4,8),(5,6),(9,10)] => 1
[(1,3),(2,6),(4,8),(5,7),(9,10)] => [(1,7),(2,3),(4,8),(5,6),(9,10)] => 1
[(1,4),(2,6),(3,8),(5,7),(9,10)] => [(1,7),(2,8),(3,4),(5,6),(9,10)] => 1
[(1,5),(2,6),(3,8),(4,7),(9,10)] => [(1,7),(2,8),(3,6),(4,5),(9,10)] => 1
[(1,6),(2,5),(3,8),(4,7),(9,10)] => [(1,7),(2,8),(3,5),(4,6),(9,10)] => 2
[(1,7),(2,5),(3,8),(4,6),(9,10)] => [(1,6),(2,8),(3,5),(4,7),(9,10)] => 3
[(1,8),(2,5),(3,7),(4,6),(9,10)] => [(1,6),(2,7),(3,5),(4,8),(9,10)] => 4
[(1,9),(2,5),(3,7),(4,6),(8,10)] => [(1,6),(2,7),(3,5),(4,10),(8,9)] => 4
[(1,10),(2,5),(3,7),(4,6),(8,9)] => [(1,6),(2,7),(3,5),(4,9),(8,10)] => 5
[(1,10),(2,6),(3,7),(4,5),(8,9)] => [(1,5),(2,7),(3,6),(4,9),(8,10)] => 6
[(1,9),(2,6),(3,7),(4,5),(8,10)] => [(1,5),(2,7),(3,6),(4,10),(8,9)] => 5
[(1,8),(2,6),(3,7),(4,5),(9,10)] => [(1,5),(2,7),(3,6),(4,8),(9,10)] => 5
[(1,7),(2,6),(3,8),(4,5),(9,10)] => [(1,5),(2,8),(3,6),(4,7),(9,10)] => 4
[(1,6),(2,7),(3,8),(4,5),(9,10)] => [(1,5),(2,8),(3,7),(4,6),(9,10)] => 3
[(1,5),(2,7),(3,8),(4,6),(9,10)] => [(1,6),(2,8),(3,7),(4,5),(9,10)] => 2
[(1,4),(2,7),(3,8),(5,6),(9,10)] => [(1,6),(2,8),(3,4),(5,7),(9,10)] => 2
[(1,3),(2,7),(4,8),(5,6),(9,10)] => [(1,6),(2,3),(4,8),(5,7),(9,10)] => 2
[(1,2),(3,7),(4,8),(5,6),(9,10)] => [(1,2),(3,6),(4,8),(5,7),(9,10)] => 2
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [(1,2),(3,6),(4,7),(5,8),(9,10)] => 3
[(1,3),(2,8),(4,7),(5,6),(9,10)] => [(1,6),(2,3),(4,7),(5,8),(9,10)] => 3
[(1,4),(2,8),(3,7),(5,6),(9,10)] => [(1,6),(2,7),(3,4),(5,8),(9,10)] => 3
[(1,5),(2,8),(3,7),(4,6),(9,10)] => [(1,6),(2,7),(3,8),(4,5),(9,10)] => 3
[(1,6),(2,8),(3,7),(4,5),(9,10)] => [(1,5),(2,7),(3,8),(4,6),(9,10)] => 4
[(1,7),(2,8),(3,6),(4,5),(9,10)] => [(1,5),(2,6),(3,8),(4,7),(9,10)] => 5
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [(1,5),(2,6),(3,7),(4,8),(9,10)] => 6
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [(1,5),(2,6),(3,7),(4,10),(8,9)] => 6
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [(1,5),(2,6),(3,7),(4,9),(8,10)] => 7
[(1,10),(2,8),(3,6),(4,5),(7,9)] => [(1,5),(2,6),(3,9),(4,8),(7,10)] => 7
[(1,9),(2,8),(3,6),(4,5),(7,10)] => [(1,5),(2,6),(3,10),(4,8),(7,9)] => 6
[(1,8),(2,9),(3,6),(4,5),(7,10)] => [(1,5),(2,6),(3,10),(4,9),(7,8)] => 5
[(1,7),(2,9),(3,6),(4,5),(8,10)] => [(1,5),(2,6),(3,10),(4,7),(8,9)] => 5
[(1,6),(2,9),(3,7),(4,5),(8,10)] => [(1,5),(2,7),(3,10),(4,6),(8,9)] => 4
[(1,5),(2,9),(3,7),(4,6),(8,10)] => [(1,6),(2,7),(3,10),(4,5),(8,9)] => 3
[(1,4),(2,9),(3,7),(5,6),(8,10)] => [(1,6),(2,7),(3,4),(5,10),(8,9)] => 3
[(1,3),(2,9),(4,7),(5,6),(8,10)] => [(1,6),(2,3),(4,7),(5,10),(8,9)] => 3
[(1,2),(3,9),(4,7),(5,6),(8,10)] => [(1,2),(3,6),(4,7),(5,10),(8,9)] => 3
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [(1,2),(3,6),(4,7),(5,9),(8,10)] => 4
[(1,3),(2,10),(4,7),(5,6),(8,9)] => [(1,6),(2,3),(4,7),(5,9),(8,10)] => 4
[(1,4),(2,10),(3,7),(5,6),(8,9)] => [(1,6),(2,7),(3,4),(5,9),(8,10)] => 4
[(1,5),(2,10),(3,7),(4,6),(8,9)] => [(1,6),(2,7),(3,9),(4,5),(8,10)] => 4
[(1,6),(2,10),(3,7),(4,5),(8,9)] => [(1,5),(2,7),(3,9),(4,6),(8,10)] => 5
[(1,7),(2,10),(3,6),(4,5),(8,9)] => [(1,5),(2,6),(3,9),(4,7),(8,10)] => 6
[(1,8),(2,10),(3,6),(4,5),(7,9)] => [(1,5),(2,6),(3,9),(4,10),(7,8)] => 6
[(1,9),(2,10),(3,6),(4,5),(7,8)] => [(1,5),(2,6),(3,8),(4,10),(7,9)] => 7
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [(1,5),(2,6),(3,8),(4,9),(7,10)] => 8
[(1,10),(2,9),(3,7),(4,5),(6,8)] => [(1,5),(2,8),(3,7),(4,9),(6,10)] => 8
[(1,9),(2,10),(3,7),(4,5),(6,8)] => [(1,5),(2,8),(3,7),(4,10),(6,9)] => 7
[(1,8),(2,10),(3,7),(4,5),(6,9)] => [(1,5),(2,9),(3,7),(4,10),(6,8)] => 6
[(1,7),(2,10),(3,8),(4,5),(6,9)] => [(1,5),(2,9),(3,8),(4,10),(6,7)] => 5
[(1,6),(2,10),(3,8),(4,5),(7,9)] => [(1,5),(2,9),(3,8),(4,6),(7,10)] => 5
[(1,5),(2,10),(3,8),(4,6),(7,9)] => [(1,6),(2,9),(3,8),(4,5),(7,10)] => 4
[(1,4),(2,10),(3,8),(5,6),(7,9)] => [(1,6),(2,9),(3,4),(5,8),(7,10)] => 4
[(1,3),(2,10),(4,8),(5,6),(7,9)] => [(1,6),(2,3),(4,9),(5,8),(7,10)] => 4
[(1,2),(3,10),(4,8),(5,6),(7,9)] => [(1,2),(3,6),(4,9),(5,8),(7,10)] => 4
[(1,2),(3,9),(4,8),(5,6),(7,10)] => [(1,2),(3,6),(4,10),(5,8),(7,9)] => 3
[(1,3),(2,9),(4,8),(5,6),(7,10)] => [(1,6),(2,3),(4,10),(5,8),(7,9)] => 3
[(1,4),(2,9),(3,8),(5,6),(7,10)] => [(1,6),(2,10),(3,4),(5,8),(7,9)] => 3
[(1,5),(2,9),(3,8),(4,6),(7,10)] => [(1,6),(2,10),(3,8),(4,5),(7,9)] => 3
[(1,6),(2,9),(3,8),(4,5),(7,10)] => [(1,5),(2,10),(3,8),(4,6),(7,9)] => 4
[(1,7),(2,9),(3,8),(4,5),(6,10)] => [(1,5),(2,10),(3,8),(4,9),(6,7)] => 4
[(1,8),(2,9),(3,7),(4,5),(6,10)] => [(1,5),(2,10),(3,7),(4,9),(6,8)] => 5
[(1,9),(2,8),(3,7),(4,5),(6,10)] => [(1,5),(2,10),(3,7),(4,8),(6,9)] => 6
[(1,10),(2,8),(3,7),(4,5),(6,9)] => [(1,5),(2,9),(3,7),(4,8),(6,10)] => 7
[(1,10),(2,7),(3,8),(4,5),(6,9)] => [(1,5),(2,9),(3,8),(4,7),(6,10)] => 6
[(1,9),(2,7),(3,8),(4,5),(6,10)] => [(1,5),(2,10),(3,8),(4,7),(6,9)] => 5
[(1,8),(2,7),(3,9),(4,5),(6,10)] => [(1,5),(2,10),(3,9),(4,7),(6,8)] => 4
[(1,7),(2,8),(3,9),(4,5),(6,10)] => [(1,5),(2,10),(3,9),(4,8),(6,7)] => 3
[(1,6),(2,8),(3,9),(4,5),(7,10)] => [(1,5),(2,10),(3,9),(4,6),(7,8)] => 3
[(1,5),(2,8),(3,9),(4,6),(7,10)] => [(1,6),(2,10),(3,9),(4,5),(7,8)] => 2
[(1,4),(2,8),(3,9),(5,6),(7,10)] => [(1,6),(2,10),(3,4),(5,9),(7,8)] => 2
[(1,3),(2,8),(4,9),(5,6),(7,10)] => [(1,6),(2,3),(4,10),(5,9),(7,8)] => 2
[(1,2),(3,8),(4,9),(5,6),(7,10)] => [(1,2),(3,6),(4,10),(5,9),(7,8)] => 2
[(1,2),(3,7),(4,9),(5,6),(8,10)] => [(1,2),(3,6),(4,10),(5,7),(8,9)] => 2
[(1,3),(2,7),(4,9),(5,6),(8,10)] => [(1,6),(2,3),(4,10),(5,7),(8,9)] => 2
[(1,4),(2,7),(3,9),(5,6),(8,10)] => [(1,6),(2,10),(3,4),(5,7),(8,9)] => 2
[(1,5),(2,7),(3,9),(4,6),(8,10)] => [(1,6),(2,10),(3,7),(4,5),(8,9)] => 2
[(1,6),(2,7),(3,9),(4,5),(8,10)] => [(1,5),(2,10),(3,7),(4,6),(8,9)] => 3
[(1,7),(2,6),(3,9),(4,5),(8,10)] => [(1,5),(2,10),(3,6),(4,7),(8,9)] => 4
[(1,8),(2,6),(3,9),(4,5),(7,10)] => [(1,5),(2,10),(3,6),(4,9),(7,8)] => 4
[(1,9),(2,6),(3,8),(4,5),(7,10)] => [(1,5),(2,10),(3,6),(4,8),(7,9)] => 5
[(1,10),(2,6),(3,8),(4,5),(7,9)] => [(1,5),(2,9),(3,6),(4,8),(7,10)] => 6
[(1,10),(2,5),(3,8),(4,6),(7,9)] => [(1,6),(2,9),(3,5),(4,8),(7,10)] => 5
[(1,9),(2,5),(3,8),(4,6),(7,10)] => [(1,6),(2,10),(3,5),(4,8),(7,9)] => 4
[(1,8),(2,5),(3,9),(4,6),(7,10)] => [(1,6),(2,10),(3,5),(4,9),(7,8)] => 3
[(1,7),(2,5),(3,9),(4,6),(8,10)] => [(1,6),(2,10),(3,5),(4,7),(8,9)] => 3
[(1,6),(2,5),(3,9),(4,7),(8,10)] => [(1,7),(2,10),(3,5),(4,6),(8,9)] => 2
[(1,5),(2,6),(3,9),(4,7),(8,10)] => [(1,7),(2,10),(3,6),(4,5),(8,9)] => 1
[(1,4),(2,6),(3,9),(5,7),(8,10)] => [(1,7),(2,10),(3,4),(5,6),(8,9)] => 1
[(1,3),(2,6),(4,9),(5,7),(8,10)] => [(1,7),(2,3),(4,10),(5,6),(8,9)] => 1
[(1,2),(3,6),(4,9),(5,7),(8,10)] => [(1,2),(3,7),(4,10),(5,6),(8,9)] => 1
[(1,2),(3,5),(4,9),(6,7),(8,10)] => [(1,2),(3,7),(4,5),(6,10),(8,9)] => 1
[(1,3),(2,5),(4,9),(6,7),(8,10)] => [(1,7),(2,3),(4,5),(6,10),(8,9)] => 1
[(1,4),(2,5),(3,9),(6,7),(8,10)] => [(1,7),(2,5),(3,4),(6,10),(8,9)] => 1
[(1,5),(2,4),(3,9),(6,7),(8,10)] => [(1,7),(2,4),(3,5),(6,10),(8,9)] => 2
[(1,6),(2,4),(3,9),(5,7),(8,10)] => [(1,7),(2,4),(3,10),(5,6),(8,9)] => 2
[(1,7),(2,4),(3,9),(5,6),(8,10)] => [(1,6),(2,4),(3,10),(5,7),(8,9)] => 3
[(1,8),(2,4),(3,9),(5,6),(7,10)] => [(1,6),(2,4),(3,10),(5,9),(7,8)] => 3
[(1,9),(2,4),(3,8),(5,6),(7,10)] => [(1,6),(2,4),(3,10),(5,8),(7,9)] => 4
[(1,10),(2,4),(3,8),(5,6),(7,9)] => [(1,6),(2,4),(3,9),(5,8),(7,10)] => 5
[(1,10),(2,3),(4,8),(5,6),(7,9)] => [(1,3),(2,6),(4,9),(5,8),(7,10)] => 5
[(1,9),(2,3),(4,8),(5,6),(7,10)] => [(1,3),(2,6),(4,10),(5,8),(7,9)] => 4
[(1,8),(2,3),(4,9),(5,6),(7,10)] => [(1,3),(2,6),(4,10),(5,9),(7,8)] => 3
[(1,7),(2,3),(4,9),(5,6),(8,10)] => [(1,3),(2,6),(4,10),(5,7),(8,9)] => 3
[(1,6),(2,3),(4,9),(5,7),(8,10)] => [(1,3),(2,7),(4,10),(5,6),(8,9)] => 2
[(1,5),(2,3),(4,9),(6,7),(8,10)] => [(1,3),(2,7),(4,5),(6,10),(8,9)] => 2
[(1,4),(2,3),(5,9),(6,7),(8,10)] => [(1,3),(2,4),(5,7),(6,10),(8,9)] => 2
[(1,3),(2,4),(5,9),(6,7),(8,10)] => [(1,4),(2,3),(5,7),(6,10),(8,9)] => 1
[(1,2),(3,4),(5,9),(6,7),(8,10)] => [(1,2),(3,4),(5,7),(6,10),(8,9)] => 1
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [(1,2),(3,4),(5,7),(6,9),(8,10)] => 2
[(1,3),(2,4),(5,10),(6,7),(8,9)] => [(1,4),(2,3),(5,7),(6,9),(8,10)] => 2
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [(1,3),(2,4),(5,7),(6,9),(8,10)] => 3
[(1,5),(2,3),(4,10),(6,7),(8,9)] => [(1,3),(2,7),(4,5),(6,9),(8,10)] => 3
[(1,6),(2,3),(4,10),(5,7),(8,9)] => [(1,3),(2,7),(4,9),(5,6),(8,10)] => 3
[(1,7),(2,3),(4,10),(5,6),(8,9)] => [(1,3),(2,6),(4,9),(5,7),(8,10)] => 4
[(1,8),(2,3),(4,10),(5,6),(7,9)] => [(1,3),(2,6),(4,9),(5,10),(7,8)] => 4
[(1,9),(2,3),(4,10),(5,6),(7,8)] => [(1,3),(2,6),(4,8),(5,10),(7,9)] => 5
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [(1,3),(2,6),(4,8),(5,9),(7,10)] => 6
[(1,10),(2,4),(3,9),(5,6),(7,8)] => [(1,6),(2,4),(3,8),(5,9),(7,10)] => 6
[(1,9),(2,4),(3,10),(5,6),(7,8)] => [(1,6),(2,4),(3,8),(5,10),(7,9)] => 5
[(1,8),(2,4),(3,10),(5,6),(7,9)] => [(1,6),(2,4),(3,9),(5,10),(7,8)] => 4
[(1,7),(2,4),(3,10),(5,6),(8,9)] => [(1,6),(2,4),(3,9),(5,7),(8,10)] => 4
[(1,6),(2,4),(3,10),(5,7),(8,9)] => [(1,7),(2,4),(3,9),(5,6),(8,10)] => 3
[(1,5),(2,4),(3,10),(6,7),(8,9)] => [(1,7),(2,4),(3,5),(6,9),(8,10)] => 3
[(1,4),(2,5),(3,10),(6,7),(8,9)] => [(1,7),(2,5),(3,4),(6,9),(8,10)] => 2
[(1,3),(2,5),(4,10),(6,7),(8,9)] => [(1,7),(2,3),(4,5),(6,9),(8,10)] => 2
[(1,2),(3,5),(4,10),(6,7),(8,9)] => [(1,2),(3,7),(4,5),(6,9),(8,10)] => 2
[(1,2),(3,6),(4,10),(5,7),(8,9)] => [(1,2),(3,7),(4,9),(5,6),(8,10)] => 2
[(1,3),(2,6),(4,10),(5,7),(8,9)] => [(1,7),(2,3),(4,9),(5,6),(8,10)] => 2
[(1,4),(2,6),(3,10),(5,7),(8,9)] => [(1,7),(2,9),(3,4),(5,6),(8,10)] => 2
[(1,5),(2,6),(3,10),(4,7),(8,9)] => [(1,7),(2,9),(3,6),(4,5),(8,10)] => 2
[(1,6),(2,5),(3,10),(4,7),(8,9)] => [(1,7),(2,9),(3,5),(4,6),(8,10)] => 3
[(1,7),(2,5),(3,10),(4,6),(8,9)] => [(1,6),(2,9),(3,5),(4,7),(8,10)] => 4
[(1,8),(2,5),(3,10),(4,6),(7,9)] => [(1,6),(2,9),(3,5),(4,10),(7,8)] => 4
[(1,9),(2,5),(3,10),(4,6),(7,8)] => [(1,6),(2,8),(3,5),(4,10),(7,9)] => 5
[(1,10),(2,5),(3,9),(4,6),(7,8)] => [(1,6),(2,8),(3,5),(4,9),(7,10)] => 6
[(1,10),(2,6),(3,9),(4,5),(7,8)] => [(1,5),(2,8),(3,6),(4,9),(7,10)] => 7
[(1,9),(2,6),(3,10),(4,5),(7,8)] => [(1,5),(2,8),(3,6),(4,10),(7,9)] => 6
[(1,8),(2,6),(3,10),(4,5),(7,9)] => [(1,5),(2,9),(3,6),(4,10),(7,8)] => 5
[(1,7),(2,6),(3,10),(4,5),(8,9)] => [(1,5),(2,9),(3,6),(4,7),(8,10)] => 5
[(1,6),(2,7),(3,10),(4,5),(8,9)] => [(1,5),(2,9),(3,7),(4,6),(8,10)] => 4
[(1,5),(2,7),(3,10),(4,6),(8,9)] => [(1,6),(2,9),(3,7),(4,5),(8,10)] => 3
[(1,4),(2,7),(3,10),(5,6),(8,9)] => [(1,6),(2,9),(3,4),(5,7),(8,10)] => 3
[(1,3),(2,7),(4,10),(5,6),(8,9)] => [(1,6),(2,3),(4,9),(5,7),(8,10)] => 3
[(1,2),(3,7),(4,10),(5,6),(8,9)] => [(1,2),(3,6),(4,9),(5,7),(8,10)] => 3
[(1,2),(3,8),(4,10),(5,6),(7,9)] => [(1,2),(3,6),(4,9),(5,10),(7,8)] => 3
[(1,3),(2,8),(4,10),(5,6),(7,9)] => [(1,6),(2,3),(4,9),(5,10),(7,8)] => 3
[(1,4),(2,8),(3,10),(5,6),(7,9)] => [(1,6),(2,9),(3,4),(5,10),(7,8)] => 3
[(1,5),(2,8),(3,10),(4,6),(7,9)] => [(1,6),(2,9),(3,10),(4,5),(7,8)] => 3
[(1,6),(2,8),(3,10),(4,5),(7,9)] => [(1,5),(2,9),(3,10),(4,6),(7,8)] => 4
[(1,7),(2,8),(3,10),(4,5),(6,9)] => [(1,5),(2,9),(3,10),(4,8),(6,7)] => 4
[(1,8),(2,7),(3,10),(4,5),(6,9)] => [(1,5),(2,9),(3,10),(4,7),(6,8)] => 5
[(1,9),(2,7),(3,10),(4,5),(6,8)] => [(1,5),(2,8),(3,10),(4,7),(6,9)] => 6
[(1,10),(2,7),(3,9),(4,5),(6,8)] => [(1,5),(2,8),(3,9),(4,7),(6,10)] => 7
[(1,10),(2,8),(3,9),(4,5),(6,7)] => [(1,5),(2,7),(3,9),(4,8),(6,10)] => 8
[(1,9),(2,8),(3,10),(4,5),(6,7)] => [(1,5),(2,7),(3,10),(4,8),(6,9)] => 7
[(1,8),(2,9),(3,10),(4,5),(6,7)] => [(1,5),(2,7),(3,10),(4,9),(6,8)] => 6
[(1,7),(2,9),(3,10),(4,5),(6,8)] => [(1,5),(2,8),(3,10),(4,9),(6,7)] => 5
[(1,6),(2,9),(3,10),(4,5),(7,8)] => [(1,5),(2,8),(3,10),(4,6),(7,9)] => 5
[(1,5),(2,9),(3,10),(4,6),(7,8)] => [(1,6),(2,8),(3,10),(4,5),(7,9)] => 4
[(1,4),(2,9),(3,10),(5,6),(7,8)] => [(1,6),(2,8),(3,4),(5,10),(7,9)] => 4
[(1,3),(2,9),(4,10),(5,6),(7,8)] => [(1,6),(2,3),(4,8),(5,10),(7,9)] => 4
[(1,2),(3,9),(4,10),(5,6),(7,8)] => [(1,2),(3,6),(4,8),(5,10),(7,9)] => 4
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [(1,2),(3,6),(4,8),(5,9),(7,10)] => 5
[(1,3),(2,10),(4,9),(5,6),(7,8)] => [(1,6),(2,3),(4,8),(5,9),(7,10)] => 5
[(1,4),(2,10),(3,9),(5,6),(7,8)] => [(1,6),(2,8),(3,4),(5,9),(7,10)] => 5
[(1,5),(2,10),(3,9),(4,6),(7,8)] => [(1,6),(2,8),(3,9),(4,5),(7,10)] => 5
[(1,6),(2,10),(3,9),(4,5),(7,8)] => [(1,5),(2,8),(3,9),(4,6),(7,10)] => 6
[(1,7),(2,10),(3,9),(4,5),(6,8)] => [(1,5),(2,8),(3,9),(4,10),(6,7)] => 6
[(1,8),(2,10),(3,9),(4,5),(6,7)] => [(1,5),(2,7),(3,9),(4,10),(6,8)] => 7
[(1,9),(2,10),(3,8),(4,5),(6,7)] => [(1,5),(2,7),(3,8),(4,10),(6,9)] => 8
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [(1,5),(2,7),(3,8),(4,9),(6,10)] => 9
[(1,10),(2,9),(3,8),(4,6),(5,7)] => [(1,7),(2,6),(3,8),(4,9),(5,10)] => 9
[(1,9),(2,10),(3,8),(4,6),(5,7)] => [(1,7),(2,6),(3,8),(4,10),(5,9)] => 8
[(1,8),(2,10),(3,9),(4,6),(5,7)] => [(1,7),(2,6),(3,9),(4,10),(5,8)] => 7
[(1,7),(2,10),(3,9),(4,6),(5,8)] => [(1,8),(2,6),(3,9),(4,10),(5,7)] => 6
[(1,6),(2,10),(3,9),(4,7),(5,8)] => [(1,8),(2,7),(3,9),(4,10),(5,6)] => 5
[(1,5),(2,10),(3,9),(4,7),(6,8)] => [(1,8),(2,7),(3,9),(4,5),(6,10)] => 5
[(1,4),(2,10),(3,9),(5,7),(6,8)] => [(1,8),(2,7),(3,4),(5,9),(6,10)] => 5
[(1,3),(2,10),(4,9),(5,7),(6,8)] => [(1,8),(2,3),(4,7),(5,9),(6,10)] => 5
[(1,2),(3,10),(4,9),(5,7),(6,8)] => [(1,2),(3,8),(4,7),(5,9),(6,10)] => 5
[(1,2),(3,9),(4,10),(5,7),(6,8)] => [(1,2),(3,8),(4,7),(5,10),(6,9)] => 4
[(1,3),(2,9),(4,10),(5,7),(6,8)] => [(1,8),(2,3),(4,7),(5,10),(6,9)] => 4
[(1,4),(2,9),(3,10),(5,7),(6,8)] => [(1,8),(2,7),(3,4),(5,10),(6,9)] => 4
[(1,5),(2,9),(3,10),(4,7),(6,8)] => [(1,8),(2,7),(3,10),(4,5),(6,9)] => 4
[(1,6),(2,9),(3,10),(4,7),(5,8)] => [(1,8),(2,7),(3,10),(4,9),(5,6)] => 4
[(1,7),(2,9),(3,10),(4,6),(5,8)] => [(1,8),(2,6),(3,10),(4,9),(5,7)] => 5
[(1,8),(2,9),(3,10),(4,6),(5,7)] => [(1,7),(2,6),(3,10),(4,9),(5,8)] => 6
[(1,9),(2,8),(3,10),(4,6),(5,7)] => [(1,7),(2,6),(3,10),(4,8),(5,9)] => 7
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [(1,7),(2,6),(3,9),(4,8),(5,10)] => 8
[(1,10),(2,7),(3,9),(4,6),(5,8)] => [(1,8),(2,6),(3,9),(4,7),(5,10)] => 7
[(1,9),(2,7),(3,10),(4,6),(5,8)] => [(1,8),(2,6),(3,10),(4,7),(5,9)] => 6
[(1,8),(2,7),(3,10),(4,6),(5,9)] => [(1,9),(2,6),(3,10),(4,7),(5,8)] => 5
[(1,7),(2,8),(3,10),(4,6),(5,9)] => [(1,9),(2,6),(3,10),(4,8),(5,7)] => 4
[(1,6),(2,8),(3,10),(4,7),(5,9)] => [(1,9),(2,7),(3,10),(4,8),(5,6)] => 3
[(1,5),(2,8),(3,10),(4,7),(6,9)] => [(1,9),(2,7),(3,10),(4,5),(6,8)] => 3
[(1,4),(2,8),(3,10),(5,7),(6,9)] => [(1,9),(2,7),(3,4),(5,10),(6,8)] => 3
[(1,3),(2,8),(4,10),(5,7),(6,9)] => [(1,9),(2,3),(4,7),(5,10),(6,8)] => 3
[(1,2),(3,8),(4,10),(5,7),(6,9)] => [(1,2),(3,9),(4,7),(5,10),(6,8)] => 3
[(1,2),(3,7),(4,10),(5,8),(6,9)] => [(1,2),(3,9),(4,8),(5,10),(6,7)] => 2
[(1,3),(2,7),(4,10),(5,8),(6,9)] => [(1,9),(2,3),(4,8),(5,10),(6,7)] => 2
[(1,4),(2,7),(3,10),(5,8),(6,9)] => [(1,9),(2,8),(3,4),(5,10),(6,7)] => 2
[(1,5),(2,7),(3,10),(4,8),(6,9)] => [(1,9),(2,8),(3,10),(4,5),(6,7)] => 2
[(1,6),(2,7),(3,10),(4,8),(5,9)] => [(1,9),(2,8),(3,10),(4,7),(5,6)] => 2
[(1,7),(2,6),(3,10),(4,8),(5,9)] => [(1,9),(2,8),(3,10),(4,6),(5,7)] => 3
[(1,8),(2,6),(3,10),(4,7),(5,9)] => [(1,9),(2,7),(3,10),(4,6),(5,8)] => 4
[(1,9),(2,6),(3,10),(4,7),(5,8)] => [(1,8),(2,7),(3,10),(4,6),(5,9)] => 5
[(1,10),(2,6),(3,9),(4,7),(5,8)] => [(1,8),(2,7),(3,9),(4,6),(5,10)] => 6
[(1,10),(2,5),(3,9),(4,7),(6,8)] => [(1,8),(2,7),(3,5),(4,9),(6,10)] => 6
[(1,9),(2,5),(3,10),(4,7),(6,8)] => [(1,8),(2,7),(3,5),(4,10),(6,9)] => 5
[(1,8),(2,5),(3,10),(4,7),(6,9)] => [(1,9),(2,7),(3,5),(4,10),(6,8)] => 4
[(1,7),(2,5),(3,10),(4,8),(6,9)] => [(1,9),(2,8),(3,5),(4,10),(6,7)] => 3
[(1,6),(2,5),(3,10),(4,8),(7,9)] => [(1,9),(2,8),(3,5),(4,6),(7,10)] => 3
[(1,5),(2,6),(3,10),(4,8),(7,9)] => [(1,9),(2,8),(3,6),(4,5),(7,10)] => 2
[(1,4),(2,6),(3,10),(5,8),(7,9)] => [(1,9),(2,8),(3,4),(5,6),(7,10)] => 2
[(1,3),(2,6),(4,10),(5,8),(7,9)] => [(1,9),(2,3),(4,8),(5,6),(7,10)] => 2
[(1,2),(3,6),(4,10),(5,8),(7,9)] => [(1,2),(3,9),(4,8),(5,6),(7,10)] => 2
[(1,2),(3,5),(4,10),(6,8),(7,9)] => [(1,2),(3,9),(4,5),(6,8),(7,10)] => 2
[(1,3),(2,5),(4,10),(6,8),(7,9)] => [(1,9),(2,3),(4,5),(6,8),(7,10)] => 2
[(1,4),(2,5),(3,10),(6,8),(7,9)] => [(1,9),(2,5),(3,4),(6,8),(7,10)] => 2
[(1,5),(2,4),(3,10),(6,8),(7,9)] => [(1,9),(2,4),(3,5),(6,8),(7,10)] => 3
[(1,6),(2,4),(3,10),(5,8),(7,9)] => [(1,9),(2,4),(3,8),(5,6),(7,10)] => 3
[(1,7),(2,4),(3,10),(5,8),(6,9)] => [(1,9),(2,4),(3,8),(5,10),(6,7)] => 3
[(1,8),(2,4),(3,10),(5,7),(6,9)] => [(1,9),(2,4),(3,7),(5,10),(6,8)] => 4
[(1,9),(2,4),(3,10),(5,7),(6,8)] => [(1,8),(2,4),(3,7),(5,10),(6,9)] => 5
[(1,10),(2,4),(3,9),(5,7),(6,8)] => [(1,8),(2,4),(3,7),(5,9),(6,10)] => 6
[(1,10),(2,3),(4,9),(5,7),(6,8)] => [(1,3),(2,8),(4,7),(5,9),(6,10)] => 6
[(1,9),(2,3),(4,10),(5,7),(6,8)] => [(1,3),(2,8),(4,7),(5,10),(6,9)] => 5
[(1,8),(2,3),(4,10),(5,7),(6,9)] => [(1,3),(2,9),(4,7),(5,10),(6,8)] => 4
[(1,7),(2,3),(4,10),(5,8),(6,9)] => [(1,3),(2,9),(4,8),(5,10),(6,7)] => 3
[(1,6),(2,3),(4,10),(5,8),(7,9)] => [(1,3),(2,9),(4,8),(5,6),(7,10)] => 3
[(1,5),(2,3),(4,10),(6,8),(7,9)] => [(1,3),(2,9),(4,5),(6,8),(7,10)] => 3
[(1,4),(2,3),(5,10),(6,8),(7,9)] => [(1,3),(2,4),(5,9),(6,8),(7,10)] => 3
[(1,3),(2,4),(5,10),(6,8),(7,9)] => [(1,4),(2,3),(5,9),(6,8),(7,10)] => 2
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [(1,2),(3,4),(5,9),(6,8),(7,10)] => 2
[(1,2),(3,4),(5,9),(6,8),(7,10)] => [(1,2),(3,4),(5,10),(6,8),(7,9)] => 1
[(1,3),(2,4),(5,9),(6,8),(7,10)] => [(1,4),(2,3),(5,10),(6,8),(7,9)] => 1
[(1,4),(2,3),(5,9),(6,8),(7,10)] => [(1,3),(2,4),(5,10),(6,8),(7,9)] => 2
[(1,5),(2,3),(4,9),(6,8),(7,10)] => [(1,3),(2,10),(4,5),(6,8),(7,9)] => 2
[(1,6),(2,3),(4,9),(5,8),(7,10)] => [(1,3),(2,10),(4,8),(5,6),(7,9)] => 2
[(1,7),(2,3),(4,9),(5,8),(6,10)] => [(1,3),(2,10),(4,8),(5,9),(6,7)] => 2
[(1,8),(2,3),(4,9),(5,7),(6,10)] => [(1,3),(2,10),(4,7),(5,9),(6,8)] => 3
[(1,9),(2,3),(4,8),(5,7),(6,10)] => [(1,3),(2,10),(4,7),(5,8),(6,9)] => 4
[(1,10),(2,3),(4,8),(5,7),(6,9)] => [(1,3),(2,9),(4,7),(5,8),(6,10)] => 5
[(1,10),(2,4),(3,8),(5,7),(6,9)] => [(1,9),(2,4),(3,7),(5,8),(6,10)] => 5
[(1,9),(2,4),(3,8),(5,7),(6,10)] => [(1,10),(2,4),(3,7),(5,8),(6,9)] => 4
[(1,8),(2,4),(3,9),(5,7),(6,10)] => [(1,10),(2,4),(3,7),(5,9),(6,8)] => 3
[(1,7),(2,4),(3,9),(5,8),(6,10)] => [(1,10),(2,4),(3,8),(5,9),(6,7)] => 2
[(1,6),(2,4),(3,9),(5,8),(7,10)] => [(1,10),(2,4),(3,8),(5,6),(7,9)] => 2
[(1,5),(2,4),(3,9),(6,8),(7,10)] => [(1,10),(2,4),(3,5),(6,8),(7,9)] => 2
[(1,4),(2,5),(3,9),(6,8),(7,10)] => [(1,10),(2,5),(3,4),(6,8),(7,9)] => 1
[(1,3),(2,5),(4,9),(6,8),(7,10)] => [(1,10),(2,3),(4,5),(6,8),(7,9)] => 1
[(1,2),(3,5),(4,9),(6,8),(7,10)] => [(1,2),(3,10),(4,5),(6,8),(7,9)] => 1
[(1,2),(3,6),(4,9),(5,8),(7,10)] => [(1,2),(3,10),(4,8),(5,6),(7,9)] => 1
[(1,3),(2,6),(4,9),(5,8),(7,10)] => [(1,10),(2,3),(4,8),(5,6),(7,9)] => 1
[(1,4),(2,6),(3,9),(5,8),(7,10)] => [(1,10),(2,8),(3,4),(5,6),(7,9)] => 1
[(1,5),(2,6),(3,9),(4,8),(7,10)] => [(1,10),(2,8),(3,6),(4,5),(7,9)] => 1
[(1,6),(2,5),(3,9),(4,8),(7,10)] => [(1,10),(2,8),(3,5),(4,6),(7,9)] => 2
[(1,7),(2,5),(3,9),(4,8),(6,10)] => [(1,10),(2,8),(3,5),(4,9),(6,7)] => 2
[(1,8),(2,5),(3,9),(4,7),(6,10)] => [(1,10),(2,7),(3,5),(4,9),(6,8)] => 3
[(1,9),(2,5),(3,8),(4,7),(6,10)] => [(1,10),(2,7),(3,5),(4,8),(6,9)] => 4
[(1,10),(2,5),(3,8),(4,7),(6,9)] => [(1,9),(2,7),(3,5),(4,8),(6,10)] => 5
[(1,10),(2,6),(3,8),(4,7),(5,9)] => [(1,9),(2,7),(3,8),(4,6),(5,10)] => 5
[(1,9),(2,6),(3,8),(4,7),(5,10)] => [(1,10),(2,7),(3,8),(4,6),(5,9)] => 4
[(1,8),(2,6),(3,9),(4,7),(5,10)] => [(1,10),(2,7),(3,9),(4,6),(5,8)] => 3
[(1,7),(2,6),(3,9),(4,8),(5,10)] => [(1,10),(2,8),(3,9),(4,6),(5,7)] => 2
[(1,6),(2,7),(3,9),(4,8),(5,10)] => [(1,10),(2,8),(3,9),(4,7),(5,6)] => 1
[(1,5),(2,7),(3,9),(4,8),(6,10)] => [(1,10),(2,8),(3,9),(4,5),(6,7)] => 1
[(1,4),(2,7),(3,9),(5,8),(6,10)] => [(1,10),(2,8),(3,4),(5,9),(6,7)] => 1
[(1,3),(2,7),(4,9),(5,8),(6,10)] => [(1,10),(2,3),(4,8),(5,9),(6,7)] => 1
[(1,2),(3,7),(4,9),(5,8),(6,10)] => [(1,2),(3,10),(4,8),(5,9),(6,7)] => 1
[(1,2),(3,8),(4,9),(5,7),(6,10)] => [(1,2),(3,10),(4,7),(5,9),(6,8)] => 2
[(1,3),(2,8),(4,9),(5,7),(6,10)] => [(1,10),(2,3),(4,7),(5,9),(6,8)] => 2
[(1,4),(2,8),(3,9),(5,7),(6,10)] => [(1,10),(2,7),(3,4),(5,9),(6,8)] => 2
[(1,5),(2,8),(3,9),(4,7),(6,10)] => [(1,10),(2,7),(3,9),(4,5),(6,8)] => 2
[(1,6),(2,8),(3,9),(4,7),(5,10)] => [(1,10),(2,7),(3,9),(4,8),(5,6)] => 2
[(1,7),(2,8),(3,9),(4,6),(5,10)] => [(1,10),(2,6),(3,9),(4,8),(5,7)] => 3
[(1,8),(2,7),(3,9),(4,6),(5,10)] => [(1,10),(2,6),(3,9),(4,7),(5,8)] => 4
[(1,9),(2,7),(3,8),(4,6),(5,10)] => [(1,10),(2,6),(3,8),(4,7),(5,9)] => 5
[(1,10),(2,7),(3,8),(4,6),(5,9)] => [(1,9),(2,6),(3,8),(4,7),(5,10)] => 6
[(1,10),(2,8),(3,7),(4,6),(5,9)] => [(1,9),(2,6),(3,7),(4,8),(5,10)] => 7
[(1,9),(2,8),(3,7),(4,6),(5,10)] => [(1,10),(2,6),(3,7),(4,8),(5,9)] => 6
[(1,8),(2,9),(3,7),(4,6),(5,10)] => [(1,10),(2,6),(3,7),(4,9),(5,8)] => 5
[(1,7),(2,9),(3,8),(4,6),(5,10)] => [(1,10),(2,6),(3,8),(4,9),(5,7)] => 4
[(1,6),(2,9),(3,8),(4,7),(5,10)] => [(1,10),(2,7),(3,8),(4,9),(5,6)] => 3
[(1,5),(2,9),(3,8),(4,7),(6,10)] => [(1,10),(2,7),(3,8),(4,5),(6,9)] => 3
[(1,4),(2,9),(3,8),(5,7),(6,10)] => [(1,10),(2,7),(3,4),(5,8),(6,9)] => 3
[(1,3),(2,9),(4,8),(5,7),(6,10)] => [(1,10),(2,3),(4,7),(5,8),(6,9)] => 3
[(1,2),(3,9),(4,8),(5,7),(6,10)] => [(1,2),(3,10),(4,7),(5,8),(6,9)] => 3
[(1,2),(3,10),(4,8),(5,7),(6,9)] => [(1,2),(3,9),(4,7),(5,8),(6,10)] => 4
[(1,3),(2,10),(4,8),(5,7),(6,9)] => [(1,9),(2,3),(4,7),(5,8),(6,10)] => 4
[(1,4),(2,10),(3,8),(5,7),(6,9)] => [(1,9),(2,7),(3,4),(5,8),(6,10)] => 4
[(1,5),(2,10),(3,8),(4,7),(6,9)] => [(1,9),(2,7),(3,8),(4,5),(6,10)] => 4
[(1,6),(2,10),(3,8),(4,7),(5,9)] => [(1,9),(2,7),(3,8),(4,10),(5,6)] => 4
[(1,7),(2,10),(3,8),(4,6),(5,9)] => [(1,9),(2,6),(3,8),(4,10),(5,7)] => 5
[(1,8),(2,10),(3,7),(4,6),(5,9)] => [(1,9),(2,6),(3,7),(4,10),(5,8)] => 6
[(1,9),(2,10),(3,7),(4,6),(5,8)] => [(1,8),(2,6),(3,7),(4,10),(5,9)] => 7
[(1,10),(2,9),(3,7),(4,6),(5,8)] => [(1,8),(2,6),(3,7),(4,9),(5,10)] => 8
[(1,10),(2,9),(3,6),(4,7),(5,8)] => [(1,8),(2,7),(3,6),(4,9),(5,10)] => 7
[(1,9),(2,10),(3,6),(4,7),(5,8)] => [(1,8),(2,7),(3,6),(4,10),(5,9)] => 6
[(1,8),(2,10),(3,6),(4,7),(5,9)] => [(1,9),(2,7),(3,6),(4,10),(5,8)] => 5
[(1,7),(2,10),(3,6),(4,8),(5,9)] => [(1,9),(2,8),(3,6),(4,10),(5,7)] => 4
[(1,6),(2,10),(3,7),(4,8),(5,9)] => [(1,9),(2,8),(3,7),(4,10),(5,6)] => 3
[(1,5),(2,10),(3,7),(4,8),(6,9)] => [(1,9),(2,8),(3,7),(4,5),(6,10)] => 3
[(1,4),(2,10),(3,7),(5,8),(6,9)] => [(1,9),(2,8),(3,4),(5,7),(6,10)] => 3
[(1,3),(2,10),(4,7),(5,8),(6,9)] => [(1,9),(2,3),(4,8),(5,7),(6,10)] => 3
[(1,2),(3,10),(4,7),(5,8),(6,9)] => [(1,2),(3,9),(4,8),(5,7),(6,10)] => 3
[(1,2),(3,9),(4,7),(5,8),(6,10)] => [(1,2),(3,10),(4,8),(5,7),(6,9)] => 2
[(1,3),(2,9),(4,7),(5,8),(6,10)] => [(1,10),(2,3),(4,8),(5,7),(6,9)] => 2
[(1,4),(2,9),(3,7),(5,8),(6,10)] => [(1,10),(2,8),(3,4),(5,7),(6,9)] => 2
[(1,5),(2,9),(3,7),(4,8),(6,10)] => [(1,10),(2,8),(3,7),(4,5),(6,9)] => 2
[(1,6),(2,9),(3,7),(4,8),(5,10)] => [(1,10),(2,8),(3,7),(4,9),(5,6)] => 2
[(1,7),(2,9),(3,6),(4,8),(5,10)] => [(1,10),(2,8),(3,6),(4,9),(5,7)] => 3
[(1,8),(2,9),(3,6),(4,7),(5,10)] => [(1,10),(2,7),(3,6),(4,9),(5,8)] => 4
[(1,9),(2,8),(3,6),(4,7),(5,10)] => [(1,10),(2,7),(3,6),(4,8),(5,9)] => 5
[(1,10),(2,8),(3,6),(4,7),(5,9)] => [(1,9),(2,7),(3,6),(4,8),(5,10)] => 6
[(1,10),(2,7),(3,6),(4,8),(5,9)] => [(1,9),(2,8),(3,6),(4,7),(5,10)] => 5
[(1,9),(2,7),(3,6),(4,8),(5,10)] => [(1,10),(2,8),(3,6),(4,7),(5,9)] => 4
[(1,8),(2,7),(3,6),(4,9),(5,10)] => [(1,10),(2,9),(3,6),(4,7),(5,8)] => 3
[(1,7),(2,8),(3,6),(4,9),(5,10)] => [(1,10),(2,9),(3,6),(4,8),(5,7)] => 2
[(1,6),(2,8),(3,7),(4,9),(5,10)] => [(1,10),(2,9),(3,7),(4,8),(5,6)] => 1
[(1,5),(2,8),(3,7),(4,9),(6,10)] => [(1,10),(2,9),(3,7),(4,5),(6,8)] => 1
[(1,4),(2,8),(3,7),(5,9),(6,10)] => [(1,10),(2,9),(3,4),(5,7),(6,8)] => 1
[(1,3),(2,8),(4,7),(5,9),(6,10)] => [(1,10),(2,3),(4,9),(5,7),(6,8)] => 1
[(1,2),(3,8),(4,7),(5,9),(6,10)] => [(1,2),(3,10),(4,9),(5,7),(6,8)] => 1
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[(1,3),(2,7),(4,8),(5,9),(6,10)] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 0
[(1,4),(2,7),(3,8),(5,9),(6,10)] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 0
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 0
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 0
[(1,7),(2,6),(3,8),(4,9),(5,10)] => [(1,10),(2,9),(3,8),(4,6),(5,7)] => 1
[(1,8),(2,6),(3,7),(4,9),(5,10)] => [(1,10),(2,9),(3,7),(4,6),(5,8)] => 2
[(1,9),(2,6),(3,7),(4,8),(5,10)] => [(1,10),(2,8),(3,7),(4,6),(5,9)] => 3
[(1,10),(2,6),(3,7),(4,8),(5,9)] => [(1,9),(2,8),(3,7),(4,6),(5,10)] => 4
[(1,10),(2,5),(3,7),(4,8),(6,9)] => [(1,9),(2,8),(3,5),(4,7),(6,10)] => 4
[(1,9),(2,5),(3,7),(4,8),(6,10)] => [(1,10),(2,8),(3,5),(4,7),(6,9)] => 3
[(1,8),(2,5),(3,7),(4,9),(6,10)] => [(1,10),(2,9),(3,5),(4,7),(6,8)] => 2
[(1,7),(2,5),(3,8),(4,9),(6,10)] => [(1,10),(2,9),(3,5),(4,8),(6,7)] => 1
[(1,6),(2,5),(3,8),(4,9),(7,10)] => [(1,10),(2,9),(3,5),(4,6),(7,8)] => 1
[(1,5),(2,6),(3,8),(4,9),(7,10)] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 0
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => 0
[(1,3),(2,6),(4,8),(5,9),(7,10)] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => 0
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[(1,3),(2,5),(4,8),(6,9),(7,10)] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => 0
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 0
[(1,5),(2,4),(3,8),(6,9),(7,10)] => [(1,10),(2,4),(3,5),(6,9),(7,8)] => 1
[(1,6),(2,4),(3,8),(5,9),(7,10)] => [(1,10),(2,4),(3,9),(5,6),(7,8)] => 1
[(1,7),(2,4),(3,8),(5,9),(6,10)] => [(1,10),(2,4),(3,9),(5,8),(6,7)] => 1
[(1,8),(2,4),(3,7),(5,9),(6,10)] => [(1,10),(2,4),(3,9),(5,7),(6,8)] => 2
[(1,9),(2,4),(3,7),(5,8),(6,10)] => [(1,10),(2,4),(3,8),(5,7),(6,9)] => 3
[(1,10),(2,4),(3,7),(5,8),(6,9)] => [(1,9),(2,4),(3,8),(5,7),(6,10)] => 4
[(1,10),(2,3),(4,7),(5,8),(6,9)] => [(1,3),(2,9),(4,8),(5,7),(6,10)] => 4
[(1,9),(2,3),(4,7),(5,8),(6,10)] => [(1,3),(2,10),(4,8),(5,7),(6,9)] => 3
[(1,8),(2,3),(4,7),(5,9),(6,10)] => [(1,3),(2,10),(4,9),(5,7),(6,8)] => 2
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [(1,3),(2,10),(4,9),(5,8),(6,7)] => 1
[(1,6),(2,3),(4,8),(5,9),(7,10)] => [(1,3),(2,10),(4,9),(5,6),(7,8)] => 1
[(1,5),(2,3),(4,8),(6,9),(7,10)] => [(1,3),(2,10),(4,5),(6,9),(7,8)] => 1
[(1,4),(2,3),(5,8),(6,9),(7,10)] => [(1,3),(2,4),(5,10),(6,9),(7,8)] => 1
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[(1,4),(2,3),(5,7),(6,9),(8,10)] => [(1,3),(2,4),(5,10),(6,7),(8,9)] => 1
[(1,5),(2,3),(4,7),(6,9),(8,10)] => [(1,3),(2,10),(4,5),(6,7),(8,9)] => 1
[(1,6),(2,3),(4,7),(5,9),(8,10)] => [(1,3),(2,10),(4,7),(5,6),(8,9)] => 1
[(1,7),(2,3),(4,6),(5,9),(8,10)] => [(1,3),(2,10),(4,6),(5,7),(8,9)] => 2
[(1,8),(2,3),(4,6),(5,9),(7,10)] => [(1,3),(2,10),(4,6),(5,9),(7,8)] => 2
[(1,9),(2,3),(4,6),(5,8),(7,10)] => [(1,3),(2,10),(4,6),(5,8),(7,9)] => 3
[(1,10),(2,3),(4,6),(5,8),(7,9)] => [(1,3),(2,9),(4,6),(5,8),(7,10)] => 4
[(1,10),(2,4),(3,6),(5,8),(7,9)] => [(1,9),(2,4),(3,6),(5,8),(7,10)] => 4
[(1,9),(2,4),(3,6),(5,8),(7,10)] => [(1,10),(2,4),(3,6),(5,8),(7,9)] => 3
[(1,8),(2,4),(3,6),(5,9),(7,10)] => [(1,10),(2,4),(3,6),(5,9),(7,8)] => 2
[(1,7),(2,4),(3,6),(5,9),(8,10)] => [(1,10),(2,4),(3,6),(5,7),(8,9)] => 2
[(1,6),(2,4),(3,7),(5,9),(8,10)] => [(1,10),(2,4),(3,7),(5,6),(8,9)] => 1
[(1,5),(2,4),(3,7),(6,9),(8,10)] => [(1,10),(2,4),(3,5),(6,7),(8,9)] => 1
[(1,4),(2,5),(3,7),(6,9),(8,10)] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => 0
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => 0
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[(1,3),(2,6),(4,7),(5,9),(8,10)] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => 0
[(1,4),(2,6),(3,7),(5,9),(8,10)] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => 0
[(1,5),(2,6),(3,7),(4,9),(8,10)] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 0
[(1,6),(2,5),(3,7),(4,9),(8,10)] => [(1,10),(2,7),(3,5),(4,6),(8,9)] => 1
[(1,7),(2,5),(3,6),(4,9),(8,10)] => [(1,10),(2,6),(3,5),(4,7),(8,9)] => 2
[(1,8),(2,5),(3,6),(4,9),(7,10)] => [(1,10),(2,6),(3,5),(4,9),(7,8)] => 2
[(1,9),(2,5),(3,6),(4,8),(7,10)] => [(1,10),(2,6),(3,5),(4,8),(7,9)] => 3
[(1,10),(2,5),(3,6),(4,8),(7,9)] => [(1,9),(2,6),(3,5),(4,8),(7,10)] => 4
[(1,10),(2,6),(3,5),(4,8),(7,9)] => [(1,9),(2,5),(3,6),(4,8),(7,10)] => 5
[(1,9),(2,6),(3,5),(4,8),(7,10)] => [(1,10),(2,5),(3,6),(4,8),(7,9)] => 4
[(1,8),(2,6),(3,5),(4,9),(7,10)] => [(1,10),(2,5),(3,6),(4,9),(7,8)] => 3
[(1,7),(2,6),(3,5),(4,9),(8,10)] => [(1,10),(2,5),(3,6),(4,7),(8,9)] => 3
[(1,6),(2,7),(3,5),(4,9),(8,10)] => [(1,10),(2,5),(3,7),(4,6),(8,9)] => 2
[(1,5),(2,7),(3,6),(4,9),(8,10)] => [(1,10),(2,6),(3,7),(4,5),(8,9)] => 1
[(1,4),(2,7),(3,6),(5,9),(8,10)] => [(1,10),(2,6),(3,4),(5,7),(8,9)] => 1
[(1,3),(2,7),(4,6),(5,9),(8,10)] => [(1,10),(2,3),(4,6),(5,7),(8,9)] => 1
[(1,2),(3,7),(4,6),(5,9),(8,10)] => [(1,2),(3,10),(4,6),(5,7),(8,9)] => 1
[(1,2),(3,8),(4,6),(5,9),(7,10)] => [(1,2),(3,10),(4,6),(5,9),(7,8)] => 1
[(1,3),(2,8),(4,6),(5,9),(7,10)] => [(1,10),(2,3),(4,6),(5,9),(7,8)] => 1
[(1,4),(2,8),(3,6),(5,9),(7,10)] => [(1,10),(2,6),(3,4),(5,9),(7,8)] => 1
[(1,5),(2,8),(3,6),(4,9),(7,10)] => [(1,10),(2,6),(3,9),(4,5),(7,8)] => 1
[(1,6),(2,8),(3,5),(4,9),(7,10)] => [(1,10),(2,5),(3,9),(4,6),(7,8)] => 2
[(1,7),(2,8),(3,5),(4,9),(6,10)] => [(1,10),(2,5),(3,9),(4,8),(6,7)] => 2
[(1,8),(2,7),(3,5),(4,9),(6,10)] => [(1,10),(2,5),(3,9),(4,7),(6,8)] => 3
[(1,9),(2,7),(3,5),(4,8),(6,10)] => [(1,10),(2,5),(3,8),(4,7),(6,9)] => 4
[(1,10),(2,7),(3,5),(4,8),(6,9)] => [(1,9),(2,5),(3,8),(4,7),(6,10)] => 5
[(1,10),(2,8),(3,5),(4,7),(6,9)] => [(1,9),(2,5),(3,7),(4,8),(6,10)] => 6
[(1,9),(2,8),(3,5),(4,7),(6,10)] => [(1,10),(2,5),(3,7),(4,8),(6,9)] => 5
[(1,8),(2,9),(3,5),(4,7),(6,10)] => [(1,10),(2,5),(3,7),(4,9),(6,8)] => 4
[(1,7),(2,9),(3,5),(4,8),(6,10)] => [(1,10),(2,5),(3,8),(4,9),(6,7)] => 3
[(1,6),(2,9),(3,5),(4,8),(7,10)] => [(1,10),(2,5),(3,8),(4,6),(7,9)] => 3
[(1,5),(2,9),(3,6),(4,8),(7,10)] => [(1,10),(2,6),(3,8),(4,5),(7,9)] => 2
[(1,4),(2,9),(3,6),(5,8),(7,10)] => [(1,10),(2,6),(3,4),(5,8),(7,9)] => 2
[(1,3),(2,9),(4,6),(5,8),(7,10)] => [(1,10),(2,3),(4,6),(5,8),(7,9)] => 2
[(1,2),(3,9),(4,6),(5,8),(7,10)] => [(1,2),(3,10),(4,6),(5,8),(7,9)] => 2
[(1,2),(3,10),(4,6),(5,8),(7,9)] => [(1,2),(3,9),(4,6),(5,8),(7,10)] => 3
[(1,3),(2,10),(4,6),(5,8),(7,9)] => [(1,9),(2,3),(4,6),(5,8),(7,10)] => 3
[(1,4),(2,10),(3,6),(5,8),(7,9)] => [(1,9),(2,6),(3,4),(5,8),(7,10)] => 3
[(1,5),(2,10),(3,6),(4,8),(7,9)] => [(1,9),(2,6),(3,8),(4,5),(7,10)] => 3
[(1,6),(2,10),(3,5),(4,8),(7,9)] => [(1,9),(2,5),(3,8),(4,6),(7,10)] => 4
[(1,7),(2,10),(3,5),(4,8),(6,9)] => [(1,9),(2,5),(3,8),(4,10),(6,7)] => 4
[(1,8),(2,10),(3,5),(4,7),(6,9)] => [(1,9),(2,5),(3,7),(4,10),(6,8)] => 5
[(1,9),(2,10),(3,5),(4,7),(6,8)] => [(1,8),(2,5),(3,7),(4,10),(6,9)] => 6
[(1,10),(2,9),(3,5),(4,7),(6,8)] => [(1,8),(2,5),(3,7),(4,9),(6,10)] => 7
[(1,10),(2,9),(3,4),(5,7),(6,8)] => [(1,4),(2,8),(3,7),(5,9),(6,10)] => 7
[(1,9),(2,10),(3,4),(5,7),(6,8)] => [(1,4),(2,8),(3,7),(5,10),(6,9)] => 6
[(1,8),(2,10),(3,4),(5,7),(6,9)] => [(1,4),(2,9),(3,7),(5,10),(6,8)] => 5
[(1,7),(2,10),(3,4),(5,8),(6,9)] => [(1,4),(2,9),(3,8),(5,10),(6,7)] => 4
[(1,6),(2,10),(3,4),(5,8),(7,9)] => [(1,4),(2,9),(3,8),(5,6),(7,10)] => 4
[(1,5),(2,10),(3,4),(6,8),(7,9)] => [(1,4),(2,9),(3,5),(6,8),(7,10)] => 4
[(1,4),(2,10),(3,5),(6,8),(7,9)] => [(1,5),(2,9),(3,4),(6,8),(7,10)] => 3
[(1,3),(2,10),(4,5),(6,8),(7,9)] => [(1,5),(2,3),(4,9),(6,8),(7,10)] => 3
[(1,2),(3,10),(4,5),(6,8),(7,9)] => [(1,2),(3,5),(4,9),(6,8),(7,10)] => 3
[(1,2),(3,9),(4,5),(6,8),(7,10)] => [(1,2),(3,5),(4,10),(6,8),(7,9)] => 2
[(1,3),(2,9),(4,5),(6,8),(7,10)] => [(1,5),(2,3),(4,10),(6,8),(7,9)] => 2
[(1,4),(2,9),(3,5),(6,8),(7,10)] => [(1,5),(2,10),(3,4),(6,8),(7,9)] => 2
[(1,5),(2,9),(3,4),(6,8),(7,10)] => [(1,4),(2,10),(3,5),(6,8),(7,9)] => 3
[(1,6),(2,9),(3,4),(5,8),(7,10)] => [(1,4),(2,10),(3,8),(5,6),(7,9)] => 3
[(1,7),(2,9),(3,4),(5,8),(6,10)] => [(1,4),(2,10),(3,8),(5,9),(6,7)] => 3
[(1,8),(2,9),(3,4),(5,7),(6,10)] => [(1,4),(2,10),(3,7),(5,9),(6,8)] => 4
[(1,9),(2,8),(3,4),(5,7),(6,10)] => [(1,4),(2,10),(3,7),(5,8),(6,9)] => 5
[(1,10),(2,8),(3,4),(5,7),(6,9)] => [(1,4),(2,9),(3,7),(5,8),(6,10)] => 6
[(1,10),(2,7),(3,4),(5,8),(6,9)] => [(1,4),(2,9),(3,8),(5,7),(6,10)] => 5
[(1,9),(2,7),(3,4),(5,8),(6,10)] => [(1,4),(2,10),(3,8),(5,7),(6,9)] => 4
[(1,8),(2,7),(3,4),(5,9),(6,10)] => [(1,4),(2,10),(3,9),(5,7),(6,8)] => 3
[(1,7),(2,8),(3,4),(5,9),(6,10)] => [(1,4),(2,10),(3,9),(5,8),(6,7)] => 2
[(1,6),(2,8),(3,4),(5,9),(7,10)] => [(1,4),(2,10),(3,9),(5,6),(7,8)] => 2
[(1,5),(2,8),(3,4),(6,9),(7,10)] => [(1,4),(2,10),(3,5),(6,9),(7,8)] => 2
[(1,4),(2,8),(3,5),(6,9),(7,10)] => [(1,5),(2,10),(3,4),(6,9),(7,8)] => 1
[(1,3),(2,8),(4,5),(6,9),(7,10)] => [(1,5),(2,3),(4,10),(6,9),(7,8)] => 1
[(1,2),(3,8),(4,5),(6,9),(7,10)] => [(1,2),(3,5),(4,10),(6,9),(7,8)] => 1
[(1,2),(3,7),(4,5),(6,9),(8,10)] => [(1,2),(3,5),(4,10),(6,7),(8,9)] => 1
[(1,3),(2,7),(4,5),(6,9),(8,10)] => [(1,5),(2,3),(4,10),(6,7),(8,9)] => 1
[(1,4),(2,7),(3,5),(6,9),(8,10)] => [(1,5),(2,10),(3,4),(6,7),(8,9)] => 1
[(1,5),(2,7),(3,4),(6,9),(8,10)] => [(1,4),(2,10),(3,5),(6,7),(8,9)] => 2
[(1,6),(2,7),(3,4),(5,9),(8,10)] => [(1,4),(2,10),(3,7),(5,6),(8,9)] => 2
[(1,7),(2,6),(3,4),(5,9),(8,10)] => [(1,4),(2,10),(3,6),(5,7),(8,9)] => 3
[(1,8),(2,6),(3,4),(5,9),(7,10)] => [(1,4),(2,10),(3,6),(5,9),(7,8)] => 3
[(1,9),(2,6),(3,4),(5,8),(7,10)] => [(1,4),(2,10),(3,6),(5,8),(7,9)] => 4
[(1,10),(2,6),(3,4),(5,8),(7,9)] => [(1,4),(2,9),(3,6),(5,8),(7,10)] => 5
[(1,10),(2,5),(3,4),(6,8),(7,9)] => [(1,4),(2,5),(3,9),(6,8),(7,10)] => 5
[(1,9),(2,5),(3,4),(6,8),(7,10)] => [(1,4),(2,5),(3,10),(6,8),(7,9)] => 4
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [(1,4),(2,5),(3,10),(6,9),(7,8)] => 3
[(1,7),(2,5),(3,4),(6,9),(8,10)] => [(1,4),(2,5),(3,10),(6,7),(8,9)] => 3
[(1,6),(2,5),(3,4),(7,9),(8,10)] => [(1,4),(2,5),(3,6),(7,10),(8,9)] => 3
[(1,5),(2,6),(3,4),(7,9),(8,10)] => [(1,4),(2,6),(3,5),(7,10),(8,9)] => 2
[(1,4),(2,6),(3,5),(7,9),(8,10)] => [(1,5),(2,6),(3,4),(7,10),(8,9)] => 1
[(1,3),(2,6),(4,5),(7,9),(8,10)] => [(1,5),(2,3),(4,6),(7,10),(8,9)] => 1
[(1,2),(3,6),(4,5),(7,9),(8,10)] => [(1,2),(3,5),(4,6),(7,10),(8,9)] => 1
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[(1,5),(2,4),(3,6),(7,9),(8,10)] => [(1,6),(2,4),(3,5),(7,10),(8,9)] => 1
[(1,6),(2,4),(3,5),(7,9),(8,10)] => [(1,5),(2,4),(3,6),(7,10),(8,9)] => 2
[(1,7),(2,4),(3,5),(6,9),(8,10)] => [(1,5),(2,4),(3,10),(6,7),(8,9)] => 2
[(1,8),(2,4),(3,5),(6,9),(7,10)] => [(1,5),(2,4),(3,10),(6,9),(7,8)] => 2
[(1,9),(2,4),(3,5),(6,8),(7,10)] => [(1,5),(2,4),(3,10),(6,8),(7,9)] => 3
[(1,10),(2,4),(3,5),(6,8),(7,9)] => [(1,5),(2,4),(3,9),(6,8),(7,10)] => 4
[(1,10),(2,3),(4,5),(6,8),(7,9)] => [(1,3),(2,5),(4,9),(6,8),(7,10)] => 4
[(1,9),(2,3),(4,5),(6,8),(7,10)] => [(1,3),(2,5),(4,10),(6,8),(7,9)] => 3
[(1,8),(2,3),(4,5),(6,9),(7,10)] => [(1,3),(2,5),(4,10),(6,9),(7,8)] => 2
[(1,7),(2,3),(4,5),(6,9),(8,10)] => [(1,3),(2,5),(4,10),(6,7),(8,9)] => 2
[(1,6),(2,3),(4,5),(7,9),(8,10)] => [(1,3),(2,5),(4,6),(7,10),(8,9)] => 2
[(1,5),(2,3),(4,6),(7,9),(8,10)] => [(1,3),(2,6),(4,5),(7,10),(8,9)] => 1
[(1,4),(2,3),(5,6),(7,9),(8,10)] => [(1,3),(2,4),(5,6),(7,10),(8,9)] => 1
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [(1,2),(3,4),(5,6),(7,9),(8,10)] => 1
[(1,3),(2,4),(5,6),(7,10),(8,9)] => [(1,4),(2,3),(5,6),(7,9),(8,10)] => 1
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [(1,3),(2,4),(5,6),(7,9),(8,10)] => 2
[(1,5),(2,3),(4,6),(7,10),(8,9)] => [(1,3),(2,6),(4,5),(7,9),(8,10)] => 2
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [(1,3),(2,5),(4,6),(7,9),(8,10)] => 3
[(1,7),(2,3),(4,5),(6,10),(8,9)] => [(1,3),(2,5),(4,9),(6,7),(8,10)] => 3
[(1,8),(2,3),(4,5),(6,10),(7,9)] => [(1,3),(2,5),(4,9),(6,10),(7,8)] => 3
[(1,9),(2,3),(4,5),(6,10),(7,8)] => [(1,3),(2,5),(4,8),(6,10),(7,9)] => 4
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [(1,3),(2,5),(4,8),(6,9),(7,10)] => 5
[(1,10),(2,4),(3,5),(6,9),(7,8)] => [(1,5),(2,4),(3,8),(6,9),(7,10)] => 5
[(1,9),(2,4),(3,5),(6,10),(7,8)] => [(1,5),(2,4),(3,8),(6,10),(7,9)] => 4
[(1,8),(2,4),(3,5),(6,10),(7,9)] => [(1,5),(2,4),(3,9),(6,10),(7,8)] => 3
[(1,7),(2,4),(3,5),(6,10),(8,9)] => [(1,5),(2,4),(3,9),(6,7),(8,10)] => 3
[(1,6),(2,4),(3,5),(7,10),(8,9)] => [(1,5),(2,4),(3,6),(7,9),(8,10)] => 3
[(1,5),(2,4),(3,6),(7,10),(8,9)] => [(1,6),(2,4),(3,5),(7,9),(8,10)] => 2
[(1,4),(2,5),(3,6),(7,10),(8,9)] => [(1,6),(2,5),(3,4),(7,9),(8,10)] => 1
[(1,3),(2,5),(4,6),(7,10),(8,9)] => [(1,6),(2,3),(4,5),(7,9),(8,10)] => 1
[(1,2),(3,5),(4,6),(7,10),(8,9)] => [(1,2),(3,6),(4,5),(7,9),(8,10)] => 1
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [(1,2),(3,5),(4,6),(7,9),(8,10)] => 2
[(1,3),(2,6),(4,5),(7,10),(8,9)] => [(1,5),(2,3),(4,6),(7,9),(8,10)] => 2
[(1,4),(2,6),(3,5),(7,10),(8,9)] => [(1,5),(2,6),(3,4),(7,9),(8,10)] => 2
[(1,5),(2,6),(3,4),(7,10),(8,9)] => [(1,4),(2,6),(3,5),(7,9),(8,10)] => 3
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [(1,4),(2,5),(3,6),(7,9),(8,10)] => 4
[(1,7),(2,5),(3,4),(6,10),(8,9)] => [(1,4),(2,5),(3,9),(6,7),(8,10)] => 4
[(1,8),(2,5),(3,4),(6,10),(7,9)] => [(1,4),(2,5),(3,9),(6,10),(7,8)] => 4
[(1,9),(2,5),(3,4),(6,10),(7,8)] => [(1,4),(2,5),(3,8),(6,10),(7,9)] => 5
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [(1,4),(2,5),(3,8),(6,9),(7,10)] => 6
[(1,10),(2,6),(3,4),(5,9),(7,8)] => [(1,4),(2,8),(3,6),(5,9),(7,10)] => 6
[(1,9),(2,6),(3,4),(5,10),(7,8)] => [(1,4),(2,8),(3,6),(5,10),(7,9)] => 5
[(1,8),(2,6),(3,4),(5,10),(7,9)] => [(1,4),(2,9),(3,6),(5,10),(7,8)] => 4
[(1,7),(2,6),(3,4),(5,10),(8,9)] => [(1,4),(2,9),(3,6),(5,7),(8,10)] => 4
[(1,6),(2,7),(3,4),(5,10),(8,9)] => [(1,4),(2,9),(3,7),(5,6),(8,10)] => 3
[(1,5),(2,7),(3,4),(6,10),(8,9)] => [(1,4),(2,9),(3,5),(6,7),(8,10)] => 3
[(1,4),(2,7),(3,5),(6,10),(8,9)] => [(1,5),(2,9),(3,4),(6,7),(8,10)] => 2
[(1,3),(2,7),(4,5),(6,10),(8,9)] => [(1,5),(2,3),(4,9),(6,7),(8,10)] => 2
[(1,2),(3,7),(4,5),(6,10),(8,9)] => [(1,2),(3,5),(4,9),(6,7),(8,10)] => 2
[(1,2),(3,8),(4,5),(6,10),(7,9)] => [(1,2),(3,5),(4,9),(6,10),(7,8)] => 2
[(1,3),(2,8),(4,5),(6,10),(7,9)] => [(1,5),(2,3),(4,9),(6,10),(7,8)] => 2
[(1,4),(2,8),(3,5),(6,10),(7,9)] => [(1,5),(2,9),(3,4),(6,10),(7,8)] => 2
[(1,5),(2,8),(3,4),(6,10),(7,9)] => [(1,4),(2,9),(3,5),(6,10),(7,8)] => 3
[(1,6),(2,8),(3,4),(5,10),(7,9)] => [(1,4),(2,9),(3,10),(5,6),(7,8)] => 3
[(1,7),(2,8),(3,4),(5,10),(6,9)] => [(1,4),(2,9),(3,10),(5,8),(6,7)] => 3
[(1,8),(2,7),(3,4),(5,10),(6,9)] => [(1,4),(2,9),(3,10),(5,7),(6,8)] => 4
[(1,9),(2,7),(3,4),(5,10),(6,8)] => [(1,4),(2,8),(3,10),(5,7),(6,9)] => 5
[(1,10),(2,7),(3,4),(5,9),(6,8)] => [(1,4),(2,8),(3,9),(5,7),(6,10)] => 6
[(1,10),(2,8),(3,4),(5,9),(6,7)] => [(1,4),(2,7),(3,9),(5,8),(6,10)] => 7
[(1,9),(2,8),(3,4),(5,10),(6,7)] => [(1,4),(2,7),(3,10),(5,8),(6,9)] => 6
[(1,8),(2,9),(3,4),(5,10),(6,7)] => [(1,4),(2,7),(3,10),(5,9),(6,8)] => 5
[(1,7),(2,9),(3,4),(5,10),(6,8)] => [(1,4),(2,8),(3,10),(5,9),(6,7)] => 4
[(1,6),(2,9),(3,4),(5,10),(7,8)] => [(1,4),(2,8),(3,10),(5,6),(7,9)] => 4
[(1,5),(2,9),(3,4),(6,10),(7,8)] => [(1,4),(2,8),(3,5),(6,10),(7,9)] => 4
[(1,4),(2,9),(3,5),(6,10),(7,8)] => [(1,5),(2,8),(3,4),(6,10),(7,9)] => 3
[(1,3),(2,9),(4,5),(6,10),(7,8)] => [(1,5),(2,3),(4,8),(6,10),(7,9)] => 3
[(1,2),(3,9),(4,5),(6,10),(7,8)] => [(1,2),(3,5),(4,8),(6,10),(7,9)] => 3
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [(1,2),(3,5),(4,8),(6,9),(7,10)] => 4
[(1,3),(2,10),(4,5),(6,9),(7,8)] => [(1,5),(2,3),(4,8),(6,9),(7,10)] => 4
[(1,4),(2,10),(3,5),(6,9),(7,8)] => [(1,5),(2,8),(3,4),(6,9),(7,10)] => 4
[(1,5),(2,10),(3,4),(6,9),(7,8)] => [(1,4),(2,8),(3,5),(6,9),(7,10)] => 5
[(1,6),(2,10),(3,4),(5,9),(7,8)] => [(1,4),(2,8),(3,9),(5,6),(7,10)] => 5
[(1,7),(2,10),(3,4),(5,9),(6,8)] => [(1,4),(2,8),(3,9),(5,10),(6,7)] => 5
[(1,8),(2,10),(3,4),(5,9),(6,7)] => [(1,4),(2,7),(3,9),(5,10),(6,8)] => 6
[(1,9),(2,10),(3,4),(5,8),(6,7)] => [(1,4),(2,7),(3,8),(5,10),(6,9)] => 7
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [(1,4),(2,7),(3,8),(5,9),(6,10)] => 8
[(1,10),(2,9),(3,5),(4,8),(6,7)] => [(1,7),(2,5),(3,8),(4,9),(6,10)] => 8
[(1,9),(2,10),(3,5),(4,8),(6,7)] => [(1,7),(2,5),(3,8),(4,10),(6,9)] => 7
[(1,8),(2,10),(3,5),(4,9),(6,7)] => [(1,7),(2,5),(3,9),(4,10),(6,8)] => 6
[(1,7),(2,10),(3,5),(4,9),(6,8)] => [(1,8),(2,5),(3,9),(4,10),(6,7)] => 5
[(1,6),(2,10),(3,5),(4,9),(7,8)] => [(1,8),(2,5),(3,9),(4,6),(7,10)] => 5
[(1,5),(2,10),(3,6),(4,9),(7,8)] => [(1,8),(2,6),(3,9),(4,5),(7,10)] => 4
[(1,4),(2,10),(3,6),(5,9),(7,8)] => [(1,8),(2,6),(3,4),(5,9),(7,10)] => 4
[(1,3),(2,10),(4,6),(5,9),(7,8)] => [(1,8),(2,3),(4,6),(5,9),(7,10)] => 4
[(1,2),(3,10),(4,6),(5,9),(7,8)] => [(1,2),(3,8),(4,6),(5,9),(7,10)] => 4
[(1,2),(3,9),(4,6),(5,10),(7,8)] => [(1,2),(3,8),(4,6),(5,10),(7,9)] => 3
[(1,3),(2,9),(4,6),(5,10),(7,8)] => [(1,8),(2,3),(4,6),(5,10),(7,9)] => 3
[(1,4),(2,9),(3,6),(5,10),(7,8)] => [(1,8),(2,6),(3,4),(5,10),(7,9)] => 3
[(1,5),(2,9),(3,6),(4,10),(7,8)] => [(1,8),(2,6),(3,10),(4,5),(7,9)] => 3
[(1,6),(2,9),(3,5),(4,10),(7,8)] => [(1,8),(2,5),(3,10),(4,6),(7,9)] => 4
[(1,7),(2,9),(3,5),(4,10),(6,8)] => [(1,8),(2,5),(3,10),(4,9),(6,7)] => 4
[(1,8),(2,9),(3,5),(4,10),(6,7)] => [(1,7),(2,5),(3,10),(4,9),(6,8)] => 5
[(1,9),(2,8),(3,5),(4,10),(6,7)] => [(1,7),(2,5),(3,10),(4,8),(6,9)] => 6
[(1,10),(2,8),(3,5),(4,9),(6,7)] => [(1,7),(2,5),(3,9),(4,8),(6,10)] => 7
[(1,10),(2,7),(3,5),(4,9),(6,8)] => [(1,8),(2,5),(3,9),(4,7),(6,10)] => 6
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [(1,8),(2,5),(3,10),(4,7),(6,9)] => 5
[(1,8),(2,7),(3,5),(4,10),(6,9)] => [(1,9),(2,5),(3,10),(4,7),(6,8)] => 4
[(1,7),(2,8),(3,5),(4,10),(6,9)] => [(1,9),(2,5),(3,10),(4,8),(6,7)] => 3
[(1,6),(2,8),(3,5),(4,10),(7,9)] => [(1,9),(2,5),(3,10),(4,6),(7,8)] => 3
[(1,5),(2,8),(3,6),(4,10),(7,9)] => [(1,9),(2,6),(3,10),(4,5),(7,8)] => 2
[(1,4),(2,8),(3,6),(5,10),(7,9)] => [(1,9),(2,6),(3,4),(5,10),(7,8)] => 2
[(1,3),(2,8),(4,6),(5,10),(7,9)] => [(1,9),(2,3),(4,6),(5,10),(7,8)] => 2
[(1,2),(3,8),(4,6),(5,10),(7,9)] => [(1,2),(3,9),(4,6),(5,10),(7,8)] => 2
[(1,2),(3,7),(4,6),(5,10),(8,9)] => [(1,2),(3,9),(4,6),(5,7),(8,10)] => 2
[(1,3),(2,7),(4,6),(5,10),(8,9)] => [(1,9),(2,3),(4,6),(5,7),(8,10)] => 2
[(1,4),(2,7),(3,6),(5,10),(8,9)] => [(1,9),(2,6),(3,4),(5,7),(8,10)] => 2
[(1,5),(2,7),(3,6),(4,10),(8,9)] => [(1,9),(2,6),(3,7),(4,5),(8,10)] => 2
[(1,6),(2,7),(3,5),(4,10),(8,9)] => [(1,9),(2,5),(3,7),(4,6),(8,10)] => 3
[(1,7),(2,6),(3,5),(4,10),(8,9)] => [(1,9),(2,5),(3,6),(4,7),(8,10)] => 4
[(1,8),(2,6),(3,5),(4,10),(7,9)] => [(1,9),(2,5),(3,6),(4,10),(7,8)] => 4
[(1,9),(2,6),(3,5),(4,10),(7,8)] => [(1,8),(2,5),(3,6),(4,10),(7,9)] => 5
[(1,10),(2,6),(3,5),(4,9),(7,8)] => [(1,8),(2,5),(3,6),(4,9),(7,10)] => 6
[(1,10),(2,5),(3,6),(4,9),(7,8)] => [(1,8),(2,6),(3,5),(4,9),(7,10)] => 5
[(1,9),(2,5),(3,6),(4,10),(7,8)] => [(1,8),(2,6),(3,5),(4,10),(7,9)] => 4
[(1,8),(2,5),(3,6),(4,10),(7,9)] => [(1,9),(2,6),(3,5),(4,10),(7,8)] => 3
[(1,7),(2,5),(3,6),(4,10),(8,9)] => [(1,9),(2,6),(3,5),(4,7),(8,10)] => 3
[(1,6),(2,5),(3,7),(4,10),(8,9)] => [(1,9),(2,7),(3,5),(4,6),(8,10)] => 2
[(1,5),(2,6),(3,7),(4,10),(8,9)] => [(1,9),(2,7),(3,6),(4,5),(8,10)] => 1
[(1,4),(2,6),(3,7),(5,10),(8,9)] => [(1,9),(2,7),(3,4),(5,6),(8,10)] => 1
[(1,3),(2,6),(4,7),(5,10),(8,9)] => [(1,9),(2,3),(4,7),(5,6),(8,10)] => 1
[(1,2),(3,6),(4,7),(5,10),(8,9)] => [(1,2),(3,9),(4,7),(5,6),(8,10)] => 1
[(1,2),(3,5),(4,7),(6,10),(8,9)] => [(1,2),(3,9),(4,5),(6,7),(8,10)] => 1
[(1,3),(2,5),(4,7),(6,10),(8,9)] => [(1,9),(2,3),(4,5),(6,7),(8,10)] => 1
[(1,4),(2,5),(3,7),(6,10),(8,9)] => [(1,9),(2,5),(3,4),(6,7),(8,10)] => 1
[(1,5),(2,4),(3,7),(6,10),(8,9)] => [(1,9),(2,4),(3,5),(6,7),(8,10)] => 2
[(1,6),(2,4),(3,7),(5,10),(8,9)] => [(1,9),(2,4),(3,7),(5,6),(8,10)] => 2
[(1,7),(2,4),(3,6),(5,10),(8,9)] => [(1,9),(2,4),(3,6),(5,7),(8,10)] => 3
[(1,8),(2,4),(3,6),(5,10),(7,9)] => [(1,9),(2,4),(3,6),(5,10),(7,8)] => 3
[(1,9),(2,4),(3,6),(5,10),(7,8)] => [(1,8),(2,4),(3,6),(5,10),(7,9)] => 4
[(1,10),(2,4),(3,6),(5,9),(7,8)] => [(1,8),(2,4),(3,6),(5,9),(7,10)] => 5
[(1,10),(2,3),(4,6),(5,9),(7,8)] => [(1,3),(2,8),(4,6),(5,9),(7,10)] => 5
[(1,9),(2,3),(4,6),(5,10),(7,8)] => [(1,3),(2,8),(4,6),(5,10),(7,9)] => 4
[(1,8),(2,3),(4,6),(5,10),(7,9)] => [(1,3),(2,9),(4,6),(5,10),(7,8)] => 3
[(1,7),(2,3),(4,6),(5,10),(8,9)] => [(1,3),(2,9),(4,6),(5,7),(8,10)] => 3
[(1,6),(2,3),(4,7),(5,10),(8,9)] => [(1,3),(2,9),(4,7),(5,6),(8,10)] => 2
[(1,5),(2,3),(4,7),(6,10),(8,9)] => [(1,3),(2,9),(4,5),(6,7),(8,10)] => 2
[(1,4),(2,3),(5,7),(6,10),(8,9)] => [(1,3),(2,4),(5,9),(6,7),(8,10)] => 2
[(1,3),(2,4),(5,7),(6,10),(8,9)] => [(1,4),(2,3),(5,9),(6,7),(8,10)] => 1
[(1,2),(3,4),(5,7),(6,10),(8,9)] => [(1,2),(3,4),(5,9),(6,7),(8,10)] => 1
[(1,2),(3,4),(5,8),(6,10),(7,9)] => [(1,2),(3,4),(5,9),(6,10),(7,8)] => 1
[(1,3),(2,4),(5,8),(6,10),(7,9)] => [(1,4),(2,3),(5,9),(6,10),(7,8)] => 1
[(1,4),(2,3),(5,8),(6,10),(7,9)] => [(1,3),(2,4),(5,9),(6,10),(7,8)] => 2
[(1,5),(2,3),(4,8),(6,10),(7,9)] => [(1,3),(2,9),(4,5),(6,10),(7,8)] => 2
[(1,6),(2,3),(4,8),(5,10),(7,9)] => [(1,3),(2,9),(4,10),(5,6),(7,8)] => 2
[(1,7),(2,3),(4,8),(5,10),(6,9)] => [(1,3),(2,9),(4,10),(5,8),(6,7)] => 2
[(1,8),(2,3),(4,7),(5,10),(6,9)] => [(1,3),(2,9),(4,10),(5,7),(6,8)] => 3
[(1,9),(2,3),(4,7),(5,10),(6,8)] => [(1,3),(2,8),(4,10),(5,7),(6,9)] => 4
[(1,10),(2,3),(4,7),(5,9),(6,8)] => [(1,3),(2,8),(4,9),(5,7),(6,10)] => 5
[(1,10),(2,4),(3,7),(5,9),(6,8)] => [(1,8),(2,4),(3,9),(5,7),(6,10)] => 5
[(1,9),(2,4),(3,7),(5,10),(6,8)] => [(1,8),(2,4),(3,10),(5,7),(6,9)] => 4
[(1,8),(2,4),(3,7),(5,10),(6,9)] => [(1,9),(2,4),(3,10),(5,7),(6,8)] => 3
[(1,7),(2,4),(3,8),(5,10),(6,9)] => [(1,9),(2,4),(3,10),(5,8),(6,7)] => 2
[(1,6),(2,4),(3,8),(5,10),(7,9)] => [(1,9),(2,4),(3,10),(5,6),(7,8)] => 2
[(1,5),(2,4),(3,8),(6,10),(7,9)] => [(1,9),(2,4),(3,5),(6,10),(7,8)] => 2
[(1,4),(2,5),(3,8),(6,10),(7,9)] => [(1,9),(2,5),(3,4),(6,10),(7,8)] => 1
[(1,3),(2,5),(4,8),(6,10),(7,9)] => [(1,9),(2,3),(4,5),(6,10),(7,8)] => 1
[(1,2),(3,5),(4,8),(6,10),(7,9)] => [(1,2),(3,9),(4,5),(6,10),(7,8)] => 1
[(1,2),(3,6),(4,8),(5,10),(7,9)] => [(1,2),(3,9),(4,10),(5,6),(7,8)] => 1
[(1,3),(2,6),(4,8),(5,10),(7,9)] => [(1,9),(2,3),(4,10),(5,6),(7,8)] => 1
[(1,4),(2,6),(3,8),(5,10),(7,9)] => [(1,9),(2,10),(3,4),(5,6),(7,8)] => 1
[(1,5),(2,6),(3,8),(4,10),(7,9)] => [(1,9),(2,10),(3,6),(4,5),(7,8)] => 1
[(1,6),(2,5),(3,8),(4,10),(7,9)] => [(1,9),(2,10),(3,5),(4,6),(7,8)] => 2
[(1,7),(2,5),(3,8),(4,10),(6,9)] => [(1,9),(2,10),(3,5),(4,8),(6,7)] => 2
[(1,8),(2,5),(3,7),(4,10),(6,9)] => [(1,9),(2,10),(3,5),(4,7),(6,8)] => 3
[(1,9),(2,5),(3,7),(4,10),(6,8)] => [(1,8),(2,10),(3,5),(4,7),(6,9)] => 4
[(1,10),(2,5),(3,7),(4,9),(6,8)] => [(1,8),(2,9),(3,5),(4,7),(6,10)] => 5
[(1,10),(2,6),(3,7),(4,9),(5,8)] => [(1,8),(2,9),(3,7),(4,6),(5,10)] => 5
[(1,9),(2,6),(3,7),(4,10),(5,8)] => [(1,8),(2,10),(3,7),(4,6),(5,9)] => 4
[(1,8),(2,6),(3,7),(4,10),(5,9)] => [(1,9),(2,10),(3,7),(4,6),(5,8)] => 3
[(1,7),(2,6),(3,8),(4,10),(5,9)] => [(1,9),(2,10),(3,8),(4,6),(5,7)] => 2
[(1,6),(2,7),(3,8),(4,10),(5,9)] => [(1,9),(2,10),(3,8),(4,7),(5,6)] => 1
[(1,5),(2,7),(3,8),(4,10),(6,9)] => [(1,9),(2,10),(3,8),(4,5),(6,7)] => 1
[(1,4),(2,7),(3,8),(5,10),(6,9)] => [(1,9),(2,10),(3,4),(5,8),(6,7)] => 1
[(1,3),(2,7),(4,8),(5,10),(6,9)] => [(1,9),(2,3),(4,10),(5,8),(6,7)] => 1
[(1,2),(3,7),(4,8),(5,10),(6,9)] => [(1,2),(3,9),(4,10),(5,8),(6,7)] => 1
[(1,2),(3,8),(4,7),(5,10),(6,9)] => [(1,2),(3,9),(4,10),(5,7),(6,8)] => 2
[(1,3),(2,8),(4,7),(5,10),(6,9)] => [(1,9),(2,3),(4,10),(5,7),(6,8)] => 2
[(1,4),(2,8),(3,7),(5,10),(6,9)] => [(1,9),(2,10),(3,4),(5,7),(6,8)] => 2
[(1,5),(2,8),(3,7),(4,10),(6,9)] => [(1,9),(2,10),(3,7),(4,5),(6,8)] => 2
[(1,6),(2,8),(3,7),(4,10),(5,9)] => [(1,9),(2,10),(3,7),(4,8),(5,6)] => 2
[(1,7),(2,8),(3,6),(4,10),(5,9)] => [(1,9),(2,10),(3,6),(4,8),(5,7)] => 3
[(1,8),(2,7),(3,6),(4,10),(5,9)] => [(1,9),(2,10),(3,6),(4,7),(5,8)] => 4
[(1,9),(2,7),(3,6),(4,10),(5,8)] => [(1,8),(2,10),(3,6),(4,7),(5,9)] => 5
[(1,10),(2,7),(3,6),(4,9),(5,8)] => [(1,8),(2,9),(3,6),(4,7),(5,10)] => 6
[(1,10),(2,8),(3,6),(4,9),(5,7)] => [(1,7),(2,9),(3,6),(4,8),(5,10)] => 7
[(1,9),(2,8),(3,6),(4,10),(5,7)] => [(1,7),(2,10),(3,6),(4,8),(5,9)] => 6
[(1,8),(2,9),(3,6),(4,10),(5,7)] => [(1,7),(2,10),(3,6),(4,9),(5,8)] => 5
[(1,7),(2,9),(3,6),(4,10),(5,8)] => [(1,8),(2,10),(3,6),(4,9),(5,7)] => 4
[(1,6),(2,9),(3,7),(4,10),(5,8)] => [(1,8),(2,10),(3,7),(4,9),(5,6)] => 3
[(1,5),(2,9),(3,7),(4,10),(6,8)] => [(1,8),(2,10),(3,7),(4,5),(6,9)] => 3
[(1,4),(2,9),(3,7),(5,10),(6,8)] => [(1,8),(2,10),(3,4),(5,7),(6,9)] => 3
[(1,3),(2,9),(4,7),(5,10),(6,8)] => [(1,8),(2,3),(4,10),(5,7),(6,9)] => 3
[(1,2),(3,9),(4,7),(5,10),(6,8)] => [(1,2),(3,8),(4,10),(5,7),(6,9)] => 3
[(1,2),(3,10),(4,7),(5,9),(6,8)] => [(1,2),(3,8),(4,9),(5,7),(6,10)] => 4
[(1,3),(2,10),(4,7),(5,9),(6,8)] => [(1,8),(2,3),(4,9),(5,7),(6,10)] => 4
[(1,4),(2,10),(3,7),(5,9),(6,8)] => [(1,8),(2,9),(3,4),(5,7),(6,10)] => 4
[(1,5),(2,10),(3,7),(4,9),(6,8)] => [(1,8),(2,9),(3,7),(4,5),(6,10)] => 4
[(1,6),(2,10),(3,7),(4,9),(5,8)] => [(1,8),(2,9),(3,7),(4,10),(5,6)] => 4
[(1,7),(2,10),(3,6),(4,9),(5,8)] => [(1,8),(2,9),(3,6),(4,10),(5,7)] => 5
[(1,8),(2,10),(3,6),(4,9),(5,7)] => [(1,7),(2,9),(3,6),(4,10),(5,8)] => 6
[(1,9),(2,10),(3,6),(4,8),(5,7)] => [(1,7),(2,8),(3,6),(4,10),(5,9)] => 7
[(1,10),(2,9),(3,6),(4,8),(5,7)] => [(1,7),(2,8),(3,6),(4,9),(5,10)] => 8
[(1,10),(2,9),(3,7),(4,8),(5,6)] => [(1,6),(2,8),(3,7),(4,9),(5,10)] => 9
[(1,9),(2,10),(3,7),(4,8),(5,6)] => [(1,6),(2,8),(3,7),(4,10),(5,9)] => 8
[(1,8),(2,10),(3,7),(4,9),(5,6)] => [(1,6),(2,9),(3,7),(4,10),(5,8)] => 7
[(1,7),(2,10),(3,8),(4,9),(5,6)] => [(1,6),(2,9),(3,8),(4,10),(5,7)] => 6
[(1,6),(2,10),(3,8),(4,9),(5,7)] => [(1,7),(2,9),(3,8),(4,10),(5,6)] => 5
[(1,5),(2,10),(3,8),(4,9),(6,7)] => [(1,7),(2,9),(3,8),(4,5),(6,10)] => 5
[(1,4),(2,10),(3,8),(5,9),(6,7)] => [(1,7),(2,9),(3,4),(5,8),(6,10)] => 5
[(1,3),(2,10),(4,8),(5,9),(6,7)] => [(1,7),(2,3),(4,9),(5,8),(6,10)] => 5
[(1,2),(3,10),(4,8),(5,9),(6,7)] => [(1,2),(3,7),(4,9),(5,8),(6,10)] => 5
[(1,2),(3,9),(4,8),(5,10),(6,7)] => [(1,2),(3,7),(4,10),(5,8),(6,9)] => 4
[(1,3),(2,9),(4,8),(5,10),(6,7)] => [(1,7),(2,3),(4,10),(5,8),(6,9)] => 4
[(1,4),(2,9),(3,8),(5,10),(6,7)] => [(1,7),(2,10),(3,4),(5,8),(6,9)] => 4
[(1,5),(2,9),(3,8),(4,10),(6,7)] => [(1,7),(2,10),(3,8),(4,5),(6,9)] => 4
[(1,6),(2,9),(3,8),(4,10),(5,7)] => [(1,7),(2,10),(3,8),(4,9),(5,6)] => 4
[(1,7),(2,9),(3,8),(4,10),(5,6)] => [(1,6),(2,10),(3,8),(4,9),(5,7)] => 5
[(1,8),(2,9),(3,7),(4,10),(5,6)] => [(1,6),(2,10),(3,7),(4,9),(5,8)] => 6
[(1,9),(2,8),(3,7),(4,10),(5,6)] => [(1,6),(2,10),(3,7),(4,8),(5,9)] => 7
[(1,10),(2,8),(3,7),(4,9),(5,6)] => [(1,6),(2,9),(3,7),(4,8),(5,10)] => 8
[(1,10),(2,7),(3,8),(4,9),(5,6)] => [(1,6),(2,9),(3,8),(4,7),(5,10)] => 7
[(1,9),(2,7),(3,8),(4,10),(5,6)] => [(1,6),(2,10),(3,8),(4,7),(5,9)] => 6
[(1,8),(2,7),(3,9),(4,10),(5,6)] => [(1,6),(2,10),(3,9),(4,7),(5,8)] => 5
[(1,7),(2,8),(3,9),(4,10),(5,6)] => [(1,6),(2,10),(3,9),(4,8),(5,7)] => 4
[(1,6),(2,8),(3,9),(4,10),(5,7)] => [(1,7),(2,10),(3,9),(4,8),(5,6)] => 3
[(1,5),(2,8),(3,9),(4,10),(6,7)] => [(1,7),(2,10),(3,9),(4,5),(6,8)] => 3
[(1,4),(2,8),(3,9),(5,10),(6,7)] => [(1,7),(2,10),(3,4),(5,9),(6,8)] => 3
[(1,3),(2,8),(4,9),(5,10),(6,7)] => [(1,7),(2,3),(4,10),(5,9),(6,8)] => 3
[(1,2),(3,8),(4,9),(5,10),(6,7)] => [(1,2),(3,7),(4,10),(5,9),(6,8)] => 3
[(1,2),(3,7),(4,9),(5,10),(6,8)] => [(1,2),(3,8),(4,10),(5,9),(6,7)] => 2
[(1,3),(2,7),(4,9),(5,10),(6,8)] => [(1,8),(2,3),(4,10),(5,9),(6,7)] => 2
[(1,4),(2,7),(3,9),(5,10),(6,8)] => [(1,8),(2,10),(3,4),(5,9),(6,7)] => 2
[(1,5),(2,7),(3,9),(4,10),(6,8)] => [(1,8),(2,10),(3,9),(4,5),(6,7)] => 2
[(1,6),(2,7),(3,9),(4,10),(5,8)] => [(1,8),(2,10),(3,9),(4,7),(5,6)] => 2
[(1,7),(2,6),(3,9),(4,10),(5,8)] => [(1,8),(2,10),(3,9),(4,6),(5,7)] => 3
[(1,8),(2,6),(3,9),(4,10),(5,7)] => [(1,7),(2,10),(3,9),(4,6),(5,8)] => 4
[(1,9),(2,6),(3,8),(4,10),(5,7)] => [(1,7),(2,10),(3,8),(4,6),(5,9)] => 5
[(1,10),(2,6),(3,8),(4,9),(5,7)] => [(1,7),(2,9),(3,8),(4,6),(5,10)] => 6
[(1,10),(2,5),(3,8),(4,9),(6,7)] => [(1,7),(2,9),(3,5),(4,8),(6,10)] => 6
[(1,9),(2,5),(3,8),(4,10),(6,7)] => [(1,7),(2,10),(3,5),(4,8),(6,9)] => 5
[(1,8),(2,5),(3,9),(4,10),(6,7)] => [(1,7),(2,10),(3,5),(4,9),(6,8)] => 4
[(1,7),(2,5),(3,9),(4,10),(6,8)] => [(1,8),(2,10),(3,5),(4,9),(6,7)] => 3
[(1,6),(2,5),(3,9),(4,10),(7,8)] => [(1,8),(2,10),(3,5),(4,6),(7,9)] => 3
[(1,5),(2,6),(3,9),(4,10),(7,8)] => [(1,8),(2,10),(3,6),(4,5),(7,9)] => 2
[(1,4),(2,6),(3,9),(5,10),(7,8)] => [(1,8),(2,10),(3,4),(5,6),(7,9)] => 2
[(1,3),(2,6),(4,9),(5,10),(7,8)] => [(1,8),(2,3),(4,10),(5,6),(7,9)] => 2
[(1,2),(3,6),(4,9),(5,10),(7,8)] => [(1,2),(3,8),(4,10),(5,6),(7,9)] => 2
[(1,2),(3,5),(4,9),(6,10),(7,8)] => [(1,2),(3,8),(4,5),(6,10),(7,9)] => 2
[(1,3),(2,5),(4,9),(6,10),(7,8)] => [(1,8),(2,3),(4,5),(6,10),(7,9)] => 2
[(1,4),(2,5),(3,9),(6,10),(7,8)] => [(1,8),(2,5),(3,4),(6,10),(7,9)] => 2
[(1,5),(2,4),(3,9),(6,10),(7,8)] => [(1,8),(2,4),(3,5),(6,10),(7,9)] => 3
[(1,6),(2,4),(3,9),(5,10),(7,8)] => [(1,8),(2,4),(3,10),(5,6),(7,9)] => 3
[(1,7),(2,4),(3,9),(5,10),(6,8)] => [(1,8),(2,4),(3,10),(5,9),(6,7)] => 3
[(1,8),(2,4),(3,9),(5,10),(6,7)] => [(1,7),(2,4),(3,10),(5,9),(6,8)] => 4
[(1,9),(2,4),(3,8),(5,10),(6,7)] => [(1,7),(2,4),(3,10),(5,8),(6,9)] => 5
[(1,10),(2,4),(3,8),(5,9),(6,7)] => [(1,7),(2,4),(3,9),(5,8),(6,10)] => 6
[(1,10),(2,3),(4,8),(5,9),(6,7)] => [(1,3),(2,7),(4,9),(5,8),(6,10)] => 6
[(1,9),(2,3),(4,8),(5,10),(6,7)] => [(1,3),(2,7),(4,10),(5,8),(6,9)] => 5
[(1,8),(2,3),(4,9),(5,10),(6,7)] => [(1,3),(2,7),(4,10),(5,9),(6,8)] => 4
[(1,7),(2,3),(4,9),(5,10),(6,8)] => [(1,3),(2,8),(4,10),(5,9),(6,7)] => 3
[(1,6),(2,3),(4,9),(5,10),(7,8)] => [(1,3),(2,8),(4,10),(5,6),(7,9)] => 3
[(1,5),(2,3),(4,9),(6,10),(7,8)] => [(1,3),(2,8),(4,5),(6,10),(7,9)] => 3
[(1,4),(2,3),(5,9),(6,10),(7,8)] => [(1,3),(2,4),(5,8),(6,10),(7,9)] => 3
[(1,3),(2,4),(5,9),(6,10),(7,8)] => [(1,4),(2,3),(5,8),(6,10),(7,9)] => 2
[(1,2),(3,4),(5,9),(6,10),(7,8)] => [(1,2),(3,4),(5,8),(6,10),(7,9)] => 2
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [(1,2),(3,4),(5,8),(6,9),(7,10)] => 3
[(1,3),(2,4),(5,10),(6,9),(7,8)] => [(1,4),(2,3),(5,8),(6,9),(7,10)] => 3
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [(1,3),(2,4),(5,8),(6,9),(7,10)] => 4
[(1,5),(2,3),(4,10),(6,9),(7,8)] => [(1,3),(2,8),(4,5),(6,9),(7,10)] => 4
[(1,6),(2,3),(4,10),(5,9),(7,8)] => [(1,3),(2,8),(4,9),(5,6),(7,10)] => 4
[(1,7),(2,3),(4,10),(5,9),(6,8)] => [(1,3),(2,8),(4,9),(5,10),(6,7)] => 4
[(1,8),(2,3),(4,10),(5,9),(6,7)] => [(1,3),(2,7),(4,9),(5,10),(6,8)] => 5
[(1,9),(2,3),(4,10),(5,8),(6,7)] => [(1,3),(2,7),(4,8),(5,10),(6,9)] => 6
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [(1,3),(2,7),(4,8),(5,9),(6,10)] => 7
[(1,10),(2,4),(3,9),(5,8),(6,7)] => [(1,7),(2,4),(3,8),(5,9),(6,10)] => 7
[(1,9),(2,4),(3,10),(5,8),(6,7)] => [(1,7),(2,4),(3,8),(5,10),(6,9)] => 6
[(1,8),(2,4),(3,10),(5,9),(6,7)] => [(1,7),(2,4),(3,9),(5,10),(6,8)] => 5
[(1,7),(2,4),(3,10),(5,9),(6,8)] => [(1,8),(2,4),(3,9),(5,10),(6,7)] => 4
[(1,6),(2,4),(3,10),(5,9),(7,8)] => [(1,8),(2,4),(3,9),(5,6),(7,10)] => 4
[(1,5),(2,4),(3,10),(6,9),(7,8)] => [(1,8),(2,4),(3,5),(6,9),(7,10)] => 4
[(1,4),(2,5),(3,10),(6,9),(7,8)] => [(1,8),(2,5),(3,4),(6,9),(7,10)] => 3
[(1,3),(2,5),(4,10),(6,9),(7,8)] => [(1,8),(2,3),(4,5),(6,9),(7,10)] => 3
[(1,2),(3,5),(4,10),(6,9),(7,8)] => [(1,2),(3,8),(4,5),(6,9),(7,10)] => 3
[(1,2),(3,6),(4,10),(5,9),(7,8)] => [(1,2),(3,8),(4,9),(5,6),(7,10)] => 3
[(1,3),(2,6),(4,10),(5,9),(7,8)] => [(1,8),(2,3),(4,9),(5,6),(7,10)] => 3
[(1,4),(2,6),(3,10),(5,9),(7,8)] => [(1,8),(2,9),(3,4),(5,6),(7,10)] => 3
[(1,5),(2,6),(3,10),(4,9),(7,8)] => [(1,8),(2,9),(3,6),(4,5),(7,10)] => 3
[(1,6),(2,5),(3,10),(4,9),(7,8)] => [(1,8),(2,9),(3,5),(4,6),(7,10)] => 4
[(1,7),(2,5),(3,10),(4,9),(6,8)] => [(1,8),(2,9),(3,5),(4,10),(6,7)] => 4
[(1,8),(2,5),(3,10),(4,9),(6,7)] => [(1,7),(2,9),(3,5),(4,10),(6,8)] => 5
[(1,9),(2,5),(3,10),(4,8),(6,7)] => [(1,7),(2,8),(3,5),(4,10),(6,9)] => 6
[(1,10),(2,5),(3,9),(4,8),(6,7)] => [(1,7),(2,8),(3,5),(4,9),(6,10)] => 7
[(1,10),(2,6),(3,9),(4,8),(5,7)] => [(1,7),(2,8),(3,9),(4,6),(5,10)] => 7
[(1,9),(2,6),(3,10),(4,8),(5,7)] => [(1,7),(2,8),(3,10),(4,6),(5,9)] => 6
[(1,8),(2,6),(3,10),(4,9),(5,7)] => [(1,7),(2,9),(3,10),(4,6),(5,8)] => 5
[(1,7),(2,6),(3,10),(4,9),(5,8)] => [(1,8),(2,9),(3,10),(4,6),(5,7)] => 4
[(1,6),(2,7),(3,10),(4,9),(5,8)] => [(1,8),(2,9),(3,10),(4,7),(5,6)] => 3
[(1,5),(2,7),(3,10),(4,9),(6,8)] => [(1,8),(2,9),(3,10),(4,5),(6,7)] => 3
[(1,4),(2,7),(3,10),(5,9),(6,8)] => [(1,8),(2,9),(3,4),(5,10),(6,7)] => 3
[(1,3),(2,7),(4,10),(5,9),(6,8)] => [(1,8),(2,3),(4,9),(5,10),(6,7)] => 3
[(1,2),(3,7),(4,10),(5,9),(6,8)] => [(1,2),(3,8),(4,9),(5,10),(6,7)] => 3
[(1,2),(3,8),(4,10),(5,9),(6,7)] => [(1,2),(3,7),(4,9),(5,10),(6,8)] => 4
[(1,3),(2,8),(4,10),(5,9),(6,7)] => [(1,7),(2,3),(4,9),(5,10),(6,8)] => 4
[(1,4),(2,8),(3,10),(5,9),(6,7)] => [(1,7),(2,9),(3,4),(5,10),(6,8)] => 4
[(1,5),(2,8),(3,10),(4,9),(6,7)] => [(1,7),(2,9),(3,10),(4,5),(6,8)] => 4
[(1,6),(2,8),(3,10),(4,9),(5,7)] => [(1,7),(2,9),(3,10),(4,8),(5,6)] => 4
[(1,7),(2,8),(3,10),(4,9),(5,6)] => [(1,6),(2,9),(3,10),(4,8),(5,7)] => 5
[(1,8),(2,7),(3,10),(4,9),(5,6)] => [(1,6),(2,9),(3,10),(4,7),(5,8)] => 6
[(1,9),(2,7),(3,10),(4,8),(5,6)] => [(1,6),(2,8),(3,10),(4,7),(5,9)] => 7
[(1,10),(2,7),(3,9),(4,8),(5,6)] => [(1,6),(2,8),(3,9),(4,7),(5,10)] => 8
[(1,10),(2,8),(3,9),(4,7),(5,6)] => [(1,6),(2,7),(3,9),(4,8),(5,10)] => 9
[(1,9),(2,8),(3,10),(4,7),(5,6)] => [(1,6),(2,7),(3,10),(4,8),(5,9)] => 8
[(1,8),(2,9),(3,10),(4,7),(5,6)] => [(1,6),(2,7),(3,10),(4,9),(5,8)] => 7
[(1,7),(2,9),(3,10),(4,8),(5,6)] => [(1,6),(2,8),(3,10),(4,9),(5,7)] => 6
[(1,6),(2,9),(3,10),(4,8),(5,7)] => [(1,7),(2,8),(3,10),(4,9),(5,6)] => 5
[(1,5),(2,9),(3,10),(4,8),(6,7)] => [(1,7),(2,8),(3,10),(4,5),(6,9)] => 5
[(1,4),(2,9),(3,10),(5,8),(6,7)] => [(1,7),(2,8),(3,4),(5,10),(6,9)] => 5
[(1,3),(2,9),(4,10),(5,8),(6,7)] => [(1,7),(2,3),(4,8),(5,10),(6,9)] => 5
[(1,2),(3,9),(4,10),(5,8),(6,7)] => [(1,2),(3,7),(4,8),(5,10),(6,9)] => 5
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [(1,2),(3,7),(4,8),(5,9),(6,10)] => 6
[(1,3),(2,10),(4,9),(5,8),(6,7)] => [(1,7),(2,3),(4,8),(5,9),(6,10)] => 6
[(1,4),(2,10),(3,9),(5,8),(6,7)] => [(1,7),(2,8),(3,4),(5,9),(6,10)] => 6
[(1,5),(2,10),(3,9),(4,8),(6,7)] => [(1,7),(2,8),(3,9),(4,5),(6,10)] => 6
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [(1,7),(2,8),(3,9),(4,10),(5,6)] => 6
[(1,7),(2,10),(3,9),(4,8),(5,6)] => [(1,6),(2,8),(3,9),(4,10),(5,7)] => 7
[(1,8),(2,10),(3,9),(4,7),(5,6)] => [(1,6),(2,7),(3,9),(4,10),(5,8)] => 8
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [(1,6),(2,7),(3,8),(4,10),(5,9)] => 9
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [(1,6),(2,7),(3,8),(4,9),(5,10)] => 10
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => 15
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => 6
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => 8
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => 7
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => 7
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => 10
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => 1
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => 9
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => 8
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => 2
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => 9
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => 2
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => 8
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => 3
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => 12
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => 3
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => 5
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => 4
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => 4
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => 11
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => 2
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => 10
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => 9
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => 3
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => 6
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => 3
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => 5
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => 4
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => 11
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => 2
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => 6
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => 5
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => 3
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => 10
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => 3
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => 9
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => 4
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => 7
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => 4
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => 4
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => 5
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => 5
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => 14
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => 5
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => 7
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => 6
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => 6
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => 9
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [(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)] => [(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => 8
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => 7
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => 1
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => 8
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => 1
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => 7
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => 2
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => 13
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => 4
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => 6
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => 5
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => 5
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => 12
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => 3
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => 11
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => 10
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => 4
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => 7
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => 4
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => 6
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => 5
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => 10
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => 1
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => 7
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => 6
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => 2
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => 9
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => 2
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => 8
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => 3
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => 8
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => 5
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => 3
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => 6
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => 4
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => 13
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => 4
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => 6
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => 5
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => 5
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => 10
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => 1
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => 9
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => 8
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => 2
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => 7
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => 2
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => 6
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => 3
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => 12
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => 3
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => 7
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => 6
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => 4
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => 11
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => 4
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => 10
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => 5
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => 8
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => 3
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => 5
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => 4
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => 6
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => 11
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => 2
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => 8
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => 7
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => 3
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => 8
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => 3
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => 7
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => 4
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => 9
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => 6
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => 4
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => 7
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => 5
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => 9
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => 4
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => 6
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => 5
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => 7
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => 6
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,1 5,6,3,1 14,28,28,20,10,4,1 42,120,180,195,165,117,70,35,15,5,1
$F_{2} = 1$
$F_{4} = 2 + q$
$F_{6} = 5 + 6\ q + 3\ q^{2} + q^{3}$
$F_{8} = 14 + 28\ q + 28\ q^{2} + 20\ q^{3} + 10\ q^{4} + 4\ q^{5} + q^{6}$
$F_{10} = 42 + 120\ q + 180\ q^{2} + 195\ q^{3} + 165\ q^{4} + 117\ q^{5} + 70\ q^{6} + 35\ q^{7} + 15\ q^{8} + 5\ q^{9} + q^{10}$
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]):
$$ \sum_{M} q^{\textrm{cr}(M)} = \frac{1}{(1-q)^n} \sum_{k=0}^n\left(\binom{2n}{n-k}-\binom{2n}{n-k-1}\right)(-1)^k q^{\binom{k+1}{2}} $$
Map
Kasraoui-Zeng
Description
The Kasraoui-Zeng involution for perfect matchings.
This yields the perfect matching with the number of nestings and crossings exchanged.
This yields the perfect matching with the number of nestings and crossings exchanged.
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