Identifier
Values
[(1,2)] => 0
[(1,2),(3,4)] => 0
[(1,3),(2,4)] => 0
[(1,4),(2,3)] => 0
[(1,2),(3,4),(5,6)] => 0
[(1,3),(2,4),(5,6)] => 0
[(1,4),(2,3),(5,6)] => 0
[(1,5),(2,3),(4,6)] => 0
[(1,6),(2,3),(4,5)] => 0
[(1,6),(2,4),(3,5)] => 0
[(1,5),(2,4),(3,6)] => 0
[(1,4),(2,5),(3,6)] => 1
[(1,3),(2,5),(4,6)] => 0
[(1,2),(3,5),(4,6)] => 0
[(1,2),(3,6),(4,5)] => 0
[(1,3),(2,6),(4,5)] => 0
[(1,4),(2,6),(3,5)] => 1
[(1,5),(2,6),(3,4)] => 2
[(1,6),(2,5),(3,4)] => 0
[(1,2),(3,4),(5,6),(7,8)] => 0
[(1,3),(2,4),(5,6),(7,8)] => 0
[(1,4),(2,3),(5,6),(7,8)] => 0
[(1,5),(2,3),(4,6),(7,8)] => 0
[(1,6),(2,3),(4,5),(7,8)] => 0
[(1,7),(2,3),(4,5),(6,8)] => 0
[(1,8),(2,3),(4,5),(6,7)] => 0
[(1,8),(2,4),(3,5),(6,7)] => 0
[(1,7),(2,4),(3,5),(6,8)] => 0
[(1,6),(2,4),(3,5),(7,8)] => 0
[(1,5),(2,4),(3,6),(7,8)] => 0
[(1,4),(2,5),(3,6),(7,8)] => 1
[(1,3),(2,5),(4,6),(7,8)] => 0
[(1,2),(3,5),(4,6),(7,8)] => 0
[(1,2),(3,6),(4,5),(7,8)] => 0
[(1,3),(2,6),(4,5),(7,8)] => 0
[(1,4),(2,6),(3,5),(7,8)] => 1
[(1,5),(2,6),(3,4),(7,8)] => 2
[(1,6),(2,5),(3,4),(7,8)] => 0
[(1,7),(2,5),(3,4),(6,8)] => 0
[(1,8),(2,5),(3,4),(6,7)] => 0
[(1,8),(2,6),(3,4),(5,7)] => 0
[(1,7),(2,6),(3,4),(5,8)] => 0
[(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)] => 1
[(1,3),(2,7),(4,5),(6,8)] => 0
[(1,2),(3,7),(4,5),(6,8)] => 0
[(1,2),(3,8),(4,5),(6,7)] => 0
[(1,3),(2,8),(4,5),(6,7)] => 0
[(1,4),(2,8),(3,5),(6,7)] => 1
[(1,5),(2,8),(3,4),(6,7)] => 2
[(1,6),(2,8),(3,4),(5,7)] => 3
[(1,7),(2,8),(3,4),(5,6)] => 4
[(1,8),(2,7),(3,4),(5,6)] => 0
[(1,8),(2,7),(3,5),(4,6)] => 0
[(1,7),(2,8),(3,5),(4,6)] => 4
[(1,6),(2,8),(3,5),(4,7)] => 3
[(1,5),(2,8),(3,6),(4,7)] => 3
[(1,4),(2,8),(3,6),(5,7)] => 1
[(1,3),(2,8),(4,6),(5,7)] => 0
[(1,2),(3,8),(4,6),(5,7)] => 0
[(1,2),(3,7),(4,6),(5,8)] => 0
[(1,3),(2,7),(4,6),(5,8)] => 0
[(1,4),(2,7),(3,6),(5,8)] => 1
[(1,5),(2,7),(3,6),(4,8)] => 3
[(1,6),(2,7),(3,5),(4,8)] => 3
[(1,7),(2,6),(3,5),(4,8)] => 0
[(1,8),(2,6),(3,5),(4,7)] => 0
[(1,8),(2,5),(3,6),(4,7)] => 1
[(1,7),(2,5),(3,6),(4,8)] => 1
[(1,6),(2,5),(3,7),(4,8)] => 2
[(1,5),(2,6),(3,7),(4,8)] => 4
[(1,4),(2,6),(3,7),(5,8)] => 2
[(1,3),(2,6),(4,7),(5,8)] => 1
[(1,2),(3,6),(4,7),(5,8)] => 1
[(1,2),(3,5),(4,7),(6,8)] => 0
[(1,3),(2,5),(4,7),(6,8)] => 0
[(1,4),(2,5),(3,7),(6,8)] => 1
[(1,5),(2,4),(3,7),(6,8)] => 0
[(1,6),(2,4),(3,7),(5,8)] => 1
[(1,7),(2,4),(3,6),(5,8)] => 0
[(1,8),(2,4),(3,6),(5,7)] => 0
[(1,8),(2,3),(4,6),(5,7)] => 0
[(1,7),(2,3),(4,6),(5,8)] => 0
[(1,6),(2,3),(4,7),(5,8)] => 1
[(1,5),(2,3),(4,7),(6,8)] => 0
[(1,4),(2,3),(5,7),(6,8)] => 0
[(1,3),(2,4),(5,7),(6,8)] => 0
[(1,2),(3,4),(5,7),(6,8)] => 0
[(1,2),(3,4),(5,8),(6,7)] => 0
[(1,3),(2,4),(5,8),(6,7)] => 0
[(1,4),(2,3),(5,8),(6,7)] => 0
[(1,5),(2,3),(4,8),(6,7)] => 0
[(1,6),(2,3),(4,8),(5,7)] => 1
[(1,7),(2,3),(4,8),(5,6)] => 2
[(1,8),(2,3),(4,7),(5,6)] => 0
[(1,8),(2,4),(3,7),(5,6)] => 0
[(1,7),(2,4),(3,8),(5,6)] => 2
[(1,6),(2,4),(3,8),(5,7)] => 1
[(1,5),(2,4),(3,8),(6,7)] => 0
[(1,4),(2,5),(3,8),(6,7)] => 1
>>> Load all 1069 entries. <<<[(1,3),(2,5),(4,8),(6,7)] => 0
[(1,2),(3,5),(4,8),(6,7)] => 0
[(1,2),(3,6),(4,8),(5,7)] => 1
[(1,3),(2,6),(4,8),(5,7)] => 1
[(1,4),(2,6),(3,8),(5,7)] => 2
[(1,5),(2,6),(3,8),(4,7)] => 4
[(1,6),(2,5),(3,8),(4,7)] => 2
[(1,7),(2,5),(3,8),(4,6)] => 3
[(1,8),(2,5),(3,7),(4,6)] => 1
[(1,8),(2,6),(3,7),(4,5)] => 2
[(1,7),(2,6),(3,8),(4,5)] => 4
[(1,6),(2,7),(3,8),(4,5)] => 7
[(1,5),(2,7),(3,8),(4,6)] => 5
[(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)] => 2
[(1,2),(3,8),(4,7),(5,6)] => 0
[(1,3),(2,8),(4,7),(5,6)] => 0
[(1,4),(2,8),(3,7),(5,6)] => 1
[(1,5),(2,8),(3,7),(4,6)] => 3
[(1,6),(2,8),(3,7),(4,5)] => 5
[(1,7),(2,8),(3,6),(4,5)] => 4
[(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)] => 0
[(1,4),(2,3),(5,6),(7,8),(9,10)] => 0
[(1,5),(2,3),(4,6),(7,8),(9,10)] => 0
[(1,6),(2,3),(4,5),(7,8),(9,10)] => 0
[(1,7),(2,3),(4,5),(6,8),(9,10)] => 0
[(1,8),(2,3),(4,5),(6,7),(9,10)] => 0
[(1,9),(2,3),(4,5),(6,7),(8,10)] => 0
[(1,10),(2,3),(4,5),(6,7),(8,9)] => 0
[(1,10),(2,4),(3,5),(6,7),(8,9)] => 0
[(1,9),(2,4),(3,5),(6,7),(8,10)] => 0
[(1,8),(2,4),(3,5),(6,7),(9,10)] => 0
[(1,7),(2,4),(3,5),(6,8),(9,10)] => 0
[(1,6),(2,4),(3,5),(7,8),(9,10)] => 0
[(1,5),(2,4),(3,6),(7,8),(9,10)] => 0
[(1,4),(2,5),(3,6),(7,8),(9,10)] => 1
[(1,3),(2,5),(4,6),(7,8),(9,10)] => 0
[(1,2),(3,5),(4,6),(7,8),(9,10)] => 0
[(1,2),(3,6),(4,5),(7,8),(9,10)] => 0
[(1,3),(2,6),(4,5),(7,8),(9,10)] => 0
[(1,4),(2,6),(3,5),(7,8),(9,10)] => 1
[(1,5),(2,6),(3,4),(7,8),(9,10)] => 2
[(1,6),(2,5),(3,4),(7,8),(9,10)] => 0
[(1,7),(2,5),(3,4),(6,8),(9,10)] => 0
[(1,8),(2,5),(3,4),(6,7),(9,10)] => 0
[(1,9),(2,5),(3,4),(6,7),(8,10)] => 0
[(1,10),(2,5),(3,4),(6,7),(8,9)] => 0
[(1,10),(2,6),(3,4),(5,7),(8,9)] => 0
[(1,9),(2,6),(3,4),(5,7),(8,10)] => 0
[(1,8),(2,6),(3,4),(5,7),(9,10)] => 0
[(1,7),(2,6),(3,4),(5,8),(9,10)] => 0
[(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)] => 1
[(1,3),(2,7),(4,5),(6,8),(9,10)] => 0
[(1,2),(3,7),(4,5),(6,8),(9,10)] => 0
[(1,2),(3,8),(4,5),(6,7),(9,10)] => 0
[(1,3),(2,8),(4,5),(6,7),(9,10)] => 0
[(1,4),(2,8),(3,5),(6,7),(9,10)] => 1
[(1,5),(2,8),(3,4),(6,7),(9,10)] => 2
[(1,6),(2,8),(3,4),(5,7),(9,10)] => 3
[(1,7),(2,8),(3,4),(5,6),(9,10)] => 4
[(1,8),(2,7),(3,4),(5,6),(9,10)] => 0
[(1,9),(2,7),(3,4),(5,6),(8,10)] => 0
[(1,10),(2,7),(3,4),(5,6),(8,9)] => 0
[(1,10),(2,8),(3,4),(5,6),(7,9)] => 0
[(1,9),(2,8),(3,4),(5,6),(7,10)] => 0
[(1,8),(2,9),(3,4),(5,6),(7,10)] => 5
[(1,7),(2,9),(3,4),(5,6),(8,10)] => 4
[(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)] => 1
[(1,3),(2,9),(4,5),(6,7),(8,10)] => 0
[(1,2),(3,9),(4,5),(6,7),(8,10)] => 0
[(1,2),(3,10),(4,5),(6,7),(8,9)] => 0
[(1,3),(2,10),(4,5),(6,7),(8,9)] => 0
[(1,4),(2,10),(3,5),(6,7),(8,9)] => 1
[(1,5),(2,10),(3,4),(6,7),(8,9)] => 2
[(1,6),(2,10),(3,4),(5,7),(8,9)] => 3
[(1,7),(2,10),(3,4),(5,6),(8,9)] => 4
[(1,8),(2,10),(3,4),(5,6),(7,9)] => 5
[(1,9),(2,10),(3,4),(5,6),(7,8)] => 6
[(1,10),(2,9),(3,4),(5,6),(7,8)] => 0
[(1,10),(2,9),(3,5),(4,6),(7,8)] => 0
[(1,9),(2,10),(3,5),(4,6),(7,8)] => 6
[(1,8),(2,10),(3,5),(4,6),(7,9)] => 5
[(1,7),(2,10),(3,5),(4,6),(8,9)] => 4
[(1,6),(2,10),(3,5),(4,7),(8,9)] => 3
[(1,5),(2,10),(3,6),(4,7),(8,9)] => 3
[(1,4),(2,10),(3,6),(5,7),(8,9)] => 1
[(1,3),(2,10),(4,6),(5,7),(8,9)] => 0
[(1,2),(3,10),(4,6),(5,7),(8,9)] => 0
[(1,2),(3,9),(4,6),(5,7),(8,10)] => 0
[(1,3),(2,9),(4,6),(5,7),(8,10)] => 0
[(1,4),(2,9),(3,6),(5,7),(8,10)] => 1
[(1,5),(2,9),(3,6),(4,7),(8,10)] => 3
[(1,6),(2,9),(3,5),(4,7),(8,10)] => 3
[(1,7),(2,9),(3,5),(4,6),(8,10)] => 4
[(1,8),(2,9),(3,5),(4,6),(7,10)] => 5
[(1,9),(2,8),(3,5),(4,6),(7,10)] => 0
[(1,10),(2,8),(3,5),(4,6),(7,9)] => 0
[(1,10),(2,7),(3,5),(4,6),(8,9)] => 0
[(1,9),(2,7),(3,5),(4,6),(8,10)] => 0
[(1,8),(2,7),(3,5),(4,6),(9,10)] => 0
[(1,7),(2,8),(3,5),(4,6),(9,10)] => 4
[(1,6),(2,8),(3,5),(4,7),(9,10)] => 3
[(1,5),(2,8),(3,6),(4,7),(9,10)] => 3
[(1,4),(2,8),(3,6),(5,7),(9,10)] => 1
[(1,3),(2,8),(4,6),(5,7),(9,10)] => 0
[(1,2),(3,8),(4,6),(5,7),(9,10)] => 0
[(1,2),(3,7),(4,6),(5,8),(9,10)] => 0
[(1,3),(2,7),(4,6),(5,8),(9,10)] => 0
[(1,4),(2,7),(3,6),(5,8),(9,10)] => 1
[(1,5),(2,7),(3,6),(4,8),(9,10)] => 3
[(1,6),(2,7),(3,5),(4,8),(9,10)] => 3
[(1,7),(2,6),(3,5),(4,8),(9,10)] => 0
[(1,8),(2,6),(3,5),(4,7),(9,10)] => 0
[(1,9),(2,6),(3,5),(4,7),(8,10)] => 0
[(1,10),(2,6),(3,5),(4,7),(8,9)] => 0
[(1,10),(2,5),(3,6),(4,7),(8,9)] => 1
[(1,9),(2,5),(3,6),(4,7),(8,10)] => 1
[(1,8),(2,5),(3,6),(4,7),(9,10)] => 1
[(1,7),(2,5),(3,6),(4,8),(9,10)] => 1
[(1,6),(2,5),(3,7),(4,8),(9,10)] => 2
[(1,5),(2,6),(3,7),(4,8),(9,10)] => 4
[(1,4),(2,6),(3,7),(5,8),(9,10)] => 2
[(1,3),(2,6),(4,7),(5,8),(9,10)] => 1
[(1,2),(3,6),(4,7),(5,8),(9,10)] => 1
[(1,2),(3,5),(4,7),(6,8),(9,10)] => 0
[(1,3),(2,5),(4,7),(6,8),(9,10)] => 0
[(1,4),(2,5),(3,7),(6,8),(9,10)] => 1
[(1,5),(2,4),(3,7),(6,8),(9,10)] => 0
[(1,6),(2,4),(3,7),(5,8),(9,10)] => 1
[(1,7),(2,4),(3,6),(5,8),(9,10)] => 0
[(1,8),(2,4),(3,6),(5,7),(9,10)] => 0
[(1,9),(2,4),(3,6),(5,7),(8,10)] => 0
[(1,10),(2,4),(3,6),(5,7),(8,9)] => 0
[(1,10),(2,3),(4,6),(5,7),(8,9)] => 0
[(1,9),(2,3),(4,6),(5,7),(8,10)] => 0
[(1,8),(2,3),(4,6),(5,7),(9,10)] => 0
[(1,7),(2,3),(4,6),(5,8),(9,10)] => 0
[(1,6),(2,3),(4,7),(5,8),(9,10)] => 1
[(1,5),(2,3),(4,7),(6,8),(9,10)] => 0
[(1,4),(2,3),(5,7),(6,8),(9,10)] => 0
[(1,3),(2,4),(5,7),(6,8),(9,10)] => 0
[(1,2),(3,4),(5,7),(6,8),(9,10)] => 0
[(1,2),(3,4),(5,8),(6,7),(9,10)] => 0
[(1,3),(2,4),(5,8),(6,7),(9,10)] => 0
[(1,4),(2,3),(5,8),(6,7),(9,10)] => 0
[(1,5),(2,3),(4,8),(6,7),(9,10)] => 0
[(1,6),(2,3),(4,8),(5,7),(9,10)] => 1
[(1,7),(2,3),(4,8),(5,6),(9,10)] => 2
[(1,8),(2,3),(4,7),(5,6),(9,10)] => 0
[(1,9),(2,3),(4,7),(5,6),(8,10)] => 0
[(1,10),(2,3),(4,7),(5,6),(8,9)] => 0
[(1,10),(2,4),(3,7),(5,6),(8,9)] => 0
[(1,9),(2,4),(3,7),(5,6),(8,10)] => 0
[(1,8),(2,4),(3,7),(5,6),(9,10)] => 0
[(1,7),(2,4),(3,8),(5,6),(9,10)] => 2
[(1,6),(2,4),(3,8),(5,7),(9,10)] => 1
[(1,5),(2,4),(3,8),(6,7),(9,10)] => 0
[(1,4),(2,5),(3,8),(6,7),(9,10)] => 1
[(1,3),(2,5),(4,8),(6,7),(9,10)] => 0
[(1,2),(3,5),(4,8),(6,7),(9,10)] => 0
[(1,2),(3,6),(4,8),(5,7),(9,10)] => 1
[(1,3),(2,6),(4,8),(5,7),(9,10)] => 1
[(1,4),(2,6),(3,8),(5,7),(9,10)] => 2
[(1,5),(2,6),(3,8),(4,7),(9,10)] => 4
[(1,6),(2,5),(3,8),(4,7),(9,10)] => 2
[(1,7),(2,5),(3,8),(4,6),(9,10)] => 3
[(1,8),(2,5),(3,7),(4,6),(9,10)] => 1
[(1,9),(2,5),(3,7),(4,6),(8,10)] => 1
[(1,10),(2,5),(3,7),(4,6),(8,9)] => 1
[(1,10),(2,6),(3,7),(4,5),(8,9)] => 2
[(1,9),(2,6),(3,7),(4,5),(8,10)] => 2
[(1,8),(2,6),(3,7),(4,5),(9,10)] => 2
[(1,7),(2,6),(3,8),(4,5),(9,10)] => 4
[(1,6),(2,7),(3,8),(4,5),(9,10)] => 7
[(1,5),(2,7),(3,8),(4,6),(9,10)] => 5
[(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)] => 2
[(1,2),(3,8),(4,7),(5,6),(9,10)] => 0
[(1,3),(2,8),(4,7),(5,6),(9,10)] => 0
[(1,4),(2,8),(3,7),(5,6),(9,10)] => 1
[(1,5),(2,8),(3,7),(4,6),(9,10)] => 3
[(1,6),(2,8),(3,7),(4,5),(9,10)] => 5
[(1,7),(2,8),(3,6),(4,5),(9,10)] => 4
[(1,8),(2,7),(3,6),(4,5),(9,10)] => 0
[(1,9),(2,7),(3,6),(4,5),(8,10)] => 0
[(1,10),(2,7),(3,6),(4,5),(8,9)] => 0
[(1,10),(2,8),(3,6),(4,5),(7,9)] => 0
[(1,9),(2,8),(3,6),(4,5),(7,10)] => 0
[(1,8),(2,9),(3,6),(4,5),(7,10)] => 5
[(1,7),(2,9),(3,6),(4,5),(8,10)] => 4
[(1,6),(2,9),(3,7),(4,5),(8,10)] => 5
[(1,5),(2,9),(3,7),(4,6),(8,10)] => 3
[(1,4),(2,9),(3,7),(5,6),(8,10)] => 1
[(1,3),(2,9),(4,7),(5,6),(8,10)] => 0
[(1,2),(3,9),(4,7),(5,6),(8,10)] => 0
[(1,2),(3,10),(4,7),(5,6),(8,9)] => 0
[(1,3),(2,10),(4,7),(5,6),(8,9)] => 0
[(1,4),(2,10),(3,7),(5,6),(8,9)] => 1
[(1,5),(2,10),(3,7),(4,6),(8,9)] => 3
[(1,6),(2,10),(3,7),(4,5),(8,9)] => 5
[(1,7),(2,10),(3,6),(4,5),(8,9)] => 4
[(1,8),(2,10),(3,6),(4,5),(7,9)] => 5
[(1,9),(2,10),(3,6),(4,5),(7,8)] => 6
[(1,10),(2,9),(3,6),(4,5),(7,8)] => 0
[(1,10),(2,9),(3,7),(4,5),(6,8)] => 0
[(1,9),(2,10),(3,7),(4,5),(6,8)] => 6
[(1,8),(2,10),(3,7),(4,5),(6,9)] => 5
[(1,7),(2,10),(3,8),(4,5),(6,9)] => 7
[(1,6),(2,10),(3,8),(4,5),(7,9)] => 5
[(1,5),(2,10),(3,8),(4,6),(7,9)] => 3
[(1,4),(2,10),(3,8),(5,6),(7,9)] => 1
[(1,3),(2,10),(4,8),(5,6),(7,9)] => 0
[(1,2),(3,10),(4,8),(5,6),(7,9)] => 0
[(1,2),(3,9),(4,8),(5,6),(7,10)] => 0
[(1,3),(2,9),(4,8),(5,6),(7,10)] => 0
[(1,4),(2,9),(3,8),(5,6),(7,10)] => 1
[(1,5),(2,9),(3,8),(4,6),(7,10)] => 3
[(1,6),(2,9),(3,8),(4,5),(7,10)] => 5
[(1,7),(2,9),(3,8),(4,5),(6,10)] => 7
[(1,8),(2,9),(3,7),(4,5),(6,10)] => 5
[(1,9),(2,8),(3,7),(4,5),(6,10)] => 0
[(1,10),(2,8),(3,7),(4,5),(6,9)] => 0
[(1,10),(2,7),(3,8),(4,5),(6,9)] => 3
[(1,9),(2,7),(3,8),(4,5),(6,10)] => 3
[(1,8),(2,7),(3,9),(4,5),(6,10)] => 6
[(1,7),(2,8),(3,9),(4,5),(6,10)] => 10
[(1,6),(2,8),(3,9),(4,5),(7,10)] => 8
[(1,5),(2,8),(3,9),(4,6),(7,10)] => 6
[(1,4),(2,8),(3,9),(5,6),(7,10)] => 4
[(1,3),(2,8),(4,9),(5,6),(7,10)] => 3
[(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)] => 2
[(1,4),(2,7),(3,9),(5,6),(8,10)] => 3
[(1,5),(2,7),(3,9),(4,6),(8,10)] => 5
[(1,6),(2,7),(3,9),(4,5),(8,10)] => 7
[(1,7),(2,6),(3,9),(4,5),(8,10)] => 4
[(1,8),(2,6),(3,9),(4,5),(7,10)] => 5
[(1,9),(2,6),(3,8),(4,5),(7,10)] => 2
[(1,10),(2,6),(3,8),(4,5),(7,9)] => 2
[(1,10),(2,5),(3,8),(4,6),(7,9)] => 1
[(1,9),(2,5),(3,8),(4,6),(7,10)] => 1
[(1,8),(2,5),(3,9),(4,6),(7,10)] => 4
[(1,7),(2,5),(3,9),(4,6),(8,10)] => 3
[(1,6),(2,5),(3,9),(4,7),(8,10)] => 2
[(1,5),(2,6),(3,9),(4,7),(8,10)] => 4
[(1,4),(2,6),(3,9),(5,7),(8,10)] => 2
[(1,3),(2,6),(4,9),(5,7),(8,10)] => 1
[(1,2),(3,6),(4,9),(5,7),(8,10)] => 1
[(1,2),(3,5),(4,9),(6,7),(8,10)] => 0
[(1,3),(2,5),(4,9),(6,7),(8,10)] => 0
[(1,4),(2,5),(3,9),(6,7),(8,10)] => 1
[(1,5),(2,4),(3,9),(6,7),(8,10)] => 0
[(1,6),(2,4),(3,9),(5,7),(8,10)] => 1
[(1,7),(2,4),(3,9),(5,6),(8,10)] => 2
[(1,8),(2,4),(3,9),(5,6),(7,10)] => 3
[(1,9),(2,4),(3,8),(5,6),(7,10)] => 0
[(1,10),(2,4),(3,8),(5,6),(7,9)] => 0
[(1,10),(2,3),(4,8),(5,6),(7,9)] => 0
[(1,9),(2,3),(4,8),(5,6),(7,10)] => 0
[(1,8),(2,3),(4,9),(5,6),(7,10)] => 3
[(1,7),(2,3),(4,9),(5,6),(8,10)] => 2
[(1,6),(2,3),(4,9),(5,7),(8,10)] => 1
[(1,5),(2,3),(4,9),(6,7),(8,10)] => 0
[(1,4),(2,3),(5,9),(6,7),(8,10)] => 0
[(1,3),(2,4),(5,9),(6,7),(8,10)] => 0
[(1,2),(3,4),(5,9),(6,7),(8,10)] => 0
[(1,2),(3,4),(5,10),(6,7),(8,9)] => 0
[(1,3),(2,4),(5,10),(6,7),(8,9)] => 0
[(1,4),(2,3),(5,10),(6,7),(8,9)] => 0
[(1,5),(2,3),(4,10),(6,7),(8,9)] => 0
[(1,6),(2,3),(4,10),(5,7),(8,9)] => 1
[(1,7),(2,3),(4,10),(5,6),(8,9)] => 2
[(1,8),(2,3),(4,10),(5,6),(7,9)] => 3
[(1,9),(2,3),(4,10),(5,6),(7,8)] => 4
[(1,10),(2,3),(4,9),(5,6),(7,8)] => 0
[(1,10),(2,4),(3,9),(5,6),(7,8)] => 0
[(1,9),(2,4),(3,10),(5,6),(7,8)] => 4
[(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)] => 1
[(1,5),(2,4),(3,10),(6,7),(8,9)] => 0
[(1,4),(2,5),(3,10),(6,7),(8,9)] => 1
[(1,3),(2,5),(4,10),(6,7),(8,9)] => 0
[(1,2),(3,5),(4,10),(6,7),(8,9)] => 0
[(1,2),(3,6),(4,10),(5,7),(8,9)] => 1
[(1,3),(2,6),(4,10),(5,7),(8,9)] => 1
[(1,4),(2,6),(3,10),(5,7),(8,9)] => 2
[(1,5),(2,6),(3,10),(4,7),(8,9)] => 4
[(1,6),(2,5),(3,10),(4,7),(8,9)] => 2
[(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)] => 5
[(1,10),(2,5),(3,9),(4,6),(7,8)] => 1
[(1,10),(2,6),(3,9),(4,5),(7,8)] => 2
[(1,9),(2,6),(3,10),(4,5),(7,8)] => 6
[(1,8),(2,6),(3,10),(4,5),(7,9)] => 5
[(1,7),(2,6),(3,10),(4,5),(8,9)] => 4
[(1,6),(2,7),(3,10),(4,5),(8,9)] => 7
[(1,5),(2,7),(3,10),(4,6),(8,9)] => 5
[(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)] => 2
[(1,2),(3,8),(4,10),(5,6),(7,9)] => 3
[(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)] => 6
[(1,6),(2,8),(3,10),(4,5),(7,9)] => 8
[(1,7),(2,8),(3,10),(4,5),(6,9)] => 10
[(1,8),(2,7),(3,10),(4,5),(6,9)] => 6
[(1,9),(2,7),(3,10),(4,5),(6,8)] => 7
[(1,10),(2,7),(3,9),(4,5),(6,8)] => 3
[(1,10),(2,8),(3,9),(4,5),(6,7)] => 4
[(1,9),(2,8),(3,10),(4,5),(6,7)] => 8
[(1,8),(2,9),(3,10),(4,5),(6,7)] => 13
[(1,7),(2,9),(3,10),(4,5),(6,8)] => 11
[(1,6),(2,9),(3,10),(4,5),(7,8)] => 9
[(1,5),(2,9),(3,10),(4,6),(7,8)] => 7
[(1,4),(2,9),(3,10),(5,6),(7,8)] => 5
[(1,3),(2,9),(4,10),(5,6),(7,8)] => 4
[(1,2),(3,9),(4,10),(5,6),(7,8)] => 4
[(1,2),(3,10),(4,9),(5,6),(7,8)] => 0
[(1,3),(2,10),(4,9),(5,6),(7,8)] => 0
[(1,4),(2,10),(3,9),(5,6),(7,8)] => 1
[(1,5),(2,10),(3,9),(4,6),(7,8)] => 3
[(1,6),(2,10),(3,9),(4,5),(7,8)] => 5
[(1,7),(2,10),(3,9),(4,5),(6,8)] => 7
[(1,8),(2,10),(3,9),(4,5),(6,7)] => 9
[(1,9),(2,10),(3,8),(4,5),(6,7)] => 6
[(1,10),(2,9),(3,8),(4,5),(6,7)] => 0
[(1,10),(2,9),(3,8),(4,6),(5,7)] => 0
[(1,9),(2,10),(3,8),(4,6),(5,7)] => 6
[(1,8),(2,10),(3,9),(4,6),(5,7)] => 9
[(1,7),(2,10),(3,9),(4,6),(5,8)] => 7
[(1,6),(2,10),(3,9),(4,7),(5,8)] => 6
[(1,5),(2,10),(3,9),(4,7),(6,8)] => 3
[(1,4),(2,10),(3,9),(5,7),(6,8)] => 1
[(1,3),(2,10),(4,9),(5,7),(6,8)] => 0
[(1,2),(3,10),(4,9),(5,7),(6,8)] => 0
[(1,2),(3,9),(4,10),(5,7),(6,8)] => 4
[(1,3),(2,9),(4,10),(5,7),(6,8)] => 4
[(1,4),(2,9),(3,10),(5,7),(6,8)] => 5
[(1,5),(2,9),(3,10),(4,7),(6,8)] => 7
[(1,6),(2,9),(3,10),(4,7),(5,8)] => 10
[(1,7),(2,9),(3,10),(4,6),(5,8)] => 11
[(1,8),(2,9),(3,10),(4,6),(5,7)] => 13
[(1,9),(2,8),(3,10),(4,6),(5,7)] => 8
[(1,10),(2,8),(3,9),(4,6),(5,7)] => 4
[(1,10),(2,7),(3,9),(4,6),(5,8)] => 3
[(1,9),(2,7),(3,10),(4,6),(5,8)] => 7
[(1,8),(2,7),(3,10),(4,6),(5,9)] => 6
[(1,7),(2,8),(3,10),(4,6),(5,9)] => 10
[(1,6),(2,8),(3,10),(4,7),(5,9)] => 9
[(1,5),(2,8),(3,10),(4,7),(6,9)] => 6
[(1,4),(2,8),(3,10),(5,7),(6,9)] => 4
[(1,3),(2,8),(4,10),(5,7),(6,9)] => 3
[(1,2),(3,8),(4,10),(5,7),(6,9)] => 3
[(1,2),(3,7),(4,10),(5,8),(6,9)] => 3
[(1,3),(2,7),(4,10),(5,8),(6,9)] => 3
[(1,4),(2,7),(3,10),(5,8),(6,9)] => 4
[(1,5),(2,7),(3,10),(4,8),(6,9)] => 6
[(1,6),(2,7),(3,10),(4,8),(5,9)] => 9
[(1,7),(2,6),(3,10),(4,8),(5,9)] => 6
[(1,8),(2,6),(3,10),(4,7),(5,9)] => 6
[(1,9),(2,6),(3,10),(4,7),(5,8)] => 7
[(1,10),(2,6),(3,9),(4,7),(5,8)] => 3
[(1,10),(2,5),(3,9),(4,7),(6,8)] => 1
[(1,9),(2,5),(3,10),(4,7),(6,8)] => 5
[(1,8),(2,5),(3,10),(4,7),(6,9)] => 4
[(1,7),(2,5),(3,10),(4,8),(6,9)] => 4
[(1,6),(2,5),(3,10),(4,8),(7,9)] => 2
[(1,5),(2,6),(3,10),(4,8),(7,9)] => 4
[(1,4),(2,6),(3,10),(5,8),(7,9)] => 2
[(1,3),(2,6),(4,10),(5,8),(7,9)] => 1
[(1,2),(3,6),(4,10),(5,8),(7,9)] => 1
[(1,2),(3,5),(4,10),(6,8),(7,9)] => 0
[(1,3),(2,5),(4,10),(6,8),(7,9)] => 0
[(1,4),(2,5),(3,10),(6,8),(7,9)] => 1
[(1,5),(2,4),(3,10),(6,8),(7,9)] => 0
[(1,6),(2,4),(3,10),(5,8),(7,9)] => 1
[(1,7),(2,4),(3,10),(5,8),(6,9)] => 3
[(1,8),(2,4),(3,10),(5,7),(6,9)] => 3
[(1,9),(2,4),(3,10),(5,7),(6,8)] => 4
[(1,10),(2,4),(3,9),(5,7),(6,8)] => 0
[(1,10),(2,3),(4,9),(5,7),(6,8)] => 0
[(1,9),(2,3),(4,10),(5,7),(6,8)] => 4
[(1,8),(2,3),(4,10),(5,7),(6,9)] => 3
[(1,7),(2,3),(4,10),(5,8),(6,9)] => 3
[(1,6),(2,3),(4,10),(5,8),(7,9)] => 1
[(1,5),(2,3),(4,10),(6,8),(7,9)] => 0
[(1,4),(2,3),(5,10),(6,8),(7,9)] => 0
[(1,3),(2,4),(5,10),(6,8),(7,9)] => 0
[(1,2),(3,4),(5,10),(6,8),(7,9)] => 0
[(1,2),(3,4),(5,9),(6,8),(7,10)] => 0
[(1,3),(2,4),(5,9),(6,8),(7,10)] => 0
[(1,4),(2,3),(5,9),(6,8),(7,10)] => 0
[(1,5),(2,3),(4,9),(6,8),(7,10)] => 0
[(1,6),(2,3),(4,9),(5,8),(7,10)] => 1
[(1,7),(2,3),(4,9),(5,8),(6,10)] => 3
[(1,8),(2,3),(4,9),(5,7),(6,10)] => 3
[(1,9),(2,3),(4,8),(5,7),(6,10)] => 0
[(1,10),(2,3),(4,8),(5,7),(6,9)] => 0
[(1,10),(2,4),(3,8),(5,7),(6,9)] => 0
[(1,9),(2,4),(3,8),(5,7),(6,10)] => 0
[(1,8),(2,4),(3,9),(5,7),(6,10)] => 3
[(1,7),(2,4),(3,9),(5,8),(6,10)] => 3
[(1,6),(2,4),(3,9),(5,8),(7,10)] => 1
[(1,5),(2,4),(3,9),(6,8),(7,10)] => 0
[(1,4),(2,5),(3,9),(6,8),(7,10)] => 1
[(1,3),(2,5),(4,9),(6,8),(7,10)] => 0
[(1,2),(3,5),(4,9),(6,8),(7,10)] => 0
[(1,2),(3,6),(4,9),(5,8),(7,10)] => 1
[(1,3),(2,6),(4,9),(5,8),(7,10)] => 1
[(1,4),(2,6),(3,9),(5,8),(7,10)] => 2
[(1,5),(2,6),(3,9),(4,8),(7,10)] => 4
[(1,6),(2,5),(3,9),(4,8),(7,10)] => 2
[(1,7),(2,5),(3,9),(4,8),(6,10)] => 4
[(1,8),(2,5),(3,9),(4,7),(6,10)] => 4
[(1,9),(2,5),(3,8),(4,7),(6,10)] => 1
[(1,10),(2,5),(3,8),(4,7),(6,9)] => 1
[(1,10),(2,6),(3,8),(4,7),(5,9)] => 3
[(1,9),(2,6),(3,8),(4,7),(5,10)] => 3
[(1,8),(2,6),(3,9),(4,7),(5,10)] => 6
[(1,7),(2,6),(3,9),(4,8),(5,10)] => 6
[(1,6),(2,7),(3,9),(4,8),(5,10)] => 9
[(1,5),(2,7),(3,9),(4,8),(6,10)] => 6
[(1,4),(2,7),(3,9),(5,8),(6,10)] => 4
[(1,3),(2,7),(4,9),(5,8),(6,10)] => 3
[(1,2),(3,7),(4,9),(5,8),(6,10)] => 3
[(1,2),(3,8),(4,9),(5,7),(6,10)] => 3
[(1,3),(2,8),(4,9),(5,7),(6,10)] => 3
[(1,4),(2,8),(3,9),(5,7),(6,10)] => 4
[(1,5),(2,8),(3,9),(4,7),(6,10)] => 6
[(1,6),(2,8),(3,9),(4,7),(5,10)] => 9
[(1,7),(2,8),(3,9),(4,6),(5,10)] => 10
[(1,8),(2,7),(3,9),(4,6),(5,10)] => 6
[(1,9),(2,7),(3,8),(4,6),(5,10)] => 3
[(1,10),(2,7),(3,8),(4,6),(5,9)] => 3
[(1,10),(2,8),(3,7),(4,6),(5,9)] => 0
[(1,9),(2,8),(3,7),(4,6),(5,10)] => 0
[(1,8),(2,9),(3,7),(4,6),(5,10)] => 5
[(1,7),(2,9),(3,8),(4,6),(5,10)] => 7
[(1,6),(2,9),(3,8),(4,7),(5,10)] => 6
[(1,5),(2,9),(3,8),(4,7),(6,10)] => 3
[(1,4),(2,9),(3,8),(5,7),(6,10)] => 1
[(1,3),(2,9),(4,8),(5,7),(6,10)] => 0
[(1,2),(3,9),(4,8),(5,7),(6,10)] => 0
[(1,2),(3,10),(4,8),(5,7),(6,9)] => 0
[(1,3),(2,10),(4,8),(5,7),(6,9)] => 0
[(1,4),(2,10),(3,8),(5,7),(6,9)] => 1
[(1,5),(2,10),(3,8),(4,7),(6,9)] => 3
[(1,6),(2,10),(3,8),(4,7),(5,9)] => 6
[(1,7),(2,10),(3,8),(4,6),(5,9)] => 7
[(1,8),(2,10),(3,7),(4,6),(5,9)] => 5
[(1,9),(2,10),(3,7),(4,6),(5,8)] => 6
[(1,10),(2,9),(3,7),(4,6),(5,8)] => 0
[(1,10),(2,9),(3,6),(4,7),(5,8)] => 1
[(1,9),(2,10),(3,6),(4,7),(5,8)] => 7
[(1,8),(2,10),(3,6),(4,7),(5,9)] => 6
[(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)] => 4
[(1,4),(2,10),(3,7),(5,8),(6,9)] => 2
[(1,3),(2,10),(4,7),(5,8),(6,9)] => 1
[(1,2),(3,10),(4,7),(5,8),(6,9)] => 1
[(1,2),(3,9),(4,7),(5,8),(6,10)] => 1
[(1,3),(2,9),(4,7),(5,8),(6,10)] => 1
[(1,4),(2,9),(3,7),(5,8),(6,10)] => 2
[(1,5),(2,9),(3,7),(4,8),(6,10)] => 4
[(1,6),(2,9),(3,7),(4,8),(5,10)] => 7
[(1,7),(2,9),(3,6),(4,8),(5,10)] => 6
[(1,8),(2,9),(3,6),(4,7),(5,10)] => 6
[(1,9),(2,8),(3,6),(4,7),(5,10)] => 1
[(1,10),(2,8),(3,6),(4,7),(5,9)] => 1
[(1,10),(2,7),(3,6),(4,8),(5,9)] => 2
[(1,9),(2,7),(3,6),(4,8),(5,10)] => 2
[(1,8),(2,7),(3,6),(4,9),(5,10)] => 3
[(1,7),(2,8),(3,6),(4,9),(5,10)] => 7
[(1,6),(2,8),(3,7),(4,9),(5,10)] => 8
[(1,5),(2,8),(3,7),(4,9),(6,10)] => 5
[(1,4),(2,8),(3,7),(5,9),(6,10)] => 3
[(1,3),(2,8),(4,7),(5,9),(6,10)] => 2
[(1,2),(3,8),(4,7),(5,9),(6,10)] => 2
[(1,2),(3,7),(4,8),(5,9),(6,10)] => 4
[(1,3),(2,7),(4,8),(5,9),(6,10)] => 4
[(1,4),(2,7),(3,8),(5,9),(6,10)] => 5
[(1,5),(2,7),(3,8),(4,9),(6,10)] => 7
[(1,6),(2,7),(3,8),(4,9),(5,10)] => 10
[(1,7),(2,6),(3,8),(4,9),(5,10)] => 7
[(1,8),(2,6),(3,7),(4,9),(5,10)] => 5
[(1,9),(2,6),(3,7),(4,8),(5,10)] => 4
[(1,10),(2,6),(3,7),(4,8),(5,9)] => 4
[(1,10),(2,5),(3,7),(4,8),(6,9)] => 2
[(1,9),(2,5),(3,7),(4,8),(6,10)] => 2
[(1,8),(2,5),(3,7),(4,9),(6,10)] => 3
[(1,7),(2,5),(3,8),(4,9),(6,10)] => 5
[(1,6),(2,5),(3,8),(4,9),(7,10)] => 3
[(1,5),(2,6),(3,8),(4,9),(7,10)] => 5
[(1,4),(2,6),(3,8),(5,9),(7,10)] => 3
[(1,3),(2,6),(4,8),(5,9),(7,10)] => 2
[(1,2),(3,6),(4,8),(5,9),(7,10)] => 2
[(1,2),(3,5),(4,8),(6,9),(7,10)] => 1
[(1,3),(2,5),(4,8),(6,9),(7,10)] => 1
[(1,4),(2,5),(3,8),(6,9),(7,10)] => 2
[(1,5),(2,4),(3,8),(6,9),(7,10)] => 1
[(1,6),(2,4),(3,8),(5,9),(7,10)] => 2
[(1,7),(2,4),(3,8),(5,9),(6,10)] => 4
[(1,8),(2,4),(3,7),(5,9),(6,10)] => 2
[(1,9),(2,4),(3,7),(5,8),(6,10)] => 1
[(1,10),(2,4),(3,7),(5,8),(6,9)] => 1
[(1,10),(2,3),(4,7),(5,8),(6,9)] => 1
[(1,9),(2,3),(4,7),(5,8),(6,10)] => 1
[(1,8),(2,3),(4,7),(5,9),(6,10)] => 2
[(1,7),(2,3),(4,8),(5,9),(6,10)] => 4
[(1,6),(2,3),(4,8),(5,9),(7,10)] => 2
[(1,5),(2,3),(4,8),(6,9),(7,10)] => 1
[(1,4),(2,3),(5,8),(6,9),(7,10)] => 1
[(1,3),(2,4),(5,8),(6,9),(7,10)] => 1
[(1,2),(3,4),(5,8),(6,9),(7,10)] => 1
[(1,2),(3,4),(5,7),(6,9),(8,10)] => 0
[(1,3),(2,4),(5,7),(6,9),(8,10)] => 0
[(1,4),(2,3),(5,7),(6,9),(8,10)] => 0
[(1,5),(2,3),(4,7),(6,9),(8,10)] => 0
[(1,6),(2,3),(4,7),(5,9),(8,10)] => 1
[(1,7),(2,3),(4,6),(5,9),(8,10)] => 0
[(1,8),(2,3),(4,6),(5,9),(7,10)] => 1
[(1,9),(2,3),(4,6),(5,8),(7,10)] => 0
[(1,10),(2,3),(4,6),(5,8),(7,9)] => 0
[(1,10),(2,4),(3,6),(5,8),(7,9)] => 0
[(1,9),(2,4),(3,6),(5,8),(7,10)] => 0
[(1,8),(2,4),(3,6),(5,9),(7,10)] => 1
[(1,7),(2,4),(3,6),(5,9),(8,10)] => 0
[(1,6),(2,4),(3,7),(5,9),(8,10)] => 1
[(1,5),(2,4),(3,7),(6,9),(8,10)] => 0
[(1,4),(2,5),(3,7),(6,9),(8,10)] => 1
[(1,3),(2,5),(4,7),(6,9),(8,10)] => 0
[(1,2),(3,5),(4,7),(6,9),(8,10)] => 0
[(1,2),(3,6),(4,7),(5,9),(8,10)] => 1
[(1,3),(2,6),(4,7),(5,9),(8,10)] => 1
[(1,4),(2,6),(3,7),(5,9),(8,10)] => 2
[(1,5),(2,6),(3,7),(4,9),(8,10)] => 4
[(1,6),(2,5),(3,7),(4,9),(8,10)] => 2
[(1,7),(2,5),(3,6),(4,9),(8,10)] => 1
[(1,8),(2,5),(3,6),(4,9),(7,10)] => 2
[(1,9),(2,5),(3,6),(4,8),(7,10)] => 1
[(1,10),(2,5),(3,6),(4,8),(7,9)] => 1
[(1,10),(2,6),(3,5),(4,8),(7,9)] => 0
[(1,9),(2,6),(3,5),(4,8),(7,10)] => 0
[(1,8),(2,6),(3,5),(4,9),(7,10)] => 1
[(1,7),(2,6),(3,5),(4,9),(8,10)] => 0
[(1,6),(2,7),(3,5),(4,9),(8,10)] => 3
[(1,5),(2,7),(3,6),(4,9),(8,10)] => 3
[(1,4),(2,7),(3,6),(5,9),(8,10)] => 1
[(1,3),(2,7),(4,6),(5,9),(8,10)] => 0
[(1,2),(3,7),(4,6),(5,9),(8,10)] => 0
[(1,2),(3,8),(4,6),(5,9),(7,10)] => 1
[(1,3),(2,8),(4,6),(5,9),(7,10)] => 1
[(1,4),(2,8),(3,6),(5,9),(7,10)] => 2
[(1,5),(2,8),(3,6),(4,9),(7,10)] => 4
[(1,6),(2,8),(3,5),(4,9),(7,10)] => 4
[(1,7),(2,8),(3,5),(4,9),(6,10)] => 6
[(1,8),(2,7),(3,5),(4,9),(6,10)] => 2
[(1,9),(2,7),(3,5),(4,8),(6,10)] => 1
[(1,10),(2,7),(3,5),(4,8),(6,9)] => 1
[(1,10),(2,8),(3,5),(4,7),(6,9)] => 0
[(1,9),(2,8),(3,5),(4,7),(6,10)] => 0
[(1,8),(2,9),(3,5),(4,7),(6,10)] => 5
[(1,7),(2,9),(3,5),(4,8),(6,10)] => 5
[(1,6),(2,9),(3,5),(4,8),(7,10)] => 3
[(1,5),(2,9),(3,6),(4,8),(7,10)] => 3
[(1,4),(2,9),(3,6),(5,8),(7,10)] => 1
[(1,3),(2,9),(4,6),(5,8),(7,10)] => 0
[(1,2),(3,9),(4,6),(5,8),(7,10)] => 0
[(1,2),(3,10),(4,6),(5,8),(7,9)] => 0
[(1,3),(2,10),(4,6),(5,8),(7,9)] => 0
[(1,4),(2,10),(3,6),(5,8),(7,9)] => 1
[(1,5),(2,10),(3,6),(4,8),(7,9)] => 3
[(1,6),(2,10),(3,5),(4,8),(7,9)] => 3
[(1,7),(2,10),(3,5),(4,8),(6,9)] => 5
[(1,8),(2,10),(3,5),(4,7),(6,9)] => 5
[(1,9),(2,10),(3,5),(4,7),(6,8)] => 6
[(1,10),(2,9),(3,5),(4,7),(6,8)] => 0
[(1,10),(2,9),(3,4),(5,7),(6,8)] => 0
[(1,9),(2,10),(3,4),(5,7),(6,8)] => 6
[(1,8),(2,10),(3,4),(5,7),(6,9)] => 5
[(1,7),(2,10),(3,4),(5,8),(6,9)] => 5
[(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)] => 1
[(1,3),(2,10),(4,5),(6,8),(7,9)] => 0
[(1,2),(3,10),(4,5),(6,8),(7,9)] => 0
[(1,2),(3,9),(4,5),(6,8),(7,10)] => 0
[(1,3),(2,9),(4,5),(6,8),(7,10)] => 0
[(1,4),(2,9),(3,5),(6,8),(7,10)] => 1
[(1,5),(2,9),(3,4),(6,8),(7,10)] => 2
[(1,6),(2,9),(3,4),(5,8),(7,10)] => 3
[(1,7),(2,9),(3,4),(5,8),(6,10)] => 5
[(1,8),(2,9),(3,4),(5,7),(6,10)] => 5
[(1,9),(2,8),(3,4),(5,7),(6,10)] => 0
[(1,10),(2,8),(3,4),(5,7),(6,9)] => 0
[(1,10),(2,7),(3,4),(5,8),(6,9)] => 1
[(1,9),(2,7),(3,4),(5,8),(6,10)] => 1
[(1,8),(2,7),(3,4),(5,9),(6,10)] => 2
[(1,7),(2,8),(3,4),(5,9),(6,10)] => 6
[(1,6),(2,8),(3,4),(5,9),(7,10)] => 4
[(1,5),(2,8),(3,4),(6,9),(7,10)] => 3
[(1,4),(2,8),(3,5),(6,9),(7,10)] => 2
[(1,3),(2,8),(4,5),(6,9),(7,10)] => 1
[(1,2),(3,8),(4,5),(6,9),(7,10)] => 1
[(1,2),(3,7),(4,5),(6,9),(8,10)] => 0
[(1,3),(2,7),(4,5),(6,9),(8,10)] => 0
[(1,4),(2,7),(3,5),(6,9),(8,10)] => 1
[(1,5),(2,7),(3,4),(6,9),(8,10)] => 2
[(1,6),(2,7),(3,4),(5,9),(8,10)] => 3
[(1,7),(2,6),(3,4),(5,9),(8,10)] => 0
[(1,8),(2,6),(3,4),(5,9),(7,10)] => 1
[(1,9),(2,6),(3,4),(5,8),(7,10)] => 0
[(1,10),(2,6),(3,4),(5,8),(7,9)] => 0
[(1,10),(2,5),(3,4),(6,8),(7,9)] => 0
[(1,9),(2,5),(3,4),(6,8),(7,10)] => 0
[(1,8),(2,5),(3,4),(6,9),(7,10)] => 1
[(1,7),(2,5),(3,4),(6,9),(8,10)] => 0
[(1,6),(2,5),(3,4),(7,9),(8,10)] => 0
[(1,5),(2,6),(3,4),(7,9),(8,10)] => 2
[(1,4),(2,6),(3,5),(7,9),(8,10)] => 1
[(1,3),(2,6),(4,5),(7,9),(8,10)] => 0
[(1,2),(3,6),(4,5),(7,9),(8,10)] => 0
[(1,2),(3,5),(4,6),(7,9),(8,10)] => 0
[(1,3),(2,5),(4,6),(7,9),(8,10)] => 0
[(1,4),(2,5),(3,6),(7,9),(8,10)] => 1
[(1,5),(2,4),(3,6),(7,9),(8,10)] => 0
[(1,6),(2,4),(3,5),(7,9),(8,10)] => 0
[(1,7),(2,4),(3,5),(6,9),(8,10)] => 0
[(1,8),(2,4),(3,5),(6,9),(7,10)] => 1
[(1,9),(2,4),(3,5),(6,8),(7,10)] => 0
[(1,10),(2,4),(3,5),(6,8),(7,9)] => 0
[(1,10),(2,3),(4,5),(6,8),(7,9)] => 0
[(1,9),(2,3),(4,5),(6,8),(7,10)] => 0
[(1,8),(2,3),(4,5),(6,9),(7,10)] => 1
[(1,7),(2,3),(4,5),(6,9),(8,10)] => 0
[(1,6),(2,3),(4,5),(7,9),(8,10)] => 0
[(1,5),(2,3),(4,6),(7,9),(8,10)] => 0
[(1,4),(2,3),(5,6),(7,9),(8,10)] => 0
[(1,3),(2,4),(5,6),(7,9),(8,10)] => 0
[(1,2),(3,4),(5,6),(7,9),(8,10)] => 0
[(1,2),(3,4),(5,6),(7,10),(8,9)] => 0
[(1,3),(2,4),(5,6),(7,10),(8,9)] => 0
[(1,4),(2,3),(5,6),(7,10),(8,9)] => 0
[(1,5),(2,3),(4,6),(7,10),(8,9)] => 0
[(1,6),(2,3),(4,5),(7,10),(8,9)] => 0
[(1,7),(2,3),(4,5),(6,10),(8,9)] => 0
[(1,8),(2,3),(4,5),(6,10),(7,9)] => 1
[(1,9),(2,3),(4,5),(6,10),(7,8)] => 2
[(1,10),(2,3),(4,5),(6,9),(7,8)] => 0
[(1,10),(2,4),(3,5),(6,9),(7,8)] => 0
[(1,9),(2,4),(3,5),(6,10),(7,8)] => 2
[(1,8),(2,4),(3,5),(6,10),(7,9)] => 1
[(1,7),(2,4),(3,5),(6,10),(8,9)] => 0
[(1,6),(2,4),(3,5),(7,10),(8,9)] => 0
[(1,5),(2,4),(3,6),(7,10),(8,9)] => 0
[(1,4),(2,5),(3,6),(7,10),(8,9)] => 1
[(1,3),(2,5),(4,6),(7,10),(8,9)] => 0
[(1,2),(3,5),(4,6),(7,10),(8,9)] => 0
[(1,2),(3,6),(4,5),(7,10),(8,9)] => 0
[(1,3),(2,6),(4,5),(7,10),(8,9)] => 0
[(1,4),(2,6),(3,5),(7,10),(8,9)] => 1
[(1,5),(2,6),(3,4),(7,10),(8,9)] => 2
[(1,6),(2,5),(3,4),(7,10),(8,9)] => 0
[(1,7),(2,5),(3,4),(6,10),(8,9)] => 0
[(1,8),(2,5),(3,4),(6,10),(7,9)] => 1
[(1,9),(2,5),(3,4),(6,10),(7,8)] => 2
[(1,10),(2,5),(3,4),(6,9),(7,8)] => 0
[(1,10),(2,6),(3,4),(5,9),(7,8)] => 0
[(1,9),(2,6),(3,4),(5,10),(7,8)] => 2
[(1,8),(2,6),(3,4),(5,10),(7,9)] => 1
[(1,7),(2,6),(3,4),(5,10),(8,9)] => 0
[(1,6),(2,7),(3,4),(5,10),(8,9)] => 3
[(1,5),(2,7),(3,4),(6,10),(8,9)] => 2
[(1,4),(2,7),(3,5),(6,10),(8,9)] => 1
[(1,3),(2,7),(4,5),(6,10),(8,9)] => 0
[(1,2),(3,7),(4,5),(6,10),(8,9)] => 0
[(1,2),(3,8),(4,5),(6,10),(7,9)] => 1
[(1,3),(2,8),(4,5),(6,10),(7,9)] => 1
[(1,4),(2,8),(3,5),(6,10),(7,9)] => 2
[(1,5),(2,8),(3,4),(6,10),(7,9)] => 3
[(1,6),(2,8),(3,4),(5,10),(7,9)] => 4
[(1,7),(2,8),(3,4),(5,10),(6,9)] => 6
[(1,8),(2,7),(3,4),(5,10),(6,9)] => 2
[(1,9),(2,7),(3,4),(5,10),(6,8)] => 3
[(1,10),(2,7),(3,4),(5,9),(6,8)] => 1
[(1,10),(2,8),(3,4),(5,9),(6,7)] => 2
[(1,9),(2,8),(3,4),(5,10),(6,7)] => 4
[(1,8),(2,9),(3,4),(5,10),(6,7)] => 9
[(1,7),(2,9),(3,4),(5,10),(6,8)] => 7
[(1,6),(2,9),(3,4),(5,10),(7,8)] => 5
[(1,5),(2,9),(3,4),(6,10),(7,8)] => 4
[(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)] => 2
[(1,2),(3,10),(4,5),(6,9),(7,8)] => 0
[(1,3),(2,10),(4,5),(6,9),(7,8)] => 0
[(1,4),(2,10),(3,5),(6,9),(7,8)] => 1
[(1,5),(2,10),(3,4),(6,9),(7,8)] => 2
[(1,6),(2,10),(3,4),(5,9),(7,8)] => 3
[(1,7),(2,10),(3,4),(5,9),(6,8)] => 5
[(1,8),(2,10),(3,4),(5,9),(6,7)] => 7
[(1,9),(2,10),(3,4),(5,8),(6,7)] => 6
[(1,10),(2,9),(3,4),(5,8),(6,7)] => 0
[(1,10),(2,9),(3,5),(4,8),(6,7)] => 0
[(1,9),(2,10),(3,5),(4,8),(6,7)] => 6
[(1,8),(2,10),(3,5),(4,9),(6,7)] => 7
[(1,7),(2,10),(3,5),(4,9),(6,8)] => 5
[(1,6),(2,10),(3,5),(4,9),(7,8)] => 3
[(1,5),(2,10),(3,6),(4,9),(7,8)] => 3
[(1,4),(2,10),(3,6),(5,9),(7,8)] => 1
[(1,3),(2,10),(4,6),(5,9),(7,8)] => 0
[(1,2),(3,10),(4,6),(5,9),(7,8)] => 0
[(1,2),(3,9),(4,6),(5,10),(7,8)] => 2
[(1,3),(2,9),(4,6),(5,10),(7,8)] => 2
[(1,4),(2,9),(3,6),(5,10),(7,8)] => 3
[(1,5),(2,9),(3,6),(4,10),(7,8)] => 5
[(1,6),(2,9),(3,5),(4,10),(7,8)] => 5
[(1,7),(2,9),(3,5),(4,10),(6,8)] => 7
[(1,8),(2,9),(3,5),(4,10),(6,7)] => 9
[(1,9),(2,8),(3,5),(4,10),(6,7)] => 4
[(1,10),(2,8),(3,5),(4,9),(6,7)] => 2
[(1,10),(2,7),(3,5),(4,9),(6,8)] => 1
[(1,9),(2,7),(3,5),(4,10),(6,8)] => 3
[(1,8),(2,7),(3,5),(4,10),(6,9)] => 2
[(1,7),(2,8),(3,5),(4,10),(6,9)] => 6
[(1,6),(2,8),(3,5),(4,10),(7,9)] => 4
[(1,5),(2,8),(3,6),(4,10),(7,9)] => 4
[(1,4),(2,8),(3,6),(5,10),(7,9)] => 2
[(1,3),(2,8),(4,6),(5,10),(7,9)] => 1
[(1,2),(3,8),(4,6),(5,10),(7,9)] => 1
[(1,2),(3,7),(4,6),(5,10),(8,9)] => 0
[(1,3),(2,7),(4,6),(5,10),(8,9)] => 0
[(1,4),(2,7),(3,6),(5,10),(8,9)] => 1
[(1,5),(2,7),(3,6),(4,10),(8,9)] => 3
[(1,6),(2,7),(3,5),(4,10),(8,9)] => 3
[(1,7),(2,6),(3,5),(4,10),(8,9)] => 0
[(1,8),(2,6),(3,5),(4,10),(7,9)] => 1
[(1,9),(2,6),(3,5),(4,10),(7,8)] => 2
[(1,10),(2,6),(3,5),(4,9),(7,8)] => 0
[(1,10),(2,5),(3,6),(4,9),(7,8)] => 1
[(1,9),(2,5),(3,6),(4,10),(7,8)] => 3
[(1,8),(2,5),(3,6),(4,10),(7,9)] => 2
[(1,7),(2,5),(3,6),(4,10),(8,9)] => 1
[(1,6),(2,5),(3,7),(4,10),(8,9)] => 2
[(1,5),(2,6),(3,7),(4,10),(8,9)] => 4
[(1,4),(2,6),(3,7),(5,10),(8,9)] => 2
[(1,3),(2,6),(4,7),(5,10),(8,9)] => 1
[(1,2),(3,6),(4,7),(5,10),(8,9)] => 1
[(1,2),(3,5),(4,7),(6,10),(8,9)] => 0
[(1,3),(2,5),(4,7),(6,10),(8,9)] => 0
[(1,4),(2,5),(3,7),(6,10),(8,9)] => 1
[(1,5),(2,4),(3,7),(6,10),(8,9)] => 0
[(1,6),(2,4),(3,7),(5,10),(8,9)] => 1
[(1,7),(2,4),(3,6),(5,10),(8,9)] => 0
[(1,8),(2,4),(3,6),(5,10),(7,9)] => 1
[(1,9),(2,4),(3,6),(5,10),(7,8)] => 2
[(1,10),(2,4),(3,6),(5,9),(7,8)] => 0
[(1,10),(2,3),(4,6),(5,9),(7,8)] => 0
[(1,9),(2,3),(4,6),(5,10),(7,8)] => 2
[(1,8),(2,3),(4,6),(5,10),(7,9)] => 1
[(1,7),(2,3),(4,6),(5,10),(8,9)] => 0
[(1,6),(2,3),(4,7),(5,10),(8,9)] => 1
[(1,5),(2,3),(4,7),(6,10),(8,9)] => 0
[(1,4),(2,3),(5,7),(6,10),(8,9)] => 0
[(1,3),(2,4),(5,7),(6,10),(8,9)] => 0
[(1,2),(3,4),(5,7),(6,10),(8,9)] => 0
[(1,2),(3,4),(5,8),(6,10),(7,9)] => 1
[(1,3),(2,4),(5,8),(6,10),(7,9)] => 1
[(1,4),(2,3),(5,8),(6,10),(7,9)] => 1
[(1,5),(2,3),(4,8),(6,10),(7,9)] => 1
[(1,6),(2,3),(4,8),(5,10),(7,9)] => 2
[(1,7),(2,3),(4,8),(5,10),(6,9)] => 4
[(1,8),(2,3),(4,7),(5,10),(6,9)] => 2
[(1,9),(2,3),(4,7),(5,10),(6,8)] => 3
[(1,10),(2,3),(4,7),(5,9),(6,8)] => 1
[(1,10),(2,4),(3,7),(5,9),(6,8)] => 1
[(1,9),(2,4),(3,7),(5,10),(6,8)] => 3
[(1,8),(2,4),(3,7),(5,10),(6,9)] => 2
[(1,7),(2,4),(3,8),(5,10),(6,9)] => 4
[(1,6),(2,4),(3,8),(5,10),(7,9)] => 2
[(1,5),(2,4),(3,8),(6,10),(7,9)] => 1
[(1,4),(2,5),(3,8),(6,10),(7,9)] => 2
[(1,3),(2,5),(4,8),(6,10),(7,9)] => 1
[(1,2),(3,5),(4,8),(6,10),(7,9)] => 1
[(1,2),(3,6),(4,8),(5,10),(7,9)] => 2
[(1,3),(2,6),(4,8),(5,10),(7,9)] => 2
[(1,4),(2,6),(3,8),(5,10),(7,9)] => 3
[(1,5),(2,6),(3,8),(4,10),(7,9)] => 5
[(1,6),(2,5),(3,8),(4,10),(7,9)] => 3
[(1,7),(2,5),(3,8),(4,10),(6,9)] => 5
[(1,8),(2,5),(3,7),(4,10),(6,9)] => 3
[(1,9),(2,5),(3,7),(4,10),(6,8)] => 4
[(1,10),(2,5),(3,7),(4,9),(6,8)] => 2
[(1,10),(2,6),(3,7),(4,9),(5,8)] => 4
[(1,9),(2,6),(3,7),(4,10),(5,8)] => 6
[(1,8),(2,6),(3,7),(4,10),(5,9)] => 5
[(1,7),(2,6),(3,8),(4,10),(5,9)] => 7
[(1,6),(2,7),(3,8),(4,10),(5,9)] => 10
[(1,5),(2,7),(3,8),(4,10),(6,9)] => 7
[(1,4),(2,7),(3,8),(5,10),(6,9)] => 5
[(1,3),(2,7),(4,8),(5,10),(6,9)] => 4
[(1,2),(3,7),(4,8),(5,10),(6,9)] => 4
[(1,2),(3,8),(4,7),(5,10),(6,9)] => 2
[(1,3),(2,8),(4,7),(5,10),(6,9)] => 2
[(1,4),(2,8),(3,7),(5,10),(6,9)] => 3
[(1,5),(2,8),(3,7),(4,10),(6,9)] => 5
[(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)] => 3
[(1,9),(2,7),(3,6),(4,10),(5,8)] => 4
[(1,10),(2,7),(3,6),(4,9),(5,8)] => 2
[(1,10),(2,8),(3,6),(4,9),(5,7)] => 3
[(1,9),(2,8),(3,6),(4,10),(5,7)] => 5
[(1,8),(2,9),(3,6),(4,10),(5,7)] => 10
[(1,7),(2,9),(3,6),(4,10),(5,8)] => 8
[(1,6),(2,9),(3,7),(4,10),(5,8)] => 9
[(1,5),(2,9),(3,7),(4,10),(6,8)] => 6
[(1,4),(2,9),(3,7),(5,10),(6,8)] => 4
[(1,3),(2,9),(4,7),(5,10),(6,8)] => 3
[(1,2),(3,9),(4,7),(5,10),(6,8)] => 3
[(1,2),(3,10),(4,7),(5,9),(6,8)] => 1
[(1,3),(2,10),(4,7),(5,9),(6,8)] => 1
[(1,4),(2,10),(3,7),(5,9),(6,8)] => 2
[(1,5),(2,10),(3,7),(4,9),(6,8)] => 4
[(1,6),(2,10),(3,7),(4,9),(5,8)] => 7
[(1,7),(2,10),(3,6),(4,9),(5,8)] => 6
[(1,8),(2,10),(3,6),(4,9),(5,7)] => 8
[(1,9),(2,10),(3,6),(4,8),(5,7)] => 7
[(1,10),(2,9),(3,6),(4,8),(5,7)] => 1
[(1,10),(2,9),(3,7),(4,8),(5,6)] => 2
[(1,9),(2,10),(3,7),(4,8),(5,6)] => 8
[(1,8),(2,10),(3,7),(4,9),(5,6)] => 9
[(1,7),(2,10),(3,8),(4,9),(5,6)] => 11
[(1,6),(2,10),(3,8),(4,9),(5,7)] => 8
[(1,5),(2,10),(3,8),(4,9),(6,7)] => 5
[(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)] => 2
[(1,2),(3,9),(4,8),(5,10),(6,7)] => 4
[(1,3),(2,9),(4,8),(5,10),(6,7)] => 4
[(1,4),(2,9),(3,8),(5,10),(6,7)] => 5
[(1,5),(2,9),(3,8),(4,10),(6,7)] => 7
[(1,6),(2,9),(3,8),(4,10),(5,7)] => 10
[(1,7),(2,9),(3,8),(4,10),(5,6)] => 13
[(1,8),(2,9),(3,7),(4,10),(5,6)] => 11
[(1,9),(2,8),(3,7),(4,10),(5,6)] => 6
[(1,10),(2,8),(3,7),(4,9),(5,6)] => 4
[(1,10),(2,7),(3,8),(4,9),(5,6)] => 7
[(1,9),(2,7),(3,8),(4,10),(5,6)] => 9
[(1,8),(2,7),(3,9),(4,10),(5,6)] => 12
[(1,7),(2,8),(3,9),(4,10),(5,6)] => 16
[(1,6),(2,8),(3,9),(4,10),(5,7)] => 13
[(1,5),(2,8),(3,9),(4,10),(6,7)] => 10
[(1,4),(2,8),(3,9),(5,10),(6,7)] => 8
[(1,3),(2,8),(4,9),(5,10),(6,7)] => 7
[(1,2),(3,8),(4,9),(5,10),(6,7)] => 7
[(1,2),(3,7),(4,9),(5,10),(6,8)] => 5
[(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)] => 8
[(1,6),(2,7),(3,9),(4,10),(5,8)] => 11
[(1,7),(2,6),(3,9),(4,10),(5,8)] => 8
[(1,8),(2,6),(3,9),(4,10),(5,7)] => 10
[(1,9),(2,6),(3,8),(4,10),(5,7)] => 7
[(1,10),(2,6),(3,8),(4,9),(5,7)] => 5
[(1,10),(2,5),(3,8),(4,9),(6,7)] => 3
[(1,9),(2,5),(3,8),(4,10),(6,7)] => 5
[(1,8),(2,5),(3,9),(4,10),(6,7)] => 8
[(1,7),(2,5),(3,9),(4,10),(6,8)] => 6
[(1,6),(2,5),(3,9),(4,10),(7,8)] => 4
[(1,5),(2,6),(3,9),(4,10),(7,8)] => 6
[(1,4),(2,6),(3,9),(5,10),(7,8)] => 4
[(1,3),(2,6),(4,9),(5,10),(7,8)] => 3
[(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)] => 2
[(1,4),(2,5),(3,9),(6,10),(7,8)] => 3
[(1,5),(2,4),(3,9),(6,10),(7,8)] => 2
[(1,6),(2,4),(3,9),(5,10),(7,8)] => 3
[(1,7),(2,4),(3,9),(5,10),(6,8)] => 5
[(1,8),(2,4),(3,9),(5,10),(6,7)] => 7
[(1,9),(2,4),(3,8),(5,10),(6,7)] => 4
[(1,10),(2,4),(3,8),(5,9),(6,7)] => 2
[(1,10),(2,3),(4,8),(5,9),(6,7)] => 2
[(1,9),(2,3),(4,8),(5,10),(6,7)] => 4
[(1,8),(2,3),(4,9),(5,10),(6,7)] => 7
[(1,7),(2,3),(4,9),(5,10),(6,8)] => 5
[(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)] => 2
[(1,3),(2,4),(5,9),(6,10),(7,8)] => 2
[(1,2),(3,4),(5,9),(6,10),(7,8)] => 2
[(1,2),(3,4),(5,10),(6,9),(7,8)] => 0
[(1,3),(2,4),(5,10),(6,9),(7,8)] => 0
[(1,4),(2,3),(5,10),(6,9),(7,8)] => 0
[(1,5),(2,3),(4,10),(6,9),(7,8)] => 0
[(1,6),(2,3),(4,10),(5,9),(7,8)] => 1
[(1,7),(2,3),(4,10),(5,9),(6,8)] => 3
[(1,8),(2,3),(4,10),(5,9),(6,7)] => 5
[(1,9),(2,3),(4,10),(5,8),(6,7)] => 4
[(1,10),(2,3),(4,9),(5,8),(6,7)] => 0
[(1,10),(2,4),(3,9),(5,8),(6,7)] => 0
[(1,9),(2,4),(3,10),(5,8),(6,7)] => 4
[(1,8),(2,4),(3,10),(5,9),(6,7)] => 5
[(1,7),(2,4),(3,10),(5,9),(6,8)] => 3
[(1,6),(2,4),(3,10),(5,9),(7,8)] => 1
[(1,5),(2,4),(3,10),(6,9),(7,8)] => 0
[(1,4),(2,5),(3,10),(6,9),(7,8)] => 1
[(1,3),(2,5),(4,10),(6,9),(7,8)] => 0
[(1,2),(3,5),(4,10),(6,9),(7,8)] => 0
[(1,2),(3,6),(4,10),(5,9),(7,8)] => 1
[(1,3),(2,6),(4,10),(5,9),(7,8)] => 1
[(1,4),(2,6),(3,10),(5,9),(7,8)] => 2
[(1,5),(2,6),(3,10),(4,9),(7,8)] => 4
[(1,6),(2,5),(3,10),(4,9),(7,8)] => 2
[(1,7),(2,5),(3,10),(4,9),(6,8)] => 4
[(1,8),(2,5),(3,10),(4,9),(6,7)] => 6
[(1,9),(2,5),(3,10),(4,8),(6,7)] => 5
[(1,10),(2,5),(3,9),(4,8),(6,7)] => 1
[(1,10),(2,6),(3,9),(4,8),(5,7)] => 3
[(1,9),(2,6),(3,10),(4,8),(5,7)] => 7
[(1,8),(2,6),(3,10),(4,9),(5,7)] => 8
[(1,7),(2,6),(3,10),(4,9),(5,8)] => 6
[(1,6),(2,7),(3,10),(4,9),(5,8)] => 9
[(1,5),(2,7),(3,10),(4,9),(6,8)] => 6
[(1,4),(2,7),(3,10),(5,9),(6,8)] => 4
[(1,3),(2,7),(4,10),(5,9),(6,8)] => 3
[(1,2),(3,7),(4,10),(5,9),(6,8)] => 3
[(1,2),(3,8),(4,10),(5,9),(6,7)] => 5
[(1,3),(2,8),(4,10),(5,9),(6,7)] => 5
[(1,4),(2,8),(3,10),(5,9),(6,7)] => 6
[(1,5),(2,8),(3,10),(4,9),(6,7)] => 8
[(1,6),(2,8),(3,10),(4,9),(5,7)] => 11
[(1,7),(2,8),(3,10),(4,9),(5,6)] => 14
[(1,8),(2,7),(3,10),(4,9),(5,6)] => 10
[(1,9),(2,7),(3,10),(4,8),(5,6)] => 9
[(1,10),(2,7),(3,9),(4,8),(5,6)] => 5
[(1,10),(2,8),(3,9),(4,7),(5,6)] => 4
[(1,9),(2,8),(3,10),(4,7),(5,6)] => 8
[(1,8),(2,9),(3,10),(4,7),(5,6)] => 13
[(1,7),(2,9),(3,10),(4,8),(5,6)] => 13
[(1,6),(2,9),(3,10),(4,8),(5,7)] => 10
[(1,5),(2,9),(3,10),(4,8),(6,7)] => 7
[(1,4),(2,9),(3,10),(5,8),(6,7)] => 5
[(1,3),(2,9),(4,10),(5,8),(6,7)] => 4
[(1,2),(3,9),(4,10),(5,8),(6,7)] => 4
[(1,2),(3,10),(4,9),(5,8),(6,7)] => 0
[(1,3),(2,10),(4,9),(5,8),(6,7)] => 0
[(1,4),(2,10),(3,9),(5,8),(6,7)] => 1
[(1,5),(2,10),(3,9),(4,8),(6,7)] => 3
[(1,6),(2,10),(3,9),(4,8),(5,7)] => 6
[(1,7),(2,10),(3,9),(4,8),(5,6)] => 9
[(1,8),(2,10),(3,9),(4,7),(5,6)] => 9
[(1,9),(2,10),(3,8),(4,7),(5,6)] => 6
[(1,10),(2,9),(3,8),(4,7),(5,6)] => 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:
12,2,1 55,20,12,9,6,2,0,1 273,156,110,110,83,64,50,38,17,16,13,6,1,6,1,0,1
$F_{2} = 1$
$F_{4} = 3$
$F_{6} = 12 + 2\ q + q^{2}$
$F_{8} = 55 + 20\ q + 12\ q^{2} + 9\ q^{3} + 6\ q^{4} + 2\ q^{5} + q^{7}$
$F_{10} = 273 + 156\ q + 110\ q^{2} + 110\ q^{3} + 83\ q^{4} + 64\ q^{5} + 50\ q^{6} + 38\ q^{7} + 17\ q^{8} + 16\ q^{9} + 13\ q^{10} + 6\ q^{11} + q^{12} + 6\ q^{13} + q^{14} + q^{16}$
Description
The number of occurrences of a 312 pattern in the restricted growth word of a perfect matching.
Code
def to_standard(s):
a = {e: i for i, e in enumerate(sorted(set(s)))}
return [a[e] for e in s]
def pattern_occurrences(w, pat):
pat = to_standard(pat)
return sum(1 for s in Subwords(w, len(pat))
if pat == to_standard(s))
def statistic(m):
return pattern_occurrences(m.to_restricted_growth_word(), [3,1,2])
Created
Sep 30, 2022 at 17:07 by Martin Rubey
Updated
Sep 30, 2022 at 17:07 by Martin Rubey
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