Identifier
-
Mp00150:
Perfect matchings
—to Dyck path⟶
Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St000068: Posets ⟶ ℤ
Values
[(1,2)] => [1,0] => ([],1) => 1
[(1,2),(3,4)] => [1,0,1,0] => ([(0,1)],2) => 1
[(1,3),(2,4)] => [1,1,0,0] => ([],2) => 2
[(1,4),(2,3)] => [1,1,0,0] => ([],2) => 2
[(1,2),(3,4),(5,6)] => [1,0,1,0,1,0] => ([(0,2),(2,1)],3) => 1
[(1,3),(2,4),(5,6)] => [1,1,0,0,1,0] => ([(0,1),(0,2)],3) => 1
[(1,4),(2,3),(5,6)] => [1,1,0,0,1,0] => ([(0,1),(0,2)],3) => 1
[(1,5),(2,3),(4,6)] => [1,1,0,1,0,0] => ([(1,2)],3) => 2
[(1,6),(2,3),(4,5)] => [1,1,0,1,0,0] => ([(1,2)],3) => 2
[(1,6),(2,4),(3,5)] => [1,1,1,0,0,0] => ([],3) => 3
[(1,5),(2,4),(3,6)] => [1,1,1,0,0,0] => ([],3) => 3
[(1,4),(2,5),(3,6)] => [1,1,1,0,0,0] => ([],3) => 3
[(1,3),(2,5),(4,6)] => [1,1,0,1,0,0] => ([(1,2)],3) => 2
[(1,2),(3,5),(4,6)] => [1,0,1,1,0,0] => ([(0,2),(1,2)],3) => 2
[(1,2),(3,6),(4,5)] => [1,0,1,1,0,0] => ([(0,2),(1,2)],3) => 2
[(1,3),(2,6),(4,5)] => [1,1,0,1,0,0] => ([(1,2)],3) => 2
[(1,4),(2,6),(3,5)] => [1,1,1,0,0,0] => ([],3) => 3
[(1,5),(2,6),(3,4)] => [1,1,1,0,0,0] => ([],3) => 3
[(1,6),(2,5),(3,4)] => [1,1,1,0,0,0] => ([],3) => 3
[(1,2),(3,4),(5,6),(7,8)] => [1,0,1,0,1,0,1,0] => ([(0,3),(2,1),(3,2)],4) => 1
[(1,3),(2,4),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => ([(0,3),(3,1),(3,2)],4) => 1
[(1,4),(2,3),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => ([(0,3),(3,1),(3,2)],4) => 1
[(1,5),(2,3),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(3,1)],4) => 1
[(1,6),(2,3),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(3,1)],4) => 1
[(1,7),(2,3),(4,5),(6,8)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,8),(2,3),(4,5),(6,7)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,8),(2,4),(3,5),(6,7)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,7),(2,4),(3,5),(6,8)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,6),(2,4),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3)],4) => 1
[(1,5),(2,4),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3)],4) => 1
[(1,4),(2,5),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3)],4) => 1
[(1,3),(2,5),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(3,1)],4) => 1
[(1,2),(3,5),(4,6),(7,8)] => [1,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[(1,2),(3,6),(4,5),(7,8)] => [1,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[(1,3),(2,6),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(3,1)],4) => 1
[(1,4),(2,6),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3)],4) => 1
[(1,5),(2,6),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3)],4) => 1
[(1,6),(2,5),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3)],4) => 1
[(1,7),(2,5),(3,4),(6,8)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,8),(2,5),(3,4),(6,7)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,8),(2,6),(3,4),(5,7)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,7),(2,6),(3,4),(5,8)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,6),(2,7),(3,4),(5,8)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,5),(2,7),(3,4),(6,8)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,4),(2,7),(3,5),(6,8)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,3),(2,7),(4,5),(6,8)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,2),(3,7),(4,5),(6,8)] => [1,0,1,1,0,1,0,0] => ([(0,3),(1,2),(2,3)],4) => 2
[(1,2),(3,8),(4,5),(6,7)] => [1,0,1,1,0,1,0,0] => ([(0,3),(1,2),(2,3)],4) => 2
[(1,3),(2,8),(4,5),(6,7)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,4),(2,8),(3,5),(6,7)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,5),(2,8),(3,4),(6,7)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,6),(2,8),(3,4),(5,7)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,7),(2,8),(3,4),(5,6)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,8),(2,7),(3,4),(5,6)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,8),(2,7),(3,5),(4,6)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,7),(2,8),(3,5),(4,6)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,6),(2,8),(3,5),(4,7)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,5),(2,8),(3,6),(4,7)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,4),(2,8),(3,6),(5,7)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,3),(2,8),(4,6),(5,7)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,2),(3,8),(4,6),(5,7)] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,3),(2,3)],4) => 3
[(1,2),(3,7),(4,6),(5,8)] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,3),(2,3)],4) => 3
[(1,3),(2,7),(4,6),(5,8)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,4),(2,7),(3,6),(5,8)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,5),(2,7),(3,6),(4,8)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,6),(2,7),(3,5),(4,8)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,7),(2,6),(3,5),(4,8)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,8),(2,6),(3,5),(4,7)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,8),(2,5),(3,6),(4,7)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,7),(2,5),(3,6),(4,8)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,6),(2,5),(3,7),(4,8)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,5),(2,6),(3,7),(4,8)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,4),(2,6),(3,7),(5,8)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,3),(2,6),(4,7),(5,8)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,2),(3,6),(4,7),(5,8)] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,3),(2,3)],4) => 3
[(1,2),(3,5),(4,7),(6,8)] => [1,0,1,1,0,1,0,0] => ([(0,3),(1,2),(2,3)],4) => 2
[(1,3),(2,5),(4,7),(6,8)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,4),(2,5),(3,7),(6,8)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,5),(2,4),(3,7),(6,8)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,6),(2,4),(3,7),(5,8)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,7),(2,4),(3,6),(5,8)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,8),(2,4),(3,6),(5,7)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,8),(2,3),(4,6),(5,7)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,7),(2,3),(4,6),(5,8)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,6),(2,3),(4,7),(5,8)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,5),(2,3),(4,7),(6,8)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,4),(2,3),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[(1,3),(2,4),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[(1,2),(3,4),(5,7),(6,8)] => [1,0,1,0,1,1,0,0] => ([(0,3),(1,3),(3,2)],4) => 2
[(1,2),(3,4),(5,8),(6,7)] => [1,0,1,0,1,1,0,0] => ([(0,3),(1,3),(3,2)],4) => 2
[(1,3),(2,4),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[(1,4),(2,3),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => ([(0,2),(0,3),(1,2),(1,3)],4) => 2
[(1,5),(2,3),(4,8),(6,7)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,6),(2,3),(4,8),(5,7)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,7),(2,3),(4,8),(5,6)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,8),(2,3),(4,7),(5,6)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,8),(2,4),(3,7),(5,6)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,7),(2,4),(3,8),(5,6)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,6),(2,4),(3,8),(5,7)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,5),(2,4),(3,8),(6,7)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
[(1,4),(2,5),(3,8),(6,7)] => [1,1,1,0,0,1,0,0] => ([(1,2),(1,3)],4) => 2
>>> Load all 1421 entries. <<<[(1,3),(2,5),(4,8),(6,7)] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => 2
[(1,2),(3,5),(4,8),(6,7)] => [1,0,1,1,0,1,0,0] => ([(0,3),(1,2),(2,3)],4) => 2
[(1,2),(3,6),(4,8),(5,7)] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,3),(2,3)],4) => 3
[(1,3),(2,6),(4,8),(5,7)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,4),(2,6),(3,8),(5,7)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,5),(2,6),(3,8),(4,7)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,6),(2,5),(3,8),(4,7)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,7),(2,5),(3,8),(4,6)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,8),(2,5),(3,7),(4,6)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,8),(2,6),(3,7),(4,5)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,7),(2,6),(3,8),(4,5)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,6),(2,7),(3,8),(4,5)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,5),(2,7),(3,8),(4,6)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,4),(2,7),(3,8),(5,6)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,3),(2,7),(4,8),(5,6)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,2),(3,7),(4,8),(5,6)] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,3),(2,3)],4) => 3
[(1,2),(3,8),(4,7),(5,6)] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,3),(2,3)],4) => 3
[(1,3),(2,8),(4,7),(5,6)] => [1,1,0,1,1,0,0,0] => ([(1,3),(2,3)],4) => 3
[(1,4),(2,8),(3,7),(5,6)] => [1,1,1,0,1,0,0,0] => ([(2,3)],4) => 3
[(1,5),(2,8),(3,7),(4,6)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,6),(2,8),(3,7),(4,5)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,7),(2,8),(3,6),(4,5)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,8),(2,7),(3,6),(4,5)] => [1,1,1,1,0,0,0,0] => ([],4) => 4
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [1,0,1,0,1,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => ([(0,3),(3,4),(4,1),(4,2)],5) => 1
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => ([(0,3),(3,4),(4,1),(4,2)],5) => 1
[(1,5),(2,3),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => ([(0,4),(3,2),(4,1),(4,3)],5) => 1
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => ([(0,4),(3,2),(4,1),(4,3)],5) => 1
[(1,7),(2,3),(4,5),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,9),(2,3),(4,5),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,10),(2,4),(3,5),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,9),(2,4),(3,5),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,4),(3,5),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,7),(2,4),(3,5),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => ([(0,4),(4,1),(4,2),(4,3)],5) => 1
[(1,5),(2,4),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => ([(0,4),(4,1),(4,2),(4,3)],5) => 1
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => ([(0,4),(4,1),(4,2),(4,3)],5) => 1
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => ([(0,4),(3,2),(4,1),(4,3)],5) => 1
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 1
[(1,3),(2,6),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => ([(0,4),(3,2),(4,1),(4,3)],5) => 1
[(1,4),(2,6),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => ([(0,4),(4,1),(4,2),(4,3)],5) => 1
[(1,5),(2,6),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => ([(0,4),(4,1),(4,2),(4,3)],5) => 1
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => ([(0,4),(4,1),(4,2),(4,3)],5) => 1
[(1,7),(2,5),(3,4),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,9),(2,5),(3,4),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,6),(3,4),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,9),(2,6),(3,4),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,6),(3,4),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,7),(2,6),(3,4),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,6),(2,7),(3,4),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,5),(2,7),(3,4),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,4),(2,7),(3,5),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,3),(2,7),(4,5),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,2),(3,7),(4,5),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 1
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 1
[(1,3),(2,8),(4,5),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,4),(2,8),(3,5),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,5),(2,8),(3,4),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,6),(2,8),(3,4),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,7),(2,8),(3,4),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,9),(2,7),(3,4),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,8),(3,4),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,8),(3,4),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,9),(3,4),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,9),(3,4),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,9),(3,4),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,9),(3,4),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,9),(3,5),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,9),(4,5),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,2),(3,9),(4,5),(6,7),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,10),(4,5),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,4),(2,10),(3,5),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,10),(3,4),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,10),(3,4),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,10),(3,4),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,10),(3,4),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,10),(3,4),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,9),(3,5),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,10),(3,5),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,8),(2,10),(3,5),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,10),(3,5),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,10),(3,5),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,10),(3,6),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,10),(3,6),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,10),(4,6),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,2),(3,10),(4,6),(5,7),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,9),(4,6),(5,7),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,9),(4,6),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,4),(2,9),(3,6),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,9),(3,6),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,9),(3,5),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,9),(3,5),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,8),(3,5),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,8),(3,5),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,7),(3,5),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,9),(2,7),(3,5),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,7),(3,5),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,7),(2,8),(3,5),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,6),(2,8),(3,5),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,5),(2,8),(3,6),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,4),(2,8),(3,6),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,3),(2,8),(4,6),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,2),(3,8),(4,6),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[(1,2),(3,7),(4,6),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[(1,3),(2,7),(4,6),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,4),(2,7),(3,6),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,5),(2,7),(3,6),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,6),(2,7),(3,5),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,7),(2,6),(3,5),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,8),(2,6),(3,5),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,9),(2,6),(3,5),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,6),(3,5),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,5),(3,6),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,9),(2,5),(3,6),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,5),(3,6),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,7),(2,5),(3,6),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,6),(2,5),(3,7),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 1
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,5),(2,4),(3,7),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,6),(2,4),(3,7),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,7),(2,4),(3,6),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,8),(2,4),(3,6),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,9),(2,4),(3,6),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,4),(3,6),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,3),(4,6),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,9),(2,3),(4,6),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,8),(2,3),(4,6),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,7),(2,3),(4,6),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,6),(2,3),(4,7),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,5),(2,3),(4,7),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,4),(2,3),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 1
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 1
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 1
[(1,3),(2,4),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 1
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 1
[(1,5),(2,3),(4,8),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,6),(2,3),(4,8),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,7),(2,3),(4,8),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,9),(2,3),(4,7),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,10),(2,4),(3,7),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,9),(2,4),(3,7),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,4),(3,7),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,7),(2,4),(3,8),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,6),(2,4),(3,8),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,5),(2,4),(3,8),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,4),(2,5),(3,8),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(4,1),(4,2)],5) => 1
[(1,3),(2,5),(4,8),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1
[(1,2),(3,5),(4,8),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 1
[(1,2),(3,6),(4,8),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[(1,3),(2,6),(4,8),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,4),(2,6),(3,8),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,5),(2,6),(3,8),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,6),(2,5),(3,8),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,7),(2,5),(3,8),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,8),(2,5),(3,7),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,9),(2,5),(3,7),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,5),(3,7),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,6),(3,7),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,9),(2,6),(3,7),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,6),(3,7),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,7),(2,6),(3,8),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,6),(2,7),(3,8),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,5),(2,7),(3,8),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,4),(2,7),(3,8),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,3),(2,7),(4,8),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,2),(3,7),(4,8),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[(1,3),(2,8),(4,7),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 1
[(1,4),(2,8),(3,7),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(4,1)],5) => 1
[(1,5),(2,8),(3,7),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,6),(2,8),(3,7),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,7),(2,8),(3,6),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4)],5) => 1
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,10),(2,8),(3,6),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,8),(3,6),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,8),(2,9),(3,6),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,9),(3,6),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,9),(3,7),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,9),(3,7),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,9),(3,7),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,9),(4,7),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,2),(3,9),(4,7),(5,6),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,10),(4,7),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,4),(2,10),(3,7),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,10),(3,7),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,10),(3,7),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,10),(3,6),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,10),(3,6),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,10),(3,6),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,9),(3,7),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,10),(3,7),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,10),(3,7),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,10),(3,8),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,10),(3,8),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,10),(3,8),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,10),(3,8),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,10),(4,8),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,10),(4,8),(5,6),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,9),(4,8),(5,6),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,9),(4,8),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,9),(3,8),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,9),(3,8),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,9),(3,8),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,9),(3,8),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,9),(3,7),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,8),(3,7),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,8),(3,7),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,7),(3,8),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,7),(3,8),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,7),(3,9),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,8),(3,9),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,8),(3,9),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,8),(3,9),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,8),(3,9),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,8),(4,9),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,8),(4,9),(5,6),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,7),(4,9),(5,6),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,7),(4,9),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,4),(2,7),(3,9),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,7),(3,9),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,7),(3,9),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,6),(3,9),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,6),(3,9),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,6),(3,8),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,6),(3,8),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,5),(3,8),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,5),(3,8),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,8),(2,5),(3,9),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,5),(3,9),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,5),(3,9),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,6),(3,9),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,6),(3,9),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,6),(4,9),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,2),(3,6),(4,9),(5,7),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,5),(4,9),(6,7),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,5),(4,9),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,4),(2,5),(3,9),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,4),(3,9),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,4),(3,9),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,4),(3,9),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,4),(3,9),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,4),(3,8),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,4),(3,8),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,3),(4,8),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,3),(4,8),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,3),(4,9),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,3),(4,9),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,6),(2,3),(4,9),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,5),(2,3),(4,9),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,4),(2,3),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,3),(2,4),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,2),(3,4),(5,9),(6,7),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[(1,3),(2,4),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,5),(2,3),(4,10),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,6),(2,3),(4,10),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,7),(2,3),(4,10),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,8),(2,3),(4,10),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,3),(4,10),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,4),(3,9),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,4),(3,10),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,4),(3,10),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,4),(3,10),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,4),(3,10),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,4),(3,10),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,5),(3,10),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,5),(4,10),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,2),(3,5),(4,10),(6,7),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,6),(4,10),(5,7),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,6),(4,10),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,4),(2,6),(3,10),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,6),(3,10),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,5),(3,10),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,5),(3,10),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,5),(3,10),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,5),(3,10),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,5),(3,9),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,6),(3,9),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,6),(3,10),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,8),(2,6),(3,10),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,6),(3,10),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,7),(3,10),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,7),(3,10),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,7),(3,10),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,7),(4,10),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,2),(3,7),(4,10),(5,6),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,8),(4,10),(5,6),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,8),(4,10),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,8),(3,10),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,8),(3,10),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,8),(3,10),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,8),(3,10),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,7),(3,10),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,7),(3,10),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,7),(3,9),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,8),(3,9),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,8),(3,10),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,9),(3,10),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,9),(3,10),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,9),(3,10),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,9),(3,10),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,9),(3,10),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,9),(4,10),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,9),(4,10),(5,6),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,10),(4,9),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,10),(3,9),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,10),(3,9),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,10),(3,9),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,10),(3,9),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,10),(3,9),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,10),(3,8),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,9),(3,8),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,10),(3,8),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,10),(3,9),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,10),(3,9),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,10),(3,9),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,10),(3,9),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,10),(3,9),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,10),(4,9),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,10),(4,9),(5,7),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,9),(4,10),(5,7),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,9),(4,10),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,9),(3,10),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,9),(3,10),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,9),(3,10),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,9),(3,10),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,9),(3,10),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,8),(3,10),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,7),(3,9),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,7),(3,10),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,7),(3,10),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,8),(3,10),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,8),(3,10),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,8),(3,10),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,8),(3,10),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,8),(4,10),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,8),(4,10),(5,7),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,7),(4,10),(5,8),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,7),(4,10),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,7),(3,10),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,7),(3,10),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,7),(3,10),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,6),(3,10),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,6),(3,10),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,6),(3,10),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,6),(3,9),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,5),(3,9),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,5),(3,10),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,5),(3,10),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,5),(3,10),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,5),(3,10),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,6),(3,10),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,6),(3,10),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,6),(4,10),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,6),(4,10),(5,8),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,5),(4,10),(6,8),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,3),(2,5),(4,10),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,5),(3,10),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,4),(3,10),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,4),(3,10),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,4),(3,10),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,4),(3,10),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,4),(3,10),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,4),(3,9),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,3),(4,9),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,9),(2,3),(4,10),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,8),(2,3),(4,10),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,7),(2,3),(4,10),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,6),(2,3),(4,10),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,3),(4,10),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,3),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,4),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,4),(2,4),(4,3)],5) => 3
[(1,2),(3,4),(5,9),(6,8),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,4),(2,4),(4,3)],5) => 3
[(1,3),(2,4),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,3),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,3),(4,9),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,3),(4,9),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,3),(4,9),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,8),(2,3),(4,9),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,9),(2,3),(4,8),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,10),(2,3),(4,8),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,10),(2,4),(3,8),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,4),(3,8),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,4),(3,9),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,7),(2,4),(3,9),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,6),(2,4),(3,9),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,4),(3,9),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,5),(3,9),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,5),(4,9),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,5),(4,9),(6,8),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,2),(3,6),(4,9),(5,8),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,6),(4,9),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,6),(3,9),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,6),(3,9),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,5),(3,9),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,5),(3,9),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,5),(3,9),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,5),(3,8),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,5),(3,8),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,6),(3,8),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,6),(3,8),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,6),(3,9),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,6),(3,9),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,7),(3,9),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,7),(3,9),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,7),(3,9),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,7),(4,9),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,7),(4,9),(5,8),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,8),(4,9),(5,7),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,8),(4,9),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,8),(3,9),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,8),(3,9),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,8),(3,9),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,8),(3,9),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,7),(3,9),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,7),(3,8),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,7),(3,8),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,8),(3,7),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,8),(3,7),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,9),(3,7),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,9),(3,8),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,9),(3,8),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,9),(3,8),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,9),(3,8),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,9),(4,8),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,9),(4,8),(5,7),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,10),(4,8),(5,7),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,10),(4,8),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,10),(3,8),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,10),(3,8),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,10),(3,8),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,10),(3,8),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,10),(3,7),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,10),(3,7),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,9),(3,7),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,9),(3,6),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,10),(3,6),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,10),(3,6),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,10),(3,6),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,10),(3,7),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,10),(3,7),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,10),(3,7),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,10),(4,7),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,10),(4,7),(5,8),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,9),(4,7),(5,8),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,9),(4,7),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,9),(3,7),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,9),(3,7),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,9),(3,7),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,9),(3,6),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,9),(3,6),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,8),(3,6),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,8),(3,6),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,7),(3,6),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,7),(3,6),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,7),(3,6),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,8),(3,6),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,8),(3,7),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,8),(3,7),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,8),(3,7),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,8),(4,7),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,8),(4,7),(5,9),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,7),(4,8),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,7),(3,8),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,6),(3,8),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,6),(3,7),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,6),(3,7),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,6),(3,7),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,5),(3,7),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,5),(3,7),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,5),(3,7),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,5),(3,8),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,5),(3,8),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,6),(3,8),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,6),(4,8),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,3),(2,5),(4,8),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,4),(3,8),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,4),(3,8),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,4),(3,8),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,4),(3,7),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,4),(3,7),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,4),(3,7),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,3),(4,7),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,9),(2,3),(4,7),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,8),(2,3),(4,7),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,6),(2,3),(4,8),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,3),(4,8),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,3),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,4),(2,4),(4,3)],5) => 3
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,4),(2,3),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,5),(2,3),(4,7),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,6),(2,3),(4,7),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,7),(2,3),(4,6),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,8),(2,3),(4,6),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,3),(4,6),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,3),(4,6),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,4),(3,6),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,4),(3,6),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,4),(3,6),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,4),(3,6),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,4),(3,7),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,4),(3,7),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,5),(3,7),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,6),(4,7),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,4),(2,6),(3,7),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,6),(3,7),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,5),(3,7),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,5),(3,6),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,5),(3,6),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,5),(3,6),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,5),(3,6),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,6),(3,5),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,6),(3,5),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,8),(2,6),(3,5),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,6),(3,5),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,7),(3,5),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,7),(3,6),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,7),(3,6),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,7),(4,6),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,2),(3,7),(4,6),(5,9),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,8),(4,6),(5,9),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,8),(4,6),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,8),(3,6),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,8),(3,6),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,8),(3,5),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,8),(3,5),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,7),(3,5),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,7),(3,5),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,7),(3,5),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,8),(3,5),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,8),(3,5),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,9),(3,5),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,9),(3,5),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,9),(3,5),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,9),(3,6),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,9),(3,6),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,9),(4,6),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,9),(4,6),(5,8),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,10),(4,6),(5,8),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,10),(4,6),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,10),(3,6),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,10),(3,6),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,10),(3,5),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,10),(3,5),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,10),(3,5),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,10),(3,5),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,9),(3,5),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,9),(3,4),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,10),(3,4),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,10),(3,4),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,7),(2,10),(3,4),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,6),(2,10),(3,4),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,10),(3,4),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,10),(3,5),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,10),(4,5),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,10),(4,5),(6,8),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,2),(3,9),(4,5),(6,8),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,3),(2,9),(4,5),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,9),(3,5),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,9),(3,4),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,9),(3,4),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,9),(3,4),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,9),(3,4),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,8),(3,4),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,8),(3,4),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,7),(3,4),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,7),(3,4),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,7),(3,4),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,7),(2,8),(3,4),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,6),(2,8),(3,4),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,8),(3,4),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,8),(3,5),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,8),(4,5),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,8),(4,5),(6,9),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,2),(3,7),(4,5),(6,9),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,7),(4,5),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,4),(2,7),(3,5),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,7),(3,4),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,7),(3,4),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,6),(3,4),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,6),(3,4),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,6),(3,4),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,6),(3,4),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,5),(3,4),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,5),(3,4),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,5),(3,4),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,5),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,6),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,6),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,6),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,2),(3,6),(4,5),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,4),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,4),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,4),(3,5),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,4),(3,5),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,4),(3,5),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,4),(3,5),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,3),(4,5),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,3),(4,5),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,3),(4,5),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,3),(4,5),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,6),(2,3),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,5),(2,3),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,4),(2,3),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => ([(0,4),(1,4),(4,2),(4,3)],5) => 2
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => ([(0,4),(1,4),(4,2),(4,3)],5) => 2
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [1,0,1,0,1,0,1,1,0,0] => ([(0,4),(1,4),(2,3),(4,2)],5) => 2
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [1,0,1,0,1,0,1,1,0,0] => ([(0,4),(1,4),(2,3),(4,2)],5) => 2
[(1,3),(2,4),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => ([(0,4),(1,4),(4,2),(4,3)],5) => 2
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => ([(0,4),(1,4),(4,2),(4,3)],5) => 2
[(1,5),(2,3),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,7),(2,3),(4,5),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,8),(2,3),(4,5),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,3),(4,5),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,4),(3,5),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,4),(3,5),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,4),(3,5),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,4),(3,5),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,4),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,4),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,5),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,5),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,2),(3,5),(4,6),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 2
[(1,3),(2,6),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 2
[(1,4),(2,6),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,6),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,5),(3,4),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,5),(3,4),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,5),(3,4),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,6),(3,4),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,6),(3,4),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,6),(3,4),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,6),(3,4),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,7),(3,4),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,7),(3,4),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,7),(3,5),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,7),(4,5),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,2),(3,7),(4,5),(6,10),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,8),(4,5),(6,10),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,3),(2,8),(4,5),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,8),(3,5),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,8),(3,4),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,8),(3,4),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,8),(3,4),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,7),(3,4),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,7),(3,4),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,7),(3,4),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,8),(3,4),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,8),(3,4),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,9),(3,4),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,7),(2,9),(3,4),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,6),(2,9),(3,4),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,9),(3,4),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,9),(3,5),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,9),(4,5),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,9),(4,5),(6,10),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,3),(2,10),(4,5),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,10),(3,5),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,10),(3,4),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,10),(3,4),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,10),(3,4),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,10),(3,4),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,10),(3,4),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,9),(3,5),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,10),(3,5),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,10),(3,5),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,10),(3,5),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,10),(3,5),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,10),(3,6),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,10),(3,6),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,10),(4,6),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,10),(4,6),(5,9),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,9),(4,6),(5,10),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,9),(4,6),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,9),(3,6),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,9),(3,6),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,9),(3,5),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,9),(3,5),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,9),(3,5),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,8),(3,5),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,8),(3,5),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,7),(3,5),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,7),(3,5),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,8),(3,5),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,8),(3,5),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,8),(3,6),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,8),(3,6),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,8),(4,6),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,8),(4,6),(5,10),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,7),(4,6),(5,10),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,7),(4,6),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,4),(2,7),(3,6),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,7),(3,6),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,7),(3,5),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,6),(3,5),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,6),(3,5),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,6),(3,5),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,6),(3,5),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,10),(2,5),(3,6),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,9),(2,5),(3,6),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,8),(2,5),(3,6),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,5),(3,6),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,5),(3,7),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,6),(3,7),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4)],5) => 2
[(1,4),(2,6),(3,7),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,3),(2,6),(4,7),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,2),(3,6),(4,7),(5,10),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,2),(3,5),(4,7),(6,10),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 2
[(1,3),(2,5),(4,7),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,4),(2,5),(3,7),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,5),(2,4),(3,7),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,6),(2,4),(3,7),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,7),(2,4),(3,6),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4)],5) => 2
[(1,8),(2,4),(3,6),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,4),(3,6),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,4),(3,6),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,10),(2,3),(4,6),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,9),(2,3),(4,6),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,8),(2,3),(4,6),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,3),(4,6),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,6),(2,3),(4,7),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(3,4)],5) => 2
[(1,5),(2,3),(4,7),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 2
[(1,4),(2,3),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,3),(2,4),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 2
[(1,2),(3,4),(5,7),(6,10),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => ([(0,4),(1,2),(2,4),(4,3)],5) => 2
[(1,2),(3,4),(5,8),(6,10),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,4),(2,4),(4,3)],5) => 3
[(1,3),(2,4),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,3),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,3),(4,8),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,3),(4,8),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,3),(4,8),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,8),(2,3),(4,7),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,9),(2,3),(4,7),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,10),(2,3),(4,7),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,10),(2,4),(3,7),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,4),(3,7),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,4),(3,7),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,7),(2,4),(3,8),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,6),(2,4),(3,8),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,4),(3,8),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,5),(3,8),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,5),(4,8),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,5),(4,8),(6,10),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,2),(3,6),(4,8),(5,10),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,6),(4,8),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,6),(3,8),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,6),(3,8),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,5),(3,8),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,5),(3,8),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,5),(3,7),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,5),(3,7),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,5),(3,7),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,6),(3,7),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,6),(3,7),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,6),(3,7),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,6),(3,8),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,7),(3,8),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,7),(3,8),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,7),(3,8),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,7),(4,8),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,7),(4,8),(5,10),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,8),(4,7),(5,10),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,8),(4,7),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,8),(3,7),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,8),(3,7),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,8),(3,7),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,8),(3,6),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,7),(3,6),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,7),(3,6),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,7),(3,6),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,8),(3,6),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,8),(3,6),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,9),(3,6),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,9),(3,6),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,9),(3,7),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,9),(3,7),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,9),(3,7),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,9),(4,7),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,9),(4,7),(5,10),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,10),(4,7),(5,9),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,10),(4,7),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,10),(3,7),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,10),(3,7),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,10),(3,7),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,10),(3,6),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,10),(3,6),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,10),(3,6),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,9),(3,6),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,9),(3,7),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,10),(3,7),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,10),(3,7),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,10),(3,8),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,10),(3,8),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,10),(3,8),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,10),(3,8),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,10),(4,8),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,10),(4,8),(5,9),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,9),(4,8),(5,10),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,9),(4,8),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,9),(3,8),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,9),(3,8),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,9),(3,8),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,9),(3,8),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,9),(3,7),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,8),(3,7),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,8),(3,7),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,7),(3,8),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,7),(3,8),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,7),(3,9),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,8),(3,9),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,8),(3,9),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,8),(3,9),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,8),(3,9),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,8),(4,9),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,8),(4,9),(5,10),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,7),(4,9),(5,10),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,7),(4,9),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,7),(3,9),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,7),(3,9),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,7),(3,9),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,6),(3,9),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,6),(3,9),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,6),(3,8),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,6),(3,8),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,5),(3,8),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,5),(3,8),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,5),(3,9),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,7),(2,5),(3,9),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,5),(3,9),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,5),(2,6),(3,9),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,4),(2,6),(3,9),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,6),(4,9),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,6),(4,9),(5,10),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,2),(3,5),(4,9),(6,10),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,3),(2,5),(4,9),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,5),(3,9),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,4),(3,9),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,4),(3,9),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,4),(3,9),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,4),(3,9),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,4),(3,8),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,4),(3,8),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,10),(2,3),(4,8),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,9),(2,3),(4,8),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,8),(2,3),(4,9),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,7),(2,3),(4,9),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,6),(2,3),(4,9),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,3),(4,9),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,3),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,4),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,4),(5,9),(6,10),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,4),(2,4),(4,3)],5) => 3
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => ([(0,4),(1,4),(2,4),(4,3)],5) => 3
[(1,3),(2,4),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,3),(4,10),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,6),(2,3),(4,10),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,7),(2,3),(4,10),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,8),(2,3),(4,10),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,9),(2,3),(4,10),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,10),(2,4),(3,9),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,9),(2,4),(3,10),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,8),(2,4),(3,10),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,7),(2,4),(3,10),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,6),(2,4),(3,10),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,4),(3,10),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,5),(3,10),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => ([(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,3),(2,5),(4,10),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 3
[(1,2),(3,5),(4,10),(6,9),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => ([(0,4),(1,3),(2,3),(3,4)],5) => 3
[(1,2),(3,6),(4,10),(5,9),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[(1,3),(2,6),(4,10),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => ([(0,4),(1,4),(2,3),(2,4)],5) => 3
[(1,4),(2,6),(3,10),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => 3
[(1,5),(2,6),(3,10),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,6),(2,5),(3,10),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => ([(2,3),(2,4)],5) => 3
[(1,7),(2,5),(3,10),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,8),(2,5),(3,10),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,9),(2,5),(3,10),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,5),(3,9),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,10),(2,6),(3,9),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,6),(3,10),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,6),(3,10),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,6),(3,10),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,7),(3,10),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,7),(3,10),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,7),(3,10),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,7),(4,10),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,7),(4,10),(5,9),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,8),(4,10),(5,9),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,8),(4,10),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,8),(3,10),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,8),(3,10),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,8),(3,10),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,8),(3,10),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,7),(3,10),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,7),(3,10),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,7),(3,9),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,8),(3,9),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,8),(3,10),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,9),(3,10),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,9),(3,10),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,6),(2,9),(3,10),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,5),(2,9),(3,10),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,4),(2,9),(3,10),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,3),(2,9),(4,10),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,9),(4,10),(5,8),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[(1,3),(2,10),(4,9),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => ([(1,4),(2,4),(3,4)],5) => 4
[(1,4),(2,10),(3,9),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => ([(2,4),(3,4)],5) => 4
[(1,5),(2,10),(3,9),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => ([(3,4)],5) => 4
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,7),(2,10),(3,9),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,8),(2,10),(3,9),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => ([],5) => 5
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [1,0,1,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 1
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [1,0,1,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [1,1,0,1,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 1
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 1
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 3
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [1,0,1,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 3
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => 1
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 2
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => 2
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [1,1,1,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 1
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => 2
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 2
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => 2
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => 1
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 1
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [1,0,1,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => 1
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 2
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => 2
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [1,1,1,0,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) => 1
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => 2
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 1
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 3
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [1,0,1,1,0,1,0,1,1,0,0,0] => ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 3
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => 1
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => 2
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [1,1,1,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 1
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => 2
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [1,0,1,0,1,1,0,1,1,0,0,0] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 3
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [1,1,1,0,0,1,0,0,1,0,1,0] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => 1
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [1,1,0,0,1,1,0,1,1,0,0,0] => ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [1,1,1,0,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) => 2
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [1,0,1,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 1
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 2
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [1,0,1,1,1,0,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [1,1,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) => 1
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => 1
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 2
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => 1
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => 2
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 1
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 2
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) => 2
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [1,0,1,0,1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 1
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [1,0,1,1,1,1,1,0,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 2
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => 2
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [1,1,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) => 1
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 2
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 1
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [1,0,1,1,0,1,1,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) => 3
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => 1
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => 2
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [1,1,1,1,0,0,1,0,0,0,1,0] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 1
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => 2
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [1,0,1,0,1,1,1,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 3
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [1,1,1,0,0,0,1,0,1,0,1,0] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => 1
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [1,1,0,0,1,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) => 3
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [1,1,1,0,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(5,2),(5,3),(5,4)],6) => 2
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [1,0,1,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 1
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 2
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [1,0,1,1,1,0,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [1,1,0,1,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) => 1
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 1
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [1,0,1,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 4
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => 1
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 2
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 2
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [1,1,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) => 1
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => 2
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [1,0,1,1,1,0,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 1
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 3
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [1,0,1,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [1,1,0,1,1,0,0,0,1,0,1,0] => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 1
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [1,0,1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [1,1,1,1,1,0,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 1
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [1,1,0,1,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) => 2
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [1,0,1,0,1,0,1,1,1,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 3
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [1,1,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => 1
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [1,1,0,0,1,0,1,1,1,0,0,0] => ([(0,5),(1,5),(2,5),(5,3),(5,4)],6) => 3
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [1,1,1,0,1,0,0,0,1,1,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) => 2
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [1,0,1,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 4
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => 1
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [1,1,1,1,0,0,0,1,0,0,1,0] => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => 1
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => 2
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [1,0,1,0,1,1,1,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 4
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [1,1,1,0,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [1,1,0,0,1,1,1,1,0,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [1,1,1,0,0,0,1,1,0,1,0,0] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 2
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [1,0,1,1,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 3
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [1,1,1,1,0,0,0,0,1,0,1,0] => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => 1
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [1,1,0,1,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) => 3
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [1,1,1,1,0,0,0,0,1,1,0,0] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [1,1,1,0,0,0,1,1,1,0,0,0] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,11),(2,3),(4,5),(6,7),(8,9),(10,12)] => [1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 2
[(1,12),(2,3),(4,5),(6,7),(8,10),(9,11)] => [1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 3
[(1,11),(2,3),(4,5),(6,7),(8,10),(9,12)] => [1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 3
[(1,10),(2,3),(4,5),(6,7),(8,11),(9,12)] => [1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 3
[(1,12),(2,3),(4,5),(6,8),(7,9),(10,11)] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 2
[(1,11),(2,3),(4,5),(6,8),(7,9),(10,12)] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 2
[(1,12),(2,3),(4,5),(6,8),(7,10),(9,11)] => [1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,11),(2,3),(4,5),(6,8),(7,10),(9,12)] => [1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,10),(2,3),(4,5),(6,8),(7,11),(9,12)] => [1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,12),(2,3),(4,5),(6,9),(7,10),(8,11)] => [1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,3),(4,5),(6,9),(7,10),(8,12)] => [1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,3),(4,5),(6,9),(7,11),(8,12)] => [1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,3),(4,5),(6,10),(7,11),(8,12)] => [1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,3),(4,6),(5,7),(8,9),(10,11)] => [1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 2
[(1,11),(2,3),(4,6),(5,7),(8,9),(10,12)] => [1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 2
[(1,12),(2,3),(4,6),(5,7),(8,10),(9,11)] => [1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 3
[(1,11),(2,3),(4,6),(5,7),(8,10),(9,12)] => [1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 3
[(1,10),(2,3),(4,6),(5,7),(8,11),(9,12)] => [1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 3
[(1,12),(2,3),(4,6),(5,8),(7,9),(10,11)] => [1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 2
[(1,11),(2,3),(4,6),(5,8),(7,9),(10,12)] => [1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 2
[(1,12),(2,3),(4,6),(5,8),(7,10),(9,11)] => [1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,11),(2,3),(4,6),(5,8),(7,10),(9,12)] => [1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,10),(2,3),(4,6),(5,8),(7,11),(9,12)] => [1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,12),(2,3),(4,6),(5,9),(7,10),(8,11)] => [1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,3),(4,6),(5,9),(7,10),(8,12)] => [1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,3),(4,6),(5,9),(7,11),(8,12)] => [1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,3),(4,6),(5,10),(7,11),(8,12)] => [1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,3),(4,7),(5,8),(6,9),(10,11)] => [1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2
[(1,11),(2,3),(4,7),(5,8),(6,9),(10,12)] => [1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2
[(1,12),(2,3),(4,7),(5,8),(6,10),(9,11)] => [1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 3
[(1,11),(2,3),(4,7),(5,8),(6,10),(9,12)] => [1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 3
[(1,10),(2,3),(4,7),(5,8),(6,11),(9,12)] => [1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 3
[(1,12),(2,3),(4,7),(5,9),(6,10),(8,11)] => [1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,3),(4,7),(5,9),(6,10),(8,12)] => [1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,3),(4,7),(5,9),(6,11),(8,12)] => [1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,3),(4,7),(5,10),(6,11),(8,12)] => [1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,3),(4,8),(5,9),(6,10),(7,11)] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,11),(2,3),(4,8),(5,9),(6,10),(7,12)] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,10),(2,3),(4,8),(5,9),(6,11),(7,12)] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,9),(2,3),(4,8),(5,10),(6,11),(7,12)] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,8),(2,3),(4,9),(5,10),(6,11),(7,12)] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,12),(2,4),(3,5),(6,7),(8,9),(10,11)] => [1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 2
[(1,11),(2,4),(3,5),(6,7),(8,9),(10,12)] => [1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 2
[(1,12),(2,4),(3,5),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,4),(3,5),(6,7),(8,10),(9,12)] => [1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,4),(3,5),(6,7),(8,11),(9,12)] => [1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,4),(3,5),(6,8),(7,9),(10,11)] => [1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 2
[(1,11),(2,4),(3,5),(6,8),(7,9),(10,12)] => [1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 2
[(1,12),(2,4),(3,5),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,4),(3,5),(6,8),(7,10),(9,12)] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,4),(3,5),(6,8),(7,11),(9,12)] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,4),(3,5),(6,9),(7,10),(8,11)] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,4),(3,5),(6,9),(7,10),(8,12)] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,4),(3,5),(6,9),(7,11),(8,12)] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,4),(3,5),(6,10),(7,11),(8,12)] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,4),(3,6),(5,7),(8,9),(10,11)] => [1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 2
[(1,11),(2,4),(3,6),(5,7),(8,9),(10,12)] => [1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 2
[(1,12),(2,4),(3,6),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,4),(3,6),(5,7),(8,10),(9,12)] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,4),(3,6),(5,7),(8,11),(9,12)] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,4),(3,6),(5,8),(7,9),(10,11)] => [1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 2
[(1,11),(2,4),(3,6),(5,8),(7,9),(10,12)] => [1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 2
[(1,12),(2,4),(3,6),(5,8),(7,10),(9,11)] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,4),(3,6),(5,8),(7,10),(9,12)] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,4),(3,6),(5,8),(7,11),(9,12)] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,4),(3,6),(5,9),(7,10),(8,11)] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,4),(3,6),(5,9),(7,10),(8,12)] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,4),(3,6),(5,9),(7,11),(8,12)] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,4),(3,6),(5,10),(7,11),(8,12)] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,4),(3,7),(5,8),(6,9),(10,11)] => [1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 2
[(1,11),(2,4),(3,7),(5,8),(6,9),(10,12)] => [1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 2
[(1,12),(2,4),(3,7),(5,8),(6,10),(9,11)] => [1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,4),(3,7),(5,8),(6,10),(9,12)] => [1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,4),(3,7),(5,8),(6,11),(9,12)] => [1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,4),(3,7),(5,9),(6,10),(8,11)] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,4),(3,7),(5,9),(6,10),(8,12)] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,4),(3,7),(5,9),(6,11),(8,12)] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,4),(3,7),(5,10),(6,11),(8,12)] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,4),(3,8),(5,9),(6,10),(7,11)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,11),(2,4),(3,8),(5,9),(6,10),(7,12)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,10),(2,4),(3,8),(5,9),(6,11),(7,12)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,9),(2,4),(3,8),(5,10),(6,11),(7,12)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,8),(2,4),(3,9),(5,10),(6,11),(7,12)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,12),(2,5),(3,6),(4,7),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,11),(2,5),(3,6),(4,7),(8,9),(10,12)] => [1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,12),(2,5),(3,6),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,5),(3,6),(4,7),(8,10),(9,12)] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,5),(3,6),(4,7),(8,11),(9,12)] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,5),(3,6),(4,8),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,11),(2,5),(3,6),(4,8),(7,9),(10,12)] => [1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,12),(2,5),(3,6),(4,8),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,5),(3,6),(4,8),(7,10),(9,12)] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,5),(3,6),(4,8),(7,11),(9,12)] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,5),(3,6),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,5),(3,6),(4,9),(7,10),(8,12)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,5),(3,6),(4,9),(7,11),(8,12)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,5),(3,6),(4,10),(7,11),(8,12)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,5),(3,7),(4,8),(6,9),(10,11)] => [1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,11),(2,5),(3,7),(4,8),(6,9),(10,12)] => [1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,12),(2,5),(3,7),(4,8),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,5),(3,7),(4,8),(6,10),(9,12)] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,5),(3,7),(4,8),(6,11),(9,12)] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,5),(3,7),(4,9),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,5),(3,7),(4,9),(6,10),(8,12)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,5),(3,7),(4,9),(6,11),(8,12)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,5),(3,7),(4,10),(6,11),(8,12)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,5),(3,8),(4,9),(6,10),(7,11)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,11),(2,5),(3,8),(4,9),(6,10),(7,12)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,10),(2,5),(3,8),(4,9),(6,11),(7,12)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,9),(2,5),(3,8),(4,10),(6,11),(7,12)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,8),(2,5),(3,9),(4,10),(6,11),(7,12)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,12),(2,6),(3,7),(4,8),(5,9),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,11),(2,6),(3,7),(4,8),(5,9),(10,12)] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,12),(2,6),(3,7),(4,8),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,11),(2,6),(3,7),(4,8),(5,10),(9,12)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,10),(2,6),(3,7),(4,8),(5,11),(9,12)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,12),(2,6),(3,7),(4,9),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,11),(2,6),(3,7),(4,9),(5,10),(8,12)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,10),(2,6),(3,7),(4,9),(5,11),(8,12)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,9),(2,6),(3,7),(4,10),(5,11),(8,12)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,12),(2,6),(3,8),(4,9),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,11),(2,6),(3,8),(4,9),(5,10),(7,12)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,10),(2,6),(3,8),(4,9),(5,11),(7,12)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,9),(2,6),(3,8),(4,10),(5,11),(7,12)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,8),(2,6),(3,9),(4,10),(5,11),(7,12)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,12),(2,7),(3,8),(4,9),(5,10),(6,11)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,11),(2,7),(3,8),(4,9),(5,10),(6,12)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,10),(2,7),(3,8),(4,9),(5,11),(6,12)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,9),(2,7),(3,8),(4,10),(5,11),(6,12)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,8),(2,7),(3,9),(4,10),(5,11),(6,12)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,3),(2,12),(4,5),(6,7),(8,9),(10,11)] => [1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => 2
[(1,3),(2,12),(4,5),(6,7),(8,10),(9,11)] => [1,1,0,1,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) => 3
[(1,3),(2,12),(4,5),(6,8),(7,9),(10,11)] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) => 2
[(1,3),(2,12),(4,5),(6,8),(7,10),(9,11)] => [1,1,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,3),(2,12),(4,5),(6,9),(7,10),(8,11)] => [1,1,0,1,0,1,1,1,0,0,0,0] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,3),(2,12),(4,6),(5,7),(8,9),(10,11)] => [1,1,0,1,1,0,0,1,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) => 2
[(1,3),(2,12),(4,6),(5,7),(8,10),(9,11)] => [1,1,0,1,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) => 3
[(1,3),(2,12),(4,6),(5,8),(7,9),(10,11)] => [1,1,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) => 2
[(1,3),(2,12),(4,6),(5,8),(7,10),(9,11)] => [1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => 3
[(1,3),(2,12),(4,6),(5,9),(7,10),(8,11)] => [1,1,0,1,1,0,1,1,0,0,0,0] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,3),(2,12),(4,7),(5,8),(6,9),(10,11)] => [1,1,0,1,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 2
[(1,3),(2,12),(4,7),(5,8),(6,10),(9,11)] => [1,1,0,1,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(4,5)],6) => 3
[(1,3),(2,12),(4,7),(5,9),(6,10),(8,11)] => [1,1,0,1,1,1,0,1,0,0,0,0] => ([(0,5),(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,3),(2,12),(4,8),(5,9),(6,10),(7,11)] => [1,1,0,1,1,1,1,0,0,0,0,0] => ([(1,5),(2,5),(3,5),(4,5)],6) => 5
[(1,4),(2,12),(3,5),(6,7),(8,9),(10,11)] => [1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 2
[(1,4),(2,12),(3,5),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,12),(3,5),(6,8),(7,9),(10,11)] => [1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 2
[(1,4),(2,12),(3,5),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,12),(3,5),(6,9),(7,10),(8,11)] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,12),(3,6),(5,7),(8,9),(10,11)] => [1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 2
[(1,4),(2,12),(3,6),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,12),(3,6),(5,8),(7,9),(10,11)] => [1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 2
[(1,4),(2,12),(3,6),(5,8),(7,10),(9,11)] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,12),(3,6),(5,9),(7,10),(8,11)] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,12),(3,7),(5,8),(6,9),(10,11)] => [1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 2
[(1,4),(2,12),(3,7),(5,8),(6,10),(9,11)] => [1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,12),(3,7),(5,9),(6,10),(8,11)] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,12),(3,8),(5,9),(6,10),(7,11)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,5),(2,12),(3,6),(4,7),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,12),(3,6),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,12),(3,6),(4,8),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,12),(3,6),(4,8),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,12),(3,6),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,12),(3,7),(4,8),(6,9),(10,11)] => [1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,12),(3,7),(4,8),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,12),(3,7),(4,9),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,12),(3,8),(4,9),(6,10),(7,11)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,6),(2,12),(3,7),(4,8),(5,9),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,6),(2,12),(3,7),(4,8),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,6),(2,12),(3,7),(4,9),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,6),(2,12),(3,8),(4,9),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,7),(2,12),(3,8),(4,9),(5,10),(6,11)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,4),(2,5),(3,12),(6,7),(8,9),(10,11)] => [1,1,1,0,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) => 2
[(1,4),(2,5),(3,12),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,5),(3,12),(6,8),(7,9),(10,11)] => [1,1,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) => 2
[(1,4),(2,5),(3,12),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,5),(3,12),(6,9),(7,10),(8,11)] => [1,1,1,0,0,1,1,1,0,0,0,0] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,6),(3,12),(5,7),(8,9),(10,11)] => [1,1,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) => 2
[(1,4),(2,6),(3,12),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,6),(3,12),(5,8),(7,9),(10,11)] => [1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => 2
[(1,4),(2,6),(3,12),(5,8),(7,10),(9,11)] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,6),(3,12),(5,9),(7,10),(8,11)] => [1,1,1,0,1,0,1,1,0,0,0,0] => ([(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,7),(3,12),(5,8),(6,9),(10,11)] => [1,1,1,0,1,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(4,5)],6) => 2
[(1,4),(2,7),(3,12),(5,8),(6,10),(9,11)] => [1,1,1,0,1,1,0,0,1,0,0,0] => ([(0,5),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,4),(2,7),(3,12),(5,9),(6,10),(8,11)] => [1,1,1,0,1,1,0,1,0,0,0,0] => ([(1,5),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,8),(3,12),(5,9),(6,10),(7,11)] => [1,1,1,0,1,1,1,0,0,0,0,0] => ([(2,5),(3,5),(4,5)],6) => 5
[(1,5),(2,6),(3,12),(4,7),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,6),(3,12),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,6),(3,12),(4,8),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,6),(3,12),(4,8),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,6),(3,12),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,7),(3,12),(4,8),(6,9),(10,11)] => [1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,7),(3,12),(4,8),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,7),(3,12),(4,9),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,8),(3,12),(4,9),(6,10),(7,11)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,6),(2,7),(3,12),(4,8),(5,9),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,6),(2,7),(3,12),(4,8),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,6),(2,7),(3,12),(4,9),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,6),(2,8),(3,12),(4,9),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,7),(2,8),(3,12),(4,9),(5,10),(6,11)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,5),(2,6),(3,7),(4,12),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,6),(3,7),(4,12),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,6),(3,8),(4,12),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,6),(3,8),(4,12),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => ([(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,6),(3,9),(4,12),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,7),(3,8),(4,12),(6,9),(10,11)] => [1,1,1,1,0,1,0,0,0,1,0,0] => ([(0,5),(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,5),(2,7),(3,8),(4,12),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => ([(1,5),(2,3),(2,4),(2,5)],6) => 3
[(1,5),(2,7),(3,9),(4,12),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,8),(3,9),(4,12),(6,10),(7,11)] => [1,1,1,1,0,1,1,0,0,0,0,0] => ([(3,5),(4,5)],6) => 5
[(1,6),(2,7),(3,8),(4,12),(5,9),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,6),(2,7),(3,8),(4,12),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,6),(2,7),(3,9),(4,12),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,6),(2,8),(3,9),(4,12),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,7),(2,8),(3,9),(4,12),(5,10),(6,11)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
[(1,6),(2,7),(3,8),(4,9),(5,12),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => ([(1,2),(1,3),(1,4),(1,5)],6) => 2
[(1,6),(2,7),(3,8),(4,10),(5,12),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => ([(2,3),(2,4),(2,5)],6) => 3
[(1,6),(2,7),(3,9),(4,10),(5,12),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => ([(3,4),(3,5)],6) => 4
[(1,6),(2,8),(3,9),(4,10),(5,12),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => ([(4,5)],6) => 5
[(1,7),(2,8),(3,9),(4,10),(5,12),(6,11)] => [1,1,1,1,1,1,0,0,0,0,0,0] => ([],6) => 6
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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:
1,2 3,6,6 15,30,36,24 105,210,270,240,120
$F_{2} = q$
$F_{4} = q + 2\ q^{2}$
$F_{6} = 3\ q + 6\ q^{2} + 6\ q^{3}$
$F_{8} = 15\ q + 30\ q^{2} + 36\ q^{3} + 24\ q^{4}$
$F_{10} = 105\ q + 210\ q^{2} + 270\ q^{3} + 240\ q^{4} + 120\ q^{5}$
Description
The number of minimal elements in a poset.
Map
to Dyck path
Description
The Dyck path corresponding to the opener-closer sequence of the perfect matching.
Map
Hessenberg poset
Description
The Hessenberg poset of a Dyck path.
Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.
Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.
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