Identifier
-
Mp00150:
Perfect matchings
—to Dyck path⟶
Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
St000166: Ordered trees ⟶ ℤ (values match St000094The depth of an ordered tree.)
Values
[(1,2)] => [1,0] => [[]] => 1
[(1,2),(3,4)] => [1,0,1,0] => [[],[]] => 1
[(1,3),(2,4)] => [1,1,0,0] => [[[]]] => 2
[(1,4),(2,3)] => [1,1,0,0] => [[[]]] => 2
[(1,2),(3,4),(5,6)] => [1,0,1,0,1,0] => [[],[],[]] => 1
[(1,3),(2,4),(5,6)] => [1,1,0,0,1,0] => [[[]],[]] => 2
[(1,4),(2,3),(5,6)] => [1,1,0,0,1,0] => [[[]],[]] => 2
[(1,5),(2,3),(4,6)] => [1,1,0,1,0,0] => [[[],[]]] => 2
[(1,6),(2,3),(4,5)] => [1,1,0,1,0,0] => [[[],[]]] => 2
[(1,6),(2,4),(3,5)] => [1,1,1,0,0,0] => [[[[]]]] => 3
[(1,5),(2,4),(3,6)] => [1,1,1,0,0,0] => [[[[]]]] => 3
[(1,4),(2,5),(3,6)] => [1,1,1,0,0,0] => [[[[]]]] => 3
[(1,3),(2,5),(4,6)] => [1,1,0,1,0,0] => [[[],[]]] => 2
[(1,2),(3,5),(4,6)] => [1,0,1,1,0,0] => [[],[[]]] => 2
[(1,2),(3,6),(4,5)] => [1,0,1,1,0,0] => [[],[[]]] => 2
[(1,3),(2,6),(4,5)] => [1,1,0,1,0,0] => [[[],[]]] => 2
[(1,4),(2,6),(3,5)] => [1,1,1,0,0,0] => [[[[]]]] => 3
[(1,5),(2,6),(3,4)] => [1,1,1,0,0,0] => [[[[]]]] => 3
[(1,6),(2,5),(3,4)] => [1,1,1,0,0,0] => [[[[]]]] => 3
[(1,2),(3,4),(5,6),(7,8)] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[(1,3),(2,4),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 2
[(1,4),(2,3),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 2
[(1,5),(2,3),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => 2
[(1,6),(2,3),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => 2
[(1,7),(2,3),(4,5),(6,8)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,8),(2,3),(4,5),(6,7)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,8),(2,4),(3,5),(6,7)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,7),(2,4),(3,5),(6,8)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,6),(2,4),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 3
[(1,5),(2,4),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 3
[(1,4),(2,5),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 3
[(1,3),(2,5),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => 2
[(1,2),(3,5),(4,6),(7,8)] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 2
[(1,2),(3,6),(4,5),(7,8)] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 2
[(1,3),(2,6),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => 2
[(1,4),(2,6),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 3
[(1,5),(2,6),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 3
[(1,6),(2,5),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 3
[(1,7),(2,5),(3,4),(6,8)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,8),(2,5),(3,4),(6,7)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,8),(2,6),(3,4),(5,7)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,7),(2,6),(3,4),(5,8)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,6),(2,7),(3,4),(5,8)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,5),(2,7),(3,4),(6,8)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,4),(2,7),(3,5),(6,8)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,3),(2,7),(4,5),(6,8)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,2),(3,7),(4,5),(6,8)] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 2
[(1,2),(3,8),(4,5),(6,7)] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 2
[(1,3),(2,8),(4,5),(6,7)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,4),(2,8),(3,5),(6,7)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,5),(2,8),(3,4),(6,7)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,6),(2,8),(3,4),(5,7)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,7),(2,8),(3,4),(5,6)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,8),(2,7),(3,4),(5,6)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,8),(2,7),(3,5),(4,6)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,7),(2,8),(3,5),(4,6)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,6),(2,8),(3,5),(4,7)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,5),(2,8),(3,6),(4,7)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,4),(2,8),(3,6),(5,7)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,3),(2,8),(4,6),(5,7)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,2),(3,8),(4,6),(5,7)] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 3
[(1,2),(3,7),(4,6),(5,8)] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 3
[(1,3),(2,7),(4,6),(5,8)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,4),(2,7),(3,6),(5,8)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,5),(2,7),(3,6),(4,8)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,6),(2,7),(3,5),(4,8)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,7),(2,6),(3,5),(4,8)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,8),(2,6),(3,5),(4,7)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,8),(2,5),(3,6),(4,7)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,7),(2,5),(3,6),(4,8)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,6),(2,5),(3,7),(4,8)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,5),(2,6),(3,7),(4,8)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,4),(2,6),(3,7),(5,8)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,3),(2,6),(4,7),(5,8)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,2),(3,6),(4,7),(5,8)] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 3
[(1,2),(3,5),(4,7),(6,8)] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 2
[(1,3),(2,5),(4,7),(6,8)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,4),(2,5),(3,7),(6,8)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,5),(2,4),(3,7),(6,8)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,6),(2,4),(3,7),(5,8)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,7),(2,4),(3,6),(5,8)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,8),(2,4),(3,6),(5,7)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,8),(2,3),(4,6),(5,7)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,7),(2,3),(4,6),(5,8)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,6),(2,3),(4,7),(5,8)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,5),(2,3),(4,7),(6,8)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,4),(2,3),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[(1,3),(2,4),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[(1,2),(3,4),(5,7),(6,8)] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 2
[(1,2),(3,4),(5,8),(6,7)] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 2
[(1,3),(2,4),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[(1,4),(2,3),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[(1,5),(2,3),(4,8),(6,7)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,6),(2,3),(4,8),(5,7)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,7),(2,3),(4,8),(5,6)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,8),(2,3),(4,7),(5,6)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,8),(2,4),(3,7),(5,6)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,7),(2,4),(3,8),(5,6)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,6),(2,4),(3,8),(5,7)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,5),(2,4),(3,8),(6,7)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
[(1,4),(2,5),(3,8),(6,7)] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 3
>>> Load all 1421 entries. <<<[(1,3),(2,5),(4,8),(6,7)] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 2
[(1,2),(3,5),(4,8),(6,7)] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 2
[(1,2),(3,6),(4,8),(5,7)] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 3
[(1,3),(2,6),(4,8),(5,7)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,4),(2,6),(3,8),(5,7)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,5),(2,6),(3,8),(4,7)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,6),(2,5),(3,8),(4,7)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,7),(2,5),(3,8),(4,6)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,8),(2,5),(3,7),(4,6)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,8),(2,6),(3,7),(4,5)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,7),(2,6),(3,8),(4,5)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,6),(2,7),(3,8),(4,5)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,5),(2,7),(3,8),(4,6)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,4),(2,7),(3,8),(5,6)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,3),(2,7),(4,8),(5,6)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,2),(3,7),(4,8),(5,6)] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 3
[(1,2),(3,8),(4,7),(5,6)] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 3
[(1,3),(2,8),(4,7),(5,6)] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 3
[(1,4),(2,8),(3,7),(5,6)] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 3
[(1,5),(2,8),(3,7),(4,6)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,6),(2,8),(3,7),(4,5)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,7),(2,8),(3,6),(4,5)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,8),(2,7),(3,6),(4,5)] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 2
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 2
[(1,5),(2,3),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 2
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 2
[(1,7),(2,3),(4,5),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,9),(2,3),(4,5),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,10),(2,4),(3,5),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,9),(2,4),(3,5),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,8),(2,4),(3,5),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,7),(2,4),(3,5),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[(1,5),(2,4),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 2
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 2
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 2
[(1,3),(2,6),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 2
[(1,4),(2,6),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[(1,5),(2,6),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[(1,7),(2,5),(3,4),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,9),(2,5),(3,4),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,10),(2,6),(3,4),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,9),(2,6),(3,4),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,8),(2,6),(3,4),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,7),(2,6),(3,4),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,6),(2,7),(3,4),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,5),(2,7),(3,4),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,4),(2,7),(3,5),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,3),(2,7),(4,5),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,2),(3,7),(4,5),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 2
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 2
[(1,3),(2,8),(4,5),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,4),(2,8),(3,5),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,5),(2,8),(3,4),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,6),(2,8),(3,4),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,7),(2,8),(3,4),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,9),(2,7),(3,4),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,10),(2,8),(3,4),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,8),(3,4),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,8),(2,9),(3,4),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,9),(3,4),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,6),(2,9),(3,4),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,9),(3,4),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,4),(2,9),(3,5),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,3),(2,9),(4,5),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,2),(3,9),(4,5),(6,7),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,3),(2,10),(4,5),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,4),(2,10),(3,5),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,5),(2,10),(3,4),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,6),(2,10),(3,4),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,7),(2,10),(3,4),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,8),(2,10),(3,4),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,10),(3,4),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,9),(3,5),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,10),(3,5),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,8),(2,10),(3,5),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,10),(3,5),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,10),(3,5),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,5),(2,10),(3,6),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,4),(2,10),(3,6),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,3),(2,10),(4,6),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,2),(3,10),(4,6),(5,7),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,2),(3,9),(4,6),(5,7),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,3),(2,9),(4,6),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,4),(2,9),(3,6),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,9),(3,6),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,9),(3,5),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,7),(2,9),(3,5),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,8),(3,5),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,8),(3,5),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,7),(3,5),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,9),(2,7),(3,5),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,7),(3,5),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,7),(2,8),(3,5),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,6),(2,8),(3,5),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,5),(2,8),(3,6),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,4),(2,8),(3,6),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,3),(2,8),(4,6),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,2),(3,8),(4,6),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[(1,2),(3,7),(4,6),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[(1,3),(2,7),(4,6),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,4),(2,7),(3,6),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,5),(2,7),(3,6),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,6),(2,7),(3,5),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,7),(2,6),(3,5),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,8),(2,6),(3,5),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,9),(2,6),(3,5),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,10),(2,6),(3,5),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,10),(2,5),(3,6),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,9),(2,5),(3,6),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,5),(3,6),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,7),(2,5),(3,6),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,6),(2,5),(3,7),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 2
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,5),(2,4),(3,7),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,6),(2,4),(3,7),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,7),(2,4),(3,6),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,8),(2,4),(3,6),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,9),(2,4),(3,6),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,10),(2,4),(3,6),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,10),(2,3),(4,6),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,9),(2,3),(4,6),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,8),(2,3),(4,6),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,7),(2,3),(4,6),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,6),(2,3),(4,7),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,5),(2,3),(4,7),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,4),(2,3),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 2
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 2
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 2
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 2
[(1,3),(2,4),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 2
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 2
[(1,5),(2,3),(4,8),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,6),(2,3),(4,8),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,7),(2,3),(4,8),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,9),(2,3),(4,7),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,10),(2,4),(3,7),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,9),(2,4),(3,7),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,8),(2,4),(3,7),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,7),(2,4),(3,8),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,6),(2,4),(3,8),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,5),(2,4),(3,8),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,4),(2,5),(3,8),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[(1,3),(2,5),(4,8),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 2
[(1,2),(3,5),(4,8),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 2
[(1,2),(3,6),(4,8),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[(1,3),(2,6),(4,8),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,4),(2,6),(3,8),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,5),(2,6),(3,8),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,6),(2,5),(3,8),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,7),(2,5),(3,8),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,8),(2,5),(3,7),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,9),(2,5),(3,7),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,10),(2,5),(3,7),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,10),(2,6),(3,7),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,9),(2,6),(3,7),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,6),(3,7),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,7),(2,6),(3,8),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,6),(2,7),(3,8),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,5),(2,7),(3,8),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,4),(2,7),(3,8),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,3),(2,7),(4,8),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,2),(3,7),(4,8),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[(1,3),(2,8),(4,7),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[(1,4),(2,8),(3,7),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[(1,5),(2,8),(3,7),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,6),(2,8),(3,7),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,7),(2,8),(3,6),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 4
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,10),(2,8),(3,6),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,8),(3,6),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,8),(2,9),(3,6),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,9),(3,6),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,9),(3,7),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,5),(2,9),(3,7),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,4),(2,9),(3,7),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,3),(2,9),(4,7),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,2),(3,9),(4,7),(5,6),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,3),(2,10),(4,7),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,4),(2,10),(3,7),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,10),(3,7),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,10),(3,7),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,7),(2,10),(3,6),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,10),(3,6),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,10),(3,6),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,9),(3,7),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,10),(3,7),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,10),(3,7),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,10),(3,8),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,10),(3,8),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,10),(3,8),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,10),(3,8),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,10),(4,8),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,10),(4,8),(5,6),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,9),(4,8),(5,6),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,9),(4,8),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,9),(3,8),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,9),(3,8),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,9),(3,8),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,9),(3,8),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,9),(3,7),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,8),(3,7),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,8),(3,7),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,7),(3,8),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,7),(3,8),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,7),(3,9),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,8),(3,9),(4,5),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,8),(3,9),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,8),(3,9),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,8),(3,9),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,8),(4,9),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,8),(4,9),(5,6),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,7),(4,9),(5,6),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,3),(2,7),(4,9),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,4),(2,7),(3,9),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,7),(3,9),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,7),(3,9),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,7),(2,6),(3,9),(4,5),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,6),(3,9),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,6),(3,8),(4,5),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,6),(3,8),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,5),(3,8),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,5),(3,8),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,8),(2,5),(3,9),(4,6),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,5),(3,9),(4,6),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,5),(3,9),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,5),(2,6),(3,9),(4,7),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,4),(2,6),(3,9),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,3),(2,6),(4,9),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,2),(3,6),(4,9),(5,7),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,2),(3,5),(4,9),(6,7),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,3),(2,5),(4,9),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,4),(2,5),(3,9),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,5),(2,4),(3,9),(6,7),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,6),(2,4),(3,9),(5,7),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,7),(2,4),(3,9),(5,6),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,8),(2,4),(3,9),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,4),(3,8),(5,6),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,4),(3,8),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,3),(4,8),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,9),(2,3),(4,8),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,8),(2,3),(4,9),(5,6),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,7),(2,3),(4,9),(5,6),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,6),(2,3),(4,9),(5,7),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,5),(2,3),(4,9),(6,7),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,4),(2,3),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,3),(2,4),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,2),(3,4),(5,9),(6,7),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 2
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 2
[(1,3),(2,4),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,5),(2,3),(4,10),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,6),(2,3),(4,10),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,7),(2,3),(4,10),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,8),(2,3),(4,10),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,9),(2,3),(4,10),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,10),(2,4),(3,9),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,4),(3,10),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,8),(2,4),(3,10),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,4),(3,10),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,6),(2,4),(3,10),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,4),(3,10),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,4),(2,5),(3,10),(6,7),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,3),(2,5),(4,10),(6,7),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,2),(3,5),(4,10),(6,7),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,2),(3,6),(4,10),(5,7),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,3),(2,6),(4,10),(5,7),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,4),(2,6),(3,10),(5,7),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,6),(3,10),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,5),(3,10),(4,7),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,7),(2,5),(3,10),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,5),(3,10),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,5),(3,10),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,5),(3,9),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,6),(3,9),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,6),(3,10),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,8),(2,6),(3,10),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,6),(3,10),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,7),(3,10),(4,5),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,5),(2,7),(3,10),(4,6),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,4),(2,7),(3,10),(5,6),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,3),(2,7),(4,10),(5,6),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,2),(3,7),(4,10),(5,6),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,2),(3,8),(4,10),(5,6),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,8),(4,10),(5,6),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,8),(3,10),(5,6),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,8),(3,10),(4,6),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,8),(3,10),(4,5),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,8),(3,10),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,7),(3,10),(4,5),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,7),(3,10),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,7),(3,9),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,8),(3,9),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,8),(3,10),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,9),(3,10),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,9),(3,10),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,9),(3,10),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,9),(3,10),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,9),(3,10),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,9),(4,10),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,9),(4,10),(5,6),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,10),(4,9),(5,6),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,10),(3,9),(5,6),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,10),(3,9),(4,6),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,10),(3,9),(4,5),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,10),(3,9),(4,5),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,10),(3,9),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,10),(3,8),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,9),(3,8),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,10),(3,8),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,10),(3,9),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,10),(3,9),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,10),(3,9),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,10),(3,9),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,10),(3,9),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,10),(4,9),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,10),(4,9),(5,7),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,9),(4,10),(5,7),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,9),(4,10),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,9),(3,10),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,9),(3,10),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,9),(3,10),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,9),(3,10),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,9),(3,10),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,8),(3,10),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,7),(3,9),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,7),(3,10),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,7),(3,10),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,8),(3,10),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,8),(3,10),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,8),(3,10),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,8),(3,10),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,8),(4,10),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,8),(4,10),(5,7),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,7),(4,10),(5,8),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,7),(4,10),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,7),(3,10),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,7),(3,10),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,7),(3,10),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,6),(3,10),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,6),(3,10),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,6),(3,10),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,6),(3,9),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,5),(3,9),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,5),(3,10),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,5),(3,10),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,5),(3,10),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,5),(3,10),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,6),(3,10),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,6),(3,10),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,6),(4,10),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,6),(4,10),(5,8),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,5),(4,10),(6,8),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,3),(2,5),(4,10),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,5),(3,10),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,5),(2,4),(3,10),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,6),(2,4),(3,10),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,4),(3,10),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,4),(3,10),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,4),(3,10),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,4),(3,9),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,3),(4,9),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,9),(2,3),(4,10),(5,7),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,8),(2,3),(4,10),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,7),(2,3),(4,10),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,6),(2,3),(4,10),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,5),(2,3),(4,10),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,3),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,3),(2,4),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[(1,2),(3,4),(5,9),(6,8),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[(1,3),(2,4),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,4),(2,3),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,5),(2,3),(4,9),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,6),(2,3),(4,9),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,7),(2,3),(4,9),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,8),(2,3),(4,9),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,9),(2,3),(4,8),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,10),(2,3),(4,8),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,10),(2,4),(3,8),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,4),(3,8),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,4),(3,9),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,7),(2,4),(3,9),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,6),(2,4),(3,9),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,4),(3,9),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,4),(2,5),(3,9),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,3),(2,5),(4,9),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,2),(3,5),(4,9),(6,8),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,2),(3,6),(4,9),(5,8),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,6),(4,9),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,6),(3,9),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,6),(3,9),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,5),(3,9),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,5),(3,9),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,5),(3,9),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,5),(3,8),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,5),(3,8),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,6),(3,8),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,6),(3,8),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,6),(3,9),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,6),(3,9),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,7),(3,9),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,7),(3,9),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,7),(3,9),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,7),(4,9),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,7),(4,9),(5,8),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,8),(4,9),(5,7),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,8),(4,9),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,8),(3,9),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,8),(3,9),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,8),(3,9),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,8),(3,9),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,7),(3,9),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,7),(3,8),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,7),(3,8),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,8),(3,7),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,8),(3,7),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,9),(3,7),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,9),(3,8),(4,6),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,9),(3,8),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,9),(3,8),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,9),(3,8),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,9),(4,8),(5,7),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,9),(4,8),(5,7),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,10),(4,8),(5,7),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,10),(4,8),(5,7),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,10),(3,8),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,10),(3,8),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,10),(3,8),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,10),(3,8),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,10),(3,7),(4,6),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,10),(3,7),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,9),(3,7),(4,6),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,9),(3,6),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,10),(3,6),(4,7),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,10),(3,6),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,10),(3,6),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,10),(3,7),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,10),(3,7),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,10),(3,7),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,10),(4,7),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,10),(4,7),(5,8),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,9),(4,7),(5,8),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,9),(4,7),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,9),(3,7),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,9),(3,7),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,9),(3,7),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,9),(3,6),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,9),(3,6),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,8),(3,6),(4,7),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,8),(3,6),(4,7),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,7),(3,6),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,7),(3,6),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,7),(3,6),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,8),(3,6),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,8),(3,7),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,8),(3,7),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,8),(3,7),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,8),(4,7),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,8),(4,7),(5,9),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,7),(4,8),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,7),(3,8),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,6),(3,8),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,6),(3,7),(4,9),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,6),(3,7),(4,8),(5,10)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,6),(3,7),(4,8),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,5),(3,7),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,5),(3,7),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,5),(3,7),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,5),(3,8),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,5),(3,8),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,6),(3,8),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,6),(4,8),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,3),(2,5),(4,8),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,5),(2,4),(3,8),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,6),(2,4),(3,8),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,4),(3,8),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,4),(3,7),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,4),(3,7),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,4),(3,7),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,3),(4,7),(5,8),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,9),(2,3),(4,7),(5,8),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,8),(2,3),(4,7),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,7),(2,3),(4,8),(5,9),(6,10)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,6),(2,3),(4,8),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,5),(2,3),(4,8),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,3),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 2
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,4),(2,3),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,5),(2,3),(4,7),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,6),(2,3),(4,7),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,7),(2,3),(4,6),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,8),(2,3),(4,6),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,9),(2,3),(4,6),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,10),(2,3),(4,6),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,10),(2,4),(3,6),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,4),(3,6),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,8),(2,4),(3,6),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,4),(3,6),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,6),(2,4),(3,7),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,4),(3,7),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,4),(2,5),(3,7),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,3),(2,6),(4,7),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,4),(2,6),(3,7),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,6),(3,7),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,5),(3,7),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,7),(2,5),(3,6),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,5),(3,6),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,5),(3,6),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,5),(3,6),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,6),(3,5),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,6),(3,5),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,8),(2,6),(3,5),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,6),(3,5),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,7),(3,5),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,5),(2,7),(3,6),(4,9),(8,10)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,4),(2,7),(3,6),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,3),(2,7),(4,6),(5,9),(8,10)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,2),(3,7),(4,6),(5,9),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,2),(3,8),(4,6),(5,9),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,8),(4,6),(5,9),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,8),(3,6),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,8),(3,6),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,8),(3,5),(4,9),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,8),(3,5),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,7),(3,5),(4,9),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,7),(3,5),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,7),(3,5),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,8),(3,5),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,8),(3,5),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,9),(3,5),(4,7),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,9),(3,5),(4,8),(6,10)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,9),(3,5),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,9),(3,6),(4,8),(7,10)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,9),(3,6),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,9),(4,6),(5,8),(7,10)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,9),(4,6),(5,8),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,10),(4,6),(5,8),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,10),(4,6),(5,8),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,10),(3,6),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,10),(3,6),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,10),(3,5),(4,8),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,10),(3,5),(4,8),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,10),(3,5),(4,7),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,10),(3,5),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,9),(3,5),(4,7),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,9),(3,4),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,10),(3,4),(5,7),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,10),(3,4),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,7),(2,10),(3,4),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,6),(2,10),(3,4),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,10),(3,4),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,4),(2,10),(3,5),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,3),(2,10),(4,5),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,2),(3,10),(4,5),(6,8),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,2),(3,9),(4,5),(6,8),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,3),(2,9),(4,5),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,9),(3,5),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,5),(2,9),(3,4),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,6),(2,9),(3,4),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,9),(3,4),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,9),(3,4),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,8),(3,4),(5,7),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,8),(3,4),(5,7),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,7),(3,4),(5,8),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,7),(3,4),(5,8),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,7),(3,4),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,7),(2,8),(3,4),(5,9),(6,10)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,6),(2,8),(3,4),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,8),(3,4),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,4),(2,8),(3,5),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,3),(2,8),(4,5),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,2),(3,8),(4,5),(6,9),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,2),(3,7),(4,5),(6,9),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,3),(2,7),(4,5),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,4),(2,7),(3,5),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,5),(2,7),(3,4),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,6),(2,7),(3,4),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,7),(2,6),(3,4),(5,9),(8,10)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,8),(2,6),(3,4),(5,9),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,6),(3,4),(5,8),(7,10)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,6),(3,4),(5,8),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,5),(3,4),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,9),(2,5),(3,4),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,7),(2,5),(3,4),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,6),(2,5),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,5),(2,6),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,4),(2,6),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,3),(2,6),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,2),(3,6),(4,5),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 2
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 2
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,5),(2,4),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,6),(2,4),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,7),(2,4),(3,5),(6,9),(8,10)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,8),(2,4),(3,5),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,9),(2,4),(3,5),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,10),(2,4),(3,5),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,10),(2,3),(4,5),(6,8),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,9),(2,3),(4,5),(6,8),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,8),(2,3),(4,5),(6,9),(7,10)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,7),(2,3),(4,5),(6,9),(8,10)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,6),(2,3),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,5),(2,3),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,4),(2,3),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 2
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 2
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 2
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 2
[(1,3),(2,4),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 2
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 2
[(1,5),(2,3),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,7),(2,3),(4,5),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,8),(2,3),(4,5),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,9),(2,3),(4,5),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,10),(2,4),(3,5),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,9),(2,4),(3,5),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,8),(2,4),(3,5),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,7),(2,4),(3,5),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,6),(2,4),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,5),(2,4),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,4),(2,5),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,3),(2,5),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,2),(3,5),(4,6),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 2
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 2
[(1,3),(2,6),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 2
[(1,4),(2,6),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,5),(2,6),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 3
[(1,7),(2,5),(3,4),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,8),(2,5),(3,4),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,9),(2,5),(3,4),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,10),(2,6),(3,4),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,6),(3,4),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,8),(2,6),(3,4),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,6),(3,4),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,6),(2,7),(3,4),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,7),(3,4),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,4),(2,7),(3,5),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,3),(2,7),(4,5),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,2),(3,7),(4,5),(6,10),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,2),(3,8),(4,5),(6,10),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,3),(2,8),(4,5),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,8),(3,5),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,5),(2,8),(3,4),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,6),(2,8),(3,4),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,8),(3,4),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,7),(3,4),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,7),(3,4),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,7),(3,4),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,8),(3,4),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,8),(3,4),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,9),(3,4),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,7),(2,9),(3,4),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,6),(2,9),(3,4),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,9),(3,4),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,4),(2,9),(3,5),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,3),(2,9),(4,5),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,2),(3,9),(4,5),(6,10),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,3),(2,10),(4,5),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,10),(3,5),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,5),(2,10),(3,4),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,6),(2,10),(3,4),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,10),(3,4),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,10),(3,4),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,10),(3,4),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,9),(3,5),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,10),(3,5),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,10),(3,5),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,10),(3,5),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,10),(3,5),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,10),(3,6),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,10),(3,6),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,10),(4,6),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,10),(4,6),(5,9),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,9),(4,6),(5,10),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,9),(4,6),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,9),(3,6),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,9),(3,6),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,9),(3,5),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,9),(3,5),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,9),(3,5),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,8),(3,5),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,8),(3,5),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,7),(3,5),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,7),(3,5),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,8),(3,5),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,8),(3,5),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,8),(3,6),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,8),(3,6),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,8),(4,6),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,8),(4,6),(5,10),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,7),(4,6),(5,10),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,3),(2,7),(4,6),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,4),(2,7),(3,6),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,5),(2,7),(3,6),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,7),(3,5),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,7),(2,6),(3,5),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,8),(2,6),(3,5),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,6),(3,5),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,6),(3,5),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,10),(2,5),(3,6),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,9),(2,5),(3,6),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,8),(2,5),(3,6),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,5),(3,6),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,6),(2,5),(3,7),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,5),(2,6),(3,7),(4,10),(8,9)] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 4
[(1,4),(2,6),(3,7),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,3),(2,6),(4,7),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,2),(3,6),(4,7),(5,10),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[(1,2),(3,5),(4,7),(6,10),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 2
[(1,3),(2,5),(4,7),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,4),(2,5),(3,7),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,5),(2,4),(3,7),(6,10),(8,9)] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[(1,6),(2,4),(3,7),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,7),(2,4),(3,6),(5,10),(8,9)] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 3
[(1,8),(2,4),(3,6),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,9),(2,4),(3,6),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,4),(3,6),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,10),(2,3),(4,6),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,9),(2,3),(4,6),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,8),(2,3),(4,6),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,7),(2,3),(4,6),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,6),(2,3),(4,7),(5,10),(8,9)] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[(1,5),(2,3),(4,7),(6,10),(8,9)] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 2
[(1,4),(2,3),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,3),(2,4),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 2
[(1,2),(3,4),(5,7),(6,10),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 2
[(1,2),(3,4),(5,8),(6,10),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[(1,3),(2,4),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,4),(2,3),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,5),(2,3),(4,8),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,6),(2,3),(4,8),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,7),(2,3),(4,8),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,8),(2,3),(4,7),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,9),(2,3),(4,7),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,10),(2,3),(4,7),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,10),(2,4),(3,7),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,4),(3,7),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,4),(3,7),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,7),(2,4),(3,8),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,6),(2,4),(3,8),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,4),(3,8),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,4),(2,5),(3,8),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,3),(2,5),(4,8),(6,10),(7,9)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,2),(3,5),(4,8),(6,10),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,2),(3,6),(4,8),(5,10),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,6),(4,8),(5,10),(7,9)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,6),(3,8),(5,10),(7,9)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,6),(3,8),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,5),(3,8),(4,10),(7,9)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,5),(3,8),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,5),(3,7),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,5),(3,7),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,5),(3,7),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,6),(3,7),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,6),(3,7),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,6),(3,7),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,6),(3,8),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,7),(3,8),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,7),(3,8),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,7),(3,8),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,7),(4,8),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,7),(4,8),(5,10),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,8),(4,7),(5,10),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,8),(4,7),(5,10),(6,9)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,8),(3,7),(5,10),(6,9)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,8),(3,7),(4,10),(6,9)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,8),(3,7),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,8),(3,6),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,7),(3,6),(4,10),(5,9)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,7),(3,6),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,7),(3,6),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,8),(3,6),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,8),(3,6),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,9),(3,6),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,9),(3,6),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,9),(3,7),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,9),(3,7),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,9),(3,7),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,9),(4,7),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,9),(4,7),(5,10),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,10),(4,7),(5,9),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,10),(4,7),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,10),(3,7),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,10),(3,7),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,10),(3,7),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,10),(3,6),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,10),(3,6),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,10),(3,6),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,9),(3,6),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,9),(3,7),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,10),(3,7),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,10),(3,7),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,10),(3,8),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,10),(3,8),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,10),(3,8),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,10),(3,8),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,10),(4,8),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,10),(4,8),(5,9),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,9),(4,8),(5,10),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,9),(4,8),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,9),(3,8),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,9),(3,8),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,9),(3,8),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,9),(3,8),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,9),(3,7),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,8),(3,7),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,8),(3,7),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,7),(3,8),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,7),(3,8),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,7),(3,9),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,8),(3,9),(4,10),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,8),(3,9),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,8),(3,9),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,8),(3,9),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,8),(4,9),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,8),(4,9),(5,10),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,7),(4,9),(5,10),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,7),(4,9),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,7),(3,9),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,7),(3,9),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,7),(3,9),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,6),(3,9),(4,10),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,6),(3,9),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,6),(3,8),(4,10),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,6),(3,8),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,5),(3,8),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,5),(3,8),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,5),(3,9),(4,10),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,7),(2,5),(3,9),(4,10),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,5),(3,9),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,5),(2,6),(3,9),(4,10),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,4),(2,6),(3,9),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,3),(2,6),(4,9),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,2),(3,6),(4,9),(5,10),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,2),(3,5),(4,9),(6,10),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,3),(2,5),(4,9),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,5),(3,9),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,5),(2,4),(3,9),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,6),(2,4),(3,9),(5,10),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,7),(2,4),(3,9),(5,10),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,4),(3,9),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,4),(3,8),(5,10),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,4),(3,8),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,10),(2,3),(4,8),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,9),(2,3),(4,8),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,8),(2,3),(4,9),(5,10),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,7),(2,3),(4,9),(5,10),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,6),(2,3),(4,9),(5,10),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,5),(2,3),(4,9),(6,10),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,4),(2,3),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,3),(2,4),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,2),(3,4),(5,9),(6,10),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[(1,3),(2,4),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 3
[(1,5),(2,3),(4,10),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,6),(2,3),(4,10),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,7),(2,3),(4,10),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,8),(2,3),(4,10),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,9),(2,3),(4,10),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,10),(2,4),(3,9),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,9),(2,4),(3,10),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,8),(2,4),(3,10),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,7),(2,4),(3,10),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,6),(2,4),(3,10),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,4),(3,10),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,4),(2,5),(3,10),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 3
[(1,3),(2,5),(4,10),(6,9),(7,8)] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[(1,2),(3,5),(4,10),(6,9),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[(1,2),(3,6),(4,10),(5,9),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[(1,3),(2,6),(4,10),(5,9),(7,8)] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 3
[(1,4),(2,6),(3,10),(5,9),(7,8)] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 3
[(1,5),(2,6),(3,10),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,6),(2,5),(3,10),(4,9),(7,8)] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 4
[(1,7),(2,5),(3,10),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,8),(2,5),(3,10),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,9),(2,5),(3,10),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,5),(3,9),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,10),(2,6),(3,9),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,6),(3,10),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,6),(3,10),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,6),(3,10),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,7),(3,10),(4,9),(5,8)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,7),(3,10),(4,9),(6,8)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,7),(3,10),(5,9),(6,8)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,7),(4,10),(5,9),(6,8)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,7),(4,10),(5,9),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,8),(4,10),(5,9),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,8),(4,10),(5,9),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,8),(3,10),(5,9),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,8),(3,10),(4,9),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,8),(3,10),(4,9),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,8),(3,10),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,7),(3,10),(4,9),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,7),(3,10),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,7),(3,9),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,8),(3,9),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,8),(3,10),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,9),(3,10),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,9),(3,10),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,6),(2,9),(3,10),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,5),(2,9),(3,10),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,4),(2,9),(3,10),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,3),(2,9),(4,10),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,2),(3,9),(4,10),(5,8),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 4
[(1,3),(2,10),(4,9),(5,8),(6,7)] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 4
[(1,4),(2,10),(3,9),(5,8),(6,7)] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => 4
[(1,5),(2,10),(3,9),(4,8),(6,7)] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 4
[(1,6),(2,10),(3,9),(4,8),(5,7)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,7),(2,10),(3,9),(4,8),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,8),(2,10),(3,9),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 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
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 4
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[],[[[]]],[]]] => 4
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => 4
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => 4
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => 4
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 2
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => 4
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => 4
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 2
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[[[],[[]]],[]]] => 4
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 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] => [[[[],[[]]]],[]] => 4
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 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] => [[[[[],[],[]]]]] => 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] => [[],[[],[],[]],[]] => 2
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[]]] => 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] => [[],[[],[],[],[]]] => 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] => [[[],[],[],[]],[]] => 2
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[[],[]]]]] => 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] => [[],[],[[],[]],[]] => 2
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[[],[[[],[]]]]] => 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] => [[],[[[[],[]]]]] => 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] => [[[]],[[],[]],[]] => 2
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[],[],[]]] => 3
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 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] => [[[[]],[],[]],[]] => 3
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[[]],[[],[],[]]] => 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] => [[[[[],[]],[]]]] => 4
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[],[[],[]],[],[]] => 2
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[[]]]] => 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] => [[],[[],[],[[]]]] => 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] => [[[],[],[]],[],[]] => 2
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[[[[],[]]],[]]] => 4
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[],[[],[]],[[]]] => 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] => [[[[[],[]]]],[]] => 4
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[[],[],[]],[[]]] => 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] => [[[[]],[],[[]]]] => 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] => [[],[],[[],[[]]]] => 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] => [[[[]],[]],[],[]] => 3
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => 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] => [[[[]],[]],[[]]] => 3
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 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] => [[],[[[],[]]],[]] => 3
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [1,1,0,1,1,0,1,0,0,1,0,0] => [[[],[[],[]],[]]] => 3
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 3
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 3
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[]]]] => 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] => [[],[],[],[],[],[]] => 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] => [[[],[[],[],[]]]] => 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] => [[],[[[],[],[]]]] => 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] => [[[]],[],[],[],[]] => 2
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[]],[]]] => 3
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 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] => [[[[],[],[]]],[]] => 3
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 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] => [[[[[],[[]]]]]] => 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] => [[],[[],[[]]],[]] => 3
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[[]],[]]] => 3
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 3
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 3
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [1,1,1,0,1,1,1,0,0,0,0,0] => [[[[],[[[]]]]]] => 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] => [[],[],[[[]]],[]] => 3
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => 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] => [[],[[[[[]]]]]] => 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] => [[[]],[[[]]],[]] => 3
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[[[]],[[]],[]]] => 3
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[[[]],[]]] => 3
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]]],[]] => 3
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => 3
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 4
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 2
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[[],[]]]] => 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] => [[],[[],[[],[]]]] => 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] => [[[],[]],[],[],[]] => 2
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => 4
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 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] => [[[[[]],[]]],[]] => 4
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => 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] => [[[[]],[[],[]]]] => 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] => [[],[],[[[],[]]]] => 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] => [[[[]]],[],[],[]] => 3
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => 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] => [[[[]]],[],[[]]] => 3
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[],[[[]],[]],[]] => 3
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[[],[[]],[],[]]] => 3
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 3
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 3
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [1,1,1,0,1,0,1,1,0,0,0,0] => [[[[],[],[[]]]]] => 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] => [[],[],[],[[]],[]] => 2
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [1,1,0,1,1,0,1,1,0,0,0,0] => [[[],[[],[[]]]]] => 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] => [[],[[[],[[]]]]] => 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] => [[[]],[],[[]],[]] => 2
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[[[],[]],[],[]]] => 3
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[[],[]]] => 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] => [[[[],[]],[]],[]] => 3
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 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] => [[[[[[]]],[]]]] => 5
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 3
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[[],[[]],[[]]]] => 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] => [[],[[[]],[[]]]] => 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] => [[[],[[]]],[],[]] => 3
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 5
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => 3
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 5
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => 3
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[[[],[]],[[]]]] => 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] => [[],[],[],[[[]]]] => 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] => [[[[],[]]],[],[]] => 3
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 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] => [[[[],[]]],[[]]] => 3
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]]]]] => 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] => [[],[[]],[[]],[]] => 2
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [1,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[[[]]]]] => 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] => [[],[[],[[[]]]]] => 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] => [[[],[]],[[]],[]] => 2
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => 4
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 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] => [[[[[]]],[]],[]] => 4
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[[],[]],[[],[]]] => 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] => [[[[]],[[[]]]]] => 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] => [[],[],[[[[]]]]] => 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] => [[[[]]],[[]],[]] => 3
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => 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] => [[[[]]],[[],[]]] => 3
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 4
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => 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] => [[[[[]]]],[],[]] => 4
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[[],[]],[[[]]]] => 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] => [[[[[]]]],[[]]] => 4
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[[]]],[[[]]]] => 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
[(1,11),(2,3),(4,5),(6,7),(8,9),(10,12)] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[]]] => 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] => [[[],[],[],[[]]]] => 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] => [[[],[],[],[[]]]] => 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] => [[[],[],[],[[]]]] => 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] => [[[],[],[[]],[]]] => 3
[(1,11),(2,3),(4,5),(6,8),(7,9),(10,12)] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[[]],[]]] => 3
[(1,12),(2,3),(4,5),(6,8),(7,10),(9,11)] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[[],[]]]] => 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] => [[[],[],[[],[]]]] => 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] => [[[],[],[[],[]]]] => 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] => [[[],[],[[[]]]]] => 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] => [[[],[],[[[]]]]] => 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] => [[[],[],[[[]]]]] => 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] => [[[],[],[[[]]]]] => 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] => [[[],[[]],[],[]]] => 3
[(1,11),(2,3),(4,6),(5,7),(8,9),(10,12)] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[[],[[]],[],[]]] => 3
[(1,12),(2,3),(4,6),(5,7),(8,10),(9,11)] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[[],[[]],[[]]]] => 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] => [[[],[[]],[[]]]] => 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] => [[[],[[]],[[]]]] => 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] => [[[],[[],[]],[]]] => 3
[(1,11),(2,3),(4,6),(5,8),(7,9),(10,12)] => [1,1,0,1,1,0,1,0,0,1,0,0] => [[[],[[],[]],[]]] => 3
[(1,12),(2,3),(4,6),(5,8),(7,10),(9,11)] => [1,1,0,1,1,0,1,0,1,0,0,0] => [[[],[[],[],[]]]] => 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] => [[[],[[],[],[]]]] => 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] => [[[],[[],[],[]]]] => 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] => [[[],[[],[[]]]]] => 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] => [[[],[[],[[]]]]] => 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] => [[[],[[],[[]]]]] => 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] => [[[],[[],[[]]]]] => 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] => [[[],[[[]]],[]]] => 4
[(1,11),(2,3),(4,7),(5,8),(6,9),(10,12)] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[],[[[]]],[]]] => 4
[(1,12),(2,3),(4,7),(5,8),(6,10),(9,11)] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => 4
[(1,11),(2,3),(4,7),(5,8),(6,10),(9,12)] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => 4
[(1,10),(2,3),(4,7),(5,8),(6,11),(9,12)] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => 4
[(1,12),(2,3),(4,7),(5,9),(6,10),(8,11)] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[[],[[[],[]]]]] => 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] => [[[],[[[],[]]]]] => 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] => [[[],[[[],[]]]]] => 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] => [[[],[[[],[]]]]] => 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] => [[[],[[[[]]]]]] => 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] => [[[],[[[[]]]]]] => 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] => [[[],[[[[]]]]]] => 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] => [[[],[[[[]]]]]] => 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] => [[[],[[[[]]]]]] => 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] => [[[[]],[],[],[]]] => 3
[(1,11),(2,4),(3,5),(6,7),(8,9),(10,12)] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[],[],[]]] => 3
[(1,12),(2,4),(3,5),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[[[]],[],[[]]]] => 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] => [[[[]],[],[[]]]] => 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] => [[[[]],[],[[]]]] => 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] => [[[[]],[[]],[]]] => 3
[(1,11),(2,4),(3,5),(6,8),(7,9),(10,12)] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[[[]],[[]],[]]] => 3
[(1,12),(2,4),(3,5),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[[[]],[[],[]]]] => 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] => [[[[]],[[],[]]]] => 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] => [[[[]],[[],[]]]] => 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] => [[[[]],[[[]]]]] => 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] => [[[[]],[[[]]]]] => 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] => [[[[]],[[[]]]]] => 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] => [[[[]],[[[]]]]] => 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] => [[[[],[]],[],[]]] => 3
[(1,11),(2,4),(3,6),(5,7),(8,9),(10,12)] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[[[],[]],[],[]]] => 3
[(1,12),(2,4),(3,6),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[[[],[]],[[]]]] => 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] => [[[[],[]],[[]]]] => 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] => [[[[],[]],[[]]]] => 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] => [[[[],[],[]],[]]] => 3
[(1,11),(2,4),(3,6),(5,8),(7,9),(10,12)] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[]],[]]] => 3
[(1,12),(2,4),(3,6),(5,8),(7,10),(9,11)] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[]]]] => 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] => [[[[],[],[],[]]]] => 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] => [[[[],[],[],[]]]] => 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] => [[[[],[],[[]]]]] => 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] => [[[[],[],[[]]]]] => 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] => [[[[],[],[[]]]]] => 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] => [[[[],[],[[]]]]] => 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] => [[[[],[[]]],[]]] => 4
[(1,11),(2,4),(3,7),(5,8),(6,9),(10,12)] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[[[],[[]]],[]]] => 4
[(1,12),(2,4),(3,7),(5,8),(6,10),(9,11)] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => 4
[(1,11),(2,4),(3,7),(5,8),(6,10),(9,12)] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => 4
[(1,10),(2,4),(3,7),(5,8),(6,11),(9,12)] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => 4
[(1,12),(2,4),(3,7),(5,9),(6,10),(8,11)] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[[],[]]]]] => 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] => [[[[],[[],[]]]]] => 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] => [[[[],[[],[]]]]] => 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] => [[[[],[[],[]]]]] => 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] => [[[[],[[[]]]]]] => 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] => [[[[],[[[]]]]]] => 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] => [[[[],[[[]]]]]] => 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] => [[[[],[[[]]]]]] => 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] => [[[[],[[[]]]]]] => 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] => [[[[[]]],[],[]]] => 4
[(1,11),(2,5),(3,6),(4,7),(8,9),(10,12)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => 4
[(1,12),(2,5),(3,6),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 4
[(1,11),(2,5),(3,6),(4,7),(8,10),(9,12)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 4
[(1,10),(2,5),(3,6),(4,7),(8,11),(9,12)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 4
[(1,12),(2,5),(3,6),(4,8),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => 4
[(1,11),(2,5),(3,6),(4,8),(7,9),(10,12)] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => 4
[(1,12),(2,5),(3,6),(4,8),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 4
[(1,11),(2,5),(3,6),(4,8),(7,10),(9,12)] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 4
[(1,10),(2,5),(3,6),(4,8),(7,11),(9,12)] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 4
[(1,12),(2,5),(3,6),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]]]]] => 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] => [[[[[]],[[]]]]] => 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] => [[[[[]],[[]]]]] => 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] => [[[[[]],[[]]]]] => 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] => [[[[[],[]]],[]]] => 4
[(1,11),(2,5),(3,7),(4,8),(6,9),(10,12)] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[[[[],[]]],[]]] => 4
[(1,12),(2,5),(3,7),(4,8),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => 4
[(1,11),(2,5),(3,7),(4,8),(6,10),(9,12)] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => 4
[(1,10),(2,5),(3,7),(4,8),(6,11),(9,12)] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => 4
[(1,12),(2,5),(3,7),(4,9),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[],[],[]]]]] => 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] => [[[[[],[],[]]]]] => 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] => [[[[[],[],[]]]]] => 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] => [[[[[],[],[]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[[]]]],[]]] => 5
[(1,11),(2,6),(3,7),(4,8),(5,9),(10,12)] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 5
[(1,12),(2,6),(3,7),(4,8),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 5
[(1,11),(2,6),(3,7),(4,8),(5,10),(9,12)] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 5
[(1,10),(2,6),(3,7),(4,8),(5,11),(9,12)] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 5
[(1,12),(2,6),(3,7),(4,9),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,11),(2,6),(3,7),(4,9),(5,10),(8,12)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,10),(2,6),(3,7),(4,9),(5,11),(8,12)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,9),(2,6),(3,7),(4,10),(5,11),(8,12)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,12),(2,6),(3,8),(4,9),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 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] => [[[[[[],[]]]]]] => 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] => [[[[[[],[]]]]]] => 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] => [[[[[[],[]]]]]] => 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] => [[[[[[],[]]]]]] => 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
[(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
[(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
[(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
[(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
[(1,3),(2,12),(4,5),(6,7),(8,9),(10,11)] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[]]] => 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] => [[[],[],[],[[]]]] => 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] => [[[],[],[[]],[]]] => 3
[(1,3),(2,12),(4,5),(6,8),(7,10),(9,11)] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[[],[]]]] => 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] => [[[],[],[[[]]]]] => 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] => [[[],[[]],[],[]]] => 3
[(1,3),(2,12),(4,6),(5,7),(8,10),(9,11)] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[[],[[]],[[]]]] => 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] => [[[],[[],[]],[]]] => 3
[(1,3),(2,12),(4,6),(5,8),(7,10),(9,11)] => [1,1,0,1,1,0,1,0,1,0,0,0] => [[[],[[],[],[]]]] => 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] => [[[],[[],[[]]]]] => 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] => [[[],[[[]]],[]]] => 4
[(1,3),(2,12),(4,7),(5,8),(6,10),(9,11)] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => 4
[(1,3),(2,12),(4,7),(5,9),(6,10),(8,11)] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[[],[[[],[]]]]] => 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] => [[[],[[[[]]]]]] => 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] => [[[[]],[],[],[]]] => 3
[(1,4),(2,12),(3,5),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[[[]],[],[[]]]] => 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] => [[[[]],[[]],[]]] => 3
[(1,4),(2,12),(3,5),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[[[]],[[],[]]]] => 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] => [[[[]],[[[]]]]] => 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] => [[[[],[]],[],[]]] => 3
[(1,4),(2,12),(3,6),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[[[],[]],[[]]]] => 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] => [[[[],[],[]],[]]] => 3
[(1,4),(2,12),(3,6),(5,8),(7,10),(9,11)] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[]]]] => 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] => [[[[],[],[[]]]]] => 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] => [[[[],[[]]],[]]] => 4
[(1,4),(2,12),(3,7),(5,8),(6,10),(9,11)] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => 4
[(1,4),(2,12),(3,7),(5,9),(6,10),(8,11)] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[[],[]]]]] => 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] => [[[[],[[[]]]]]] => 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] => [[[[[]]],[],[]]] => 4
[(1,5),(2,12),(3,6),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 4
[(1,5),(2,12),(3,6),(4,8),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => 4
[(1,5),(2,12),(3,6),(4,8),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 4
[(1,5),(2,12),(3,6),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]]]]] => 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] => [[[[[],[]]],[]]] => 4
[(1,5),(2,12),(3,7),(4,8),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => 4
[(1,5),(2,12),(3,7),(4,9),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[],[],[]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[[]]]],[]]] => 5
[(1,6),(2,12),(3,7),(4,8),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 5
[(1,6),(2,12),(3,7),(4,9),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,6),(2,12),(3,8),(4,9),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 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
[(1,4),(2,5),(3,12),(6,7),(8,9),(10,11)] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[],[],[]]] => 3
[(1,4),(2,5),(3,12),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[[[]],[],[[]]]] => 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] => [[[[]],[[]],[]]] => 3
[(1,4),(2,5),(3,12),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[[[]],[[],[]]]] => 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] => [[[[]],[[[]]]]] => 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] => [[[[],[]],[],[]]] => 3
[(1,4),(2,6),(3,12),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[[[],[]],[[]]]] => 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] => [[[[],[],[]],[]]] => 3
[(1,4),(2,6),(3,12),(5,8),(7,10),(9,11)] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[]]]] => 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] => [[[[],[],[[]]]]] => 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] => [[[[],[[]]],[]]] => 4
[(1,4),(2,7),(3,12),(5,8),(6,10),(9,11)] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => 4
[(1,4),(2,7),(3,12),(5,9),(6,10),(8,11)] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[[],[]]]]] => 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] => [[[[],[[[]]]]]] => 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] => [[[[[]]],[],[]]] => 4
[(1,5),(2,6),(3,12),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 4
[(1,5),(2,6),(3,12),(4,8),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => 4
[(1,5),(2,6),(3,12),(4,8),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 4
[(1,5),(2,6),(3,12),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]]]]] => 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] => [[[[[],[]]],[]]] => 4
[(1,5),(2,7),(3,12),(4,8),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => 4
[(1,5),(2,7),(3,12),(4,9),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[],[],[]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[[]]]],[]]] => 5
[(1,6),(2,7),(3,12),(4,8),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 5
[(1,6),(2,7),(3,12),(4,9),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,6),(2,8),(3,12),(4,9),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 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
[(1,5),(2,6),(3,7),(4,12),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => 4
[(1,5),(2,6),(3,7),(4,12),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 4
[(1,5),(2,6),(3,8),(4,12),(7,9),(10,11)] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => 4
[(1,5),(2,6),(3,8),(4,12),(7,10),(9,11)] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 4
[(1,5),(2,6),(3,9),(4,12),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]]]]] => 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] => [[[[[],[]]],[]]] => 4
[(1,5),(2,7),(3,8),(4,12),(6,10),(9,11)] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => 4
[(1,5),(2,7),(3,9),(4,12),(6,10),(8,11)] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[],[],[]]]]] => 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] => [[[[[],[[]]]]]] => 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] => [[[[[[]]]],[]]] => 5
[(1,6),(2,7),(3,8),(4,12),(5,10),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 5
[(1,6),(2,7),(3,9),(4,12),(5,10),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,6),(2,8),(3,9),(4,12),(5,10),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 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
[(1,6),(2,7),(3,8),(4,9),(5,12),(10,11)] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 5
[(1,6),(2,7),(3,8),(4,10),(5,12),(9,11)] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 5
[(1,6),(2,7),(3,9),(4,10),(5,12),(8,11)] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 5
[(1,6),(2,8),(3,9),(4,10),(5,12),(7,11)] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 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
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,2 1,8,6 1,26,54,24 1,80,360,384,120
$F_{2} = q$
$F_{4} = q + 2\ q^{2}$
$F_{6} = q + 8\ q^{2} + 6\ q^{3}$
$F_{8} = q + 26\ q^{2} + 54\ q^{3} + 24\ q^{4}$
$F_{10} = q + 80\ q^{2} + 360\ q^{3} + 384\ q^{4} + 120\ q^{5}$
Description
The depth minus 1 of an ordered tree.
The ordered trees of size $n$ are bijection with the Dyck paths of size $n-1$, and this statistic then corresponds to St000013The height of a Dyck path..
The ordered trees of size $n$ are bijection with the Dyck paths of size $n-1$, and this statistic then corresponds to St000013The height of a Dyck path..
Map
to Dyck path
Description
The Dyck path corresponding to the opener-closer sequence of the perfect matching.
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
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