Identifier
-
Mp00046:
Ordered trees
—to graph⟶
Graphs
St000313: Graphs ⟶ ℤ
Values
[] => ([],1) => 0
[[]] => ([(0,1)],2) => 0
[[],[]] => ([(0,2),(1,2)],3) => 1
[[[]]] => ([(0,2),(1,2)],3) => 1
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 0
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 2
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => 2
[[[],[]]] => ([(0,3),(1,3),(2,3)],4) => 0
[[[[]]]] => ([(0,3),(1,2),(2,3)],4) => 2
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
[[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 3
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
[[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 0
[[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 4
[[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[],[[],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[],[[[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[],[],[[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[]],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[],[[],[[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[],[[[[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[],[[],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[[],[[[],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
>>> Load all 663 entries. <<<[[],[[[[]]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[],[[[],[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[],[[[[]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[],[[[[],[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[],[[[[[]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[]],[],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[]],[[[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[]],[[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[]],[[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[]],[[[],[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[]],[[[[]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[]]],[],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[]]],[[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[[],[]],[[[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[[]]],[[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[[]]],[[[]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[[[],[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[[],[[]]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[]],[]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[[[[]]]],[],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[],[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[]],[]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[],[]]],[[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[[[]]]],[[]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[],[[],[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[],[[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[[[[],[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[[]]],[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[[],[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[[]],[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[[],[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[[[[]]]]],[]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
[[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[],[[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[[],[],[[[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[[]],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[],[[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[[],[[[]]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[[],[[],[[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[],[[[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[[],[[[[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[]],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[[]],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[[]],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[]],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[],[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[[[[]]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[[],[]],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[[]]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 0
[[[[],[[]]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[[]],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[[[[[]]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[],[],[[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[[],[[]],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[],[[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[[]],[],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 2
[[[[[]],[[]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[[[]]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 2
[[[[[],[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[[[]],[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[[[[[[],[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[[[[[[[]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 5
[[],[],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 0
[[],[],[],[],[[[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[],[],[],[[[]]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[],[],[],[[[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[],[],[[[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[],[],[[[],[]]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[],[],[[[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[],[],[[[[[]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[],[[[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[],[[[]]],[[[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[],[[[],[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[],[[[],[],[]]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[],[[[[[]]]]],[]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[],[[[],[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[],[[[],[[[]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[],[[[[[]]],[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[],[[[[[],[]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[]],[[],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[]],[[],[[[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[]],[[[[]]],[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[]],[[[[],[]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[]]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[[]]],[],[[[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[]]],[[[]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[],[]],[[],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[],[]],[[[[]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[]]],[[[],[]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[],[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[],[],[]],[[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[[],[]]],[[[]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[[]]]],[[],[]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[],[],[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[[[[]]]]],[],[]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[],[],[],[]],[[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[],[[[]]]],[[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[[]]],[]],[[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[[],[]]]],[[]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[],[],[],[]]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[[],[[[]]]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[[[]]],[]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[[[],[]]]]],[]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[],[],[],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 0
[[[],[],[],[[[]]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[],[],[[[]]],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[],[],[[[],[]]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[],[[[]]],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[],[[[],[]]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[],[[[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[],[[[[[]]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[[]]],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[[[]]],[[[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[[],[]]],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[[[],[],[]]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 1
[[[[[[[]]]]],[]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[[[[],[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 2
[[[[[],[[[]]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[[[[]]],[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 4
[[[[[[[],[]]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 4
[[],[],[],[[[[[]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[],[],[[[]]],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[],[],[[[[[]]]]],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[],[],[[],[[],[[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[],[[],[[[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[],[[],[[[],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[],[[[]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[],[],[[[],[]],[[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[],[],[[[],[[]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[],[[[[]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[],[[[[],[]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[],[[[],[[],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[],[[[],[[[]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[],[[[[],[]],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[],[[[[[]]],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[],[[[[[],[]]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[],[[]],[[],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[]],[[[],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[]]],[],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[],[[[]]],[[[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[],[[],[]],[[],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[],[]],[[[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[],[]],[[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[[[]]],[[[],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[[],[[]]],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[]],[]],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[],[]]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[[[],[]]],[[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[[[[[]]]]],[],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[],[[],[[],[]]],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[],[]],[]],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[],[[],[[]]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[],[[[]],[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[],[[[],[]]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[[[]],[[],[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[],[[[],[]],[[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[],[[[],[[]]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[[]],[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[[],[]]],[]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[[[],[[],[]]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[[[],[[[]]]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[[[[],[]],[]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[],[[[[[]]],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[[[[[],[]]]]],[]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[],[[],[[],[[],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[],[[[],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[],[]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[],[[[],[[],[]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[[],[]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[],[[[],[],[[[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[],[[[],[[[]]],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[],[[[],[[[],[]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[[[[[]]],[],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[],[[[[[],[]]],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[],[[[[[],[],[]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[],[[[[[[[]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[[]],[],[[],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[]],[],[[[],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[]],[[],[]],[[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[]],[[],[[],[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[]],[[[],[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[]],[[],[],[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[]],[[],[[[]]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[]],[[],[[[],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[]],[[[[]]],[],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[]],[[[[],[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[]],[[[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[]],[[[[[[]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[[[]]],[],[],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[]]],[],[[[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[],[]],[],[[],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[]],[],[[[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[]],[],[[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[]]],[],[[[],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[]],[[]],[[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[[]]],[[[]]],[],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[],[]],[[],[]],[[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[],[]],[[],[[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[]],[[[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[]],[[[],[]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[]]],[[[],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[]],[[],[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[],[]],[[],[[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[]],[[[],[]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[],[]],[[[[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[]],[[[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[[[]]],[[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[]]],[[[[[]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[[],[[]]],[],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[]],[]],[],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[]]],[],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[],[]]],[],[[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[[]]],[[],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[]],[]],[[],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[]]],[[],[]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[],[]]],[[[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[],[]],[[[[]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[],[]]],[[[],[]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[[[[]]]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[[]]]],[[[[]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[[[[[]]]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[],[[],[]]],[],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[]],[]],[],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[],[]]],[[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[]],[]],[[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[],[]]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[],[[[]]]],[[],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[],[]],[]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[]]],[]],[[],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[],[],[]]],[[[]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[[],[]]]],[[],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[[[[[]]]]],[[[]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[[],[[],[[]]]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[[]],[]]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[[],[]]]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[]],[[],[]]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[[],[]],[[]]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[[],[[]]],[]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[]],[]],[]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[],[]]],[]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[],[[],[]]]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[],[[[]]]]],[],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[],[]],[]]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[[]]],[]]],[],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[],[]]]]],[],[]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[[],[],[[[]]]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[],[[[]]],[]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[],[[[],[]]]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[]]],[],[]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[[],[]]],[]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[],[],[]]]],[[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[[[[]]]]]],[[]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[[],[[],[[],[]]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[[],[]],[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[]],[[],[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[[],[[],[]]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[],[]],[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[],[[[]]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[],[[[]]],[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[],[[[],[]]]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[]]],[],[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[[[],[]]],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[],[],[]]]]],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[[[[[]]]]]]],[]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[[],[],[[[[[]]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[],[[[]]],[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[],[[[[[]]]]],[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[],[[],[[],[[]]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[],[[[]],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[],[[[],[]]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[],[[[]],[[],[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[],[[[],[]],[[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[],[[[],[[]]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[[[]],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[],[[[[],[]]],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[],[[[],[[],[]]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[],[[[],[[[]]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[[[[],[]],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[],[[[[[]]],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[],[[[[[],[]]]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[[[]],[[],[[],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[]],[[[],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[]]],[],[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[[]]],[[[]]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[],[]],[[],[[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[]],[[[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[]],[[[],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[]]],[[[],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[],[[]]],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[]],[]],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[],[]]],[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[],[]]],[[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[[]]]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[],[[],[]]],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[],[]],[]],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[[],[[]]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[[[]],[]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[[[],[]]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[]],[[],[]]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[[[],[]],[[]]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[[[],[[]]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[[]],[]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[[],[]]],[]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[],[[],[]]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[],[[[]]]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[],[]],[]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 1
[[[[[[[]]],[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[[],[]]]]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 3
[[[[],[[],[[],[]]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[],[[[],[]],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[],[]],[[],[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 1
[[[[[],[[],[]]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[[],[]],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 1
[[[[[],[],[[[]]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[[],[[[]]],[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[[],[[[],[]]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[[]]],[],[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[[[[[[[],[]]],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 3
[[[[[[[],[],[]]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[[[[[[[[[]]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 7
[[],[[],[[],[[],[[],[]]]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[],[[],[[[],[]],[]]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[],[[[],[]],[[],[]]]]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => 1
[[],[[],[[[],[[],[]]],[]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[],[[[[],[]],[]],[]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[[],[]],[[],[[],[]]]]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[],[[[],[]],[[[],[]],[]]]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[],[[[],[[],[]]],[[],[]]]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[],[[[[],[]],[]],[[],[]]]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[],[[[],[[],[[],[]]]],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[[],[[[],[]],[]]],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[[[],[]],[[],[]]],[]]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => 1
[[],[[[[],[[],[]]],[]],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[[[[],[]],[]],[]],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[],[]],[[],[[],[[],[]]]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[],[]],[[],[[[],[]],[]]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[],[]],[[[],[]],[[],[]]]] => ([(0,9),(1,9),(2,8),(3,8),(4,7),(5,7),(6,9),(6,10),(7,10),(8,10)],11) => 1
[[[],[]],[[[],[[],[]]],[]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[],[]],[[[[],[]],[]],[]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[],[[],[]]],[[],[[],[]]]] => ([(0,10),(1,9),(2,7),(3,7),(4,8),(5,8),(6,9),(6,10),(7,9),(8,10)],11) => 1
[[[],[[],[]]],[[[],[]],[]]] => ([(0,10),(1,9),(2,7),(3,7),(4,8),(5,8),(6,9),(6,10),(7,9),(8,10)],11) => 1
[[[[],[]],[]],[[],[[],[]]]] => ([(0,10),(1,9),(2,7),(3,7),(4,8),(5,8),(6,9),(6,10),(7,9),(8,10)],11) => 1
[[[[],[]],[]],[[[],[]],[]]] => ([(0,10),(1,9),(2,7),(3,7),(4,8),(5,8),(6,9),(6,10),(7,9),(8,10)],11) => 1
[[[],[[],[[],[]]]],[[],[]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[],[[[],[]],[]]],[[],[]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[[],[]],[[],[]]],[[],[]]] => ([(0,9),(1,9),(2,8),(3,8),(4,7),(5,7),(6,9),(6,10),(7,10),(8,10)],11) => 1
[[[[],[[],[]]],[]],[[],[]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[[[],[]],[]],[]],[[],[]]] => ([(0,10),(1,9),(2,9),(3,7),(4,8),(5,8),(6,9),(6,10),(7,8),(7,10)],11) => 1
[[[],[[],[[],[[],[]]]]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[],[[],[[[],[]],[]]]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[],[[[],[]],[[],[]]]],[]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => 1
[[[],[[[],[[],[]]],[]]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[],[[[[],[]],[]],[]]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[[],[]],[[],[[],[]]]],[]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[[[],[]],[[[],[]],[]]],[]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[[[],[[],[]]],[[],[]]],[]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[[[[],[]],[]],[[],[]]],[]] => ([(0,8),(1,8),(2,9),(3,7),(4,7),(5,6),(6,10),(7,10),(8,9),(9,10)],11) => 1
[[[[],[[],[[],[]]]],[]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[[],[[[],[]],[]]],[]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[[[],[]],[[],[]]],[]],[]] => ([(0,10),(1,8),(2,8),(3,7),(4,7),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => 1
[[[[[],[[],[]]],[]],[]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[[[[[],[]],[]],[]],[]],[]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11) => 1
[[],[[],[[],[[],[[],[[],[]]]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[],[[],[[],[[[],[]],[]]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[],[[],[[[],[]],[[],[]]]]]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[],[[],[[],[[[],[[],[]]],[]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[],[[],[[[[],[]],[]],[]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[],[[[],[]],[[],[[],[]]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[],[[[],[]],[[[],[]],[]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[],[[[],[[],[]]],[[],[]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[],[[[[],[]],[]],[[],[]]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[],[[[],[[],[[],[]]]],[]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[],[[[],[[[],[]],[]]],[]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[],[[[[],[]],[[],[]]],[]]]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[],[[],[[[[],[[],[]]],[]],[]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[],[[[[[],[]],[]],[]],[]]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[],[]],[[],[[],[[],[]]]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[],[]],[[],[[[],[]],[]]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[],[]],[[[],[]],[[],[]]]]] => ([(0,10),(1,10),(2,9),(3,9),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(11,12)],13) => 1
[[],[[[],[]],[[[],[[],[]]],[]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[],[]],[[[[],[]],[]],[]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[],[[],[]]],[[],[[],[]]]]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[],[[[],[[],[]]],[[[],[]],[]]]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[],[[[[],[]],[]],[[],[[],[]]]]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[],[[[[],[]],[]],[[[],[]],[]]]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[],[[[],[[],[[],[]]]],[[],[]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[],[[[],[]],[]]],[[],[]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[[],[]],[[],[]]],[[],[]]]] => ([(0,10),(1,10),(2,9),(3,9),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(11,12)],13) => 1
[[],[[[[],[[],[]]],[]],[[],[]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[[[],[]],[]],[]],[[],[]]]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[],[[[],[[],[[],[[],[]]]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[],[[],[[[],[]],[]]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[],[[[],[]],[[],[]]]],[]]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[],[[[],[[[],[[],[]]],[]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[],[[[[],[]],[]],[]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[[],[]],[[],[[],[]]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[[[],[]],[[[],[]],[]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[[[],[[],[]]],[[],[]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[[[[],[]],[]],[[],[]]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[],[[[[],[[],[[],[]]]],[]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[[],[[[],[]],[]]],[]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[[[],[]],[[],[]]],[]],[]]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[],[[[[[],[[],[]]],[]],[]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[],[[[[[[],[]],[]],[]],[]],[]]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[]],[[],[[],[[],[[],[]]]]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[]],[[],[[],[[[],[]],[]]]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[]],[[],[[[],[]],[[],[]]]]] => ([(0,11),(1,12),(2,12),(3,9),(4,9),(5,8),(6,8),(7,11),(7,12),(8,10),(9,10),(10,11)],13) => 1
[[[],[]],[[],[[[],[[],[]]],[]]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[]],[[],[[[[],[]],[]],[]]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[]],[[[],[]],[[],[[],[]]]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[],[]],[[[],[]],[[[],[]],[]]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[],[]],[[[],[[],[]]],[[],[]]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[],[]],[[[[],[]],[]],[[],[]]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[],[]],[[[],[[],[[],[]]]],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[]],[[[],[[[],[]],[]]],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[]],[[[[],[]],[[],[]]],[]]] => ([(0,11),(1,12),(2,12),(3,9),(4,9),(5,8),(6,8),(7,11),(7,12),(8,10),(9,10),(10,11)],13) => 1
[[[],[]],[[[[],[[],[]]],[]],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[]],[[[[[],[]],[]],[]],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[[],[]]],[[],[[],[[],[]]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[],[]]],[[],[[[],[]],[]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[],[]]],[[[],[]],[[],[]]]] => ([(0,11),(1,9),(2,9),(3,8),(4,8),(5,10),(6,10),(7,11),(7,12),(8,12),(9,12),(10,11)],13) => 1
[[[],[[],[]]],[[[],[[],[]]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[],[]]],[[[[],[]],[]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[],[]],[]],[[],[[],[[],[]]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[],[]],[]],[[],[[[],[]],[]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[],[]],[]],[[[],[]],[[],[]]]] => ([(0,11),(1,9),(2,9),(3,8),(4,8),(5,10),(6,10),(7,11),(7,12),(8,12),(9,12),(10,11)],13) => 1
[[[[],[]],[]],[[[],[[],[]]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[],[]],[]],[[[[],[]],[]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[],[[],[]]]],[[],[[],[]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[],[[],[]]]],[[[],[]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[[],[]],[]]],[[],[[],[]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[[],[]],[]]],[[[],[]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[],[]],[[],[]]],[[],[[],[]]]] => ([(0,11),(1,9),(2,9),(3,8),(4,8),(5,10),(6,10),(7,11),(7,12),(8,12),(9,12),(10,11)],13) => 1
[[[[],[]],[[],[]]],[[[],[]],[]]] => ([(0,11),(1,9),(2,9),(3,8),(4,8),(5,10),(6,10),(7,11),(7,12),(8,12),(9,12),(10,11)],13) => 1
[[[[],[[],[]]],[]],[[],[[],[]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[],[[],[]]],[]],[[[],[]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[[],[]],[]],[]],[[],[[],[]]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[[[],[]],[]],[]],[[[],[]],[]]] => ([(0,12),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,11),(9,10),(10,12)],13) => 1
[[[],[[],[[],[[],[]]]]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[[],[[[],[]],[]]]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[[[],[]],[[],[]]]],[[],[]]] => ([(0,11),(1,12),(2,12),(3,9),(4,9),(5,8),(6,8),(7,11),(7,12),(8,10),(9,10),(10,11)],13) => 1
[[[],[[[],[[],[]]],[]]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[[[[],[]],[]],[]]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[[],[]],[[],[[],[]]]],[[],[]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[[],[]],[[[],[]],[]]],[[],[]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[[],[[],[]]],[[],[]]],[[],[]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[[[],[]],[]],[[],[]]],[[],[]]] => ([(0,11),(1,11),(2,9),(3,9),(4,10),(5,8),(6,8),(7,11),(7,12),(8,12),(9,10),(10,12)],13) => 1
[[[[],[[],[[],[]]]],[]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[[],[[[],[]],[]]],[]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[[[],[]],[[],[]]],[]],[[],[]]] => ([(0,11),(1,12),(2,12),(3,9),(4,9),(5,8),(6,8),(7,11),(7,12),(8,10),(9,10),(10,11)],13) => 1
[[[[[],[[],[]]],[]],[]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[[[[],[]],[]],[]],[]],[[],[]]] => ([(0,12),(1,11),(2,11),(3,8),(4,8),(5,9),(6,10),(7,11),(7,12),(8,10),(9,10),(9,12)],13) => 1
[[[],[[],[[],[[],[[],[]]]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[[],[[],[[[],[]],[]]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[[],[[[],[]],[[],[]]]]],[]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[[],[[],[[[],[[],[]]],[]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[[],[[[[],[]],[]],[]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[[[],[]],[[],[[],[]]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[],[[[],[]],[[[],[]],[]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[],[[[],[[],[]]],[[],[]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[],[[[[],[]],[]],[[],[]]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[],[[[],[[],[[],[]]]],[]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[[[],[[[],[]],[]]],[]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[[[[],[]],[[],[]]],[]]],[]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[[],[[[[],[[],[]]],[]],[]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[],[[[[[],[]],[]],[]],[]]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[],[]],[[],[[],[[],[]]]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[],[]],[[],[[[],[]],[]]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[],[]],[[[],[]],[[],[]]]],[]] => ([(0,10),(1,10),(2,9),(3,9),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(11,12)],13) => 1
[[[[],[]],[[[],[[],[]]],[]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[],[]],[[[[],[]],[]],[]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[],[[],[]]],[[],[[],[]]]],[]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[[[],[[],[]]],[[[],[]],[]]],[]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[[[[],[]],[]],[[],[[],[]]]],[]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[[[[],[]],[]],[[[],[]],[]]],[]] => ([(0,8),(1,8),(2,9),(3,9),(4,11),(5,10),(6,7),(7,12),(8,10),(9,11),(10,12),(11,12)],13) => 1
[[[[],[[],[[],[]]]],[[],[]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[],[[[],[]],[]]],[[],[]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[[],[]],[[],[]]],[[],[]]],[]] => ([(0,10),(1,10),(2,9),(3,9),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(11,12)],13) => 1
[[[[[],[[],[]]],[]],[[],[]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[[[],[]],[]],[]],[[],[]]],[]] => ([(0,9),(1,9),(2,10),(3,11),(4,8),(5,8),(6,7),(7,12),(8,12),(9,11),(10,11),(10,12)],13) => 1
[[[[],[[],[[],[[],[]]]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[],[[],[[[],[]],[]]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[],[[[],[]],[[],[]]]],[]],[]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[[[],[[[],[[],[]]],[]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[],[[[[],[]],[]],[]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[[],[]],[[],[[],[]]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[[[],[]],[[[],[]],[]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[[[],[[],[]]],[[],[]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[[[[],[]],[]],[[],[]]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,9),(5,10),(6,7),(7,12),(8,11),(9,10),(10,11),(11,12)],13) => 1
[[[[[],[[],[[],[]]]],[]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[[],[[[],[]],[]]],[]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[[[],[]],[[],[]]],[]],[]],[]] => ([(0,12),(1,9),(2,9),(3,8),(4,8),(5,10),(6,7),(7,12),(8,11),(9,11),(10,11),(10,12)],13) => 1
[[[[[[],[[],[]]],[]],[]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[[[[],[]],[]],[]],[]],[]],[]] => ([(0,12),(1,8),(2,8),(3,9),(4,10),(5,11),(6,7),(7,12),(8,10),(9,11),(9,12),(10,11)],13) => 1
[[[[[[[[[[]]]]]]]]],[]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[[[[[[],[]]]]]]],[]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[],[[[[[[[],[]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[],[[[[[[[[[]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[],[[[[[[[]]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[[[[]]]]]]],[]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[[[[[[]]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[],[],[[[[[[[]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[]],[[[[[[[[]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[],[]],[[[[[[]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[]]],[[[[[[[]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[[],[]]],[[[[[]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[]]]],[[[[[[]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[[[],[]]]],[[[[]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[]]]]],[[[[[]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[[[[],[]]]]],[[[]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[[]]]]]],[[[[]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[[[[[],[]]]]]],[[]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[[[]]]]]]],[[[]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[[[[[[[]]]]]]]],[[]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 9
[[[[[[[[[],[]]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[[[[]]]]],[]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 6
[[[[[[[[[]]],[]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 6
[[[[[[[[]]]]]]],[],[]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[[]]]]]],[[],[]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[[]]]]],[[[],[]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[[]]]],[[[[],[]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[[]]],[[[[[],[]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[]],[[[[[[],[]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
[[[]],[[],[[[[[]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 6
[[[[]]],[[[],[[[]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 6
[[[[[[[],[[[]]]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 6
[[[[[],[[[[[]]]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 6
[[],[[[[[[[]]]]]]],[]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,0,3 2,8,0,4 7,10,20,0,5 14,42,30,40,0,6
$F_{1} = 1$
$F_{2} = 1$
$F_{3} = 2\ q$
$F_{4} = 2 + 3\ q^{2}$
$F_{5} = 2 + 8\ q + 4\ q^{3}$
$F_{6} = 7 + 10\ q + 20\ q^{2} + 5\ q^{4}$
$F_{7} = 14 + 42\ q + 30\ q^{2} + 40\ q^{3} + 6\ q^{5}$
Description
The number of degree 2 vertices of a graph.
A vertex has degree 2 if and only if it lies on a unique maximal path.
A vertex has degree 2 if and only if it lies on a unique maximal path.
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Description
Return the undirected graph obtained from the tree nodes and edges.
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