Identifier
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Images
[] => [] => [] => ([],0)
[[]] => [1,0] => [1] => ([],1)
[[],[]] => [1,0,1,0] => [1,2] => ([(0,1)],2)
[[[]]] => [1,1,0,0] => [2,1] => ([],2)
[[],[],[]] => [1,0,1,0,1,0] => [1,2,3] => ([(0,2),(2,1)],3)
[[],[[]]] => [1,0,1,1,0,0] => [1,3,2] => ([(0,1),(0,2)],3)
[[[]],[]] => [1,1,0,0,1,0] => [2,1,3] => ([(0,2),(1,2)],3)
[[[],[]]] => [1,1,0,1,0,0] => [2,3,1] => ([(1,2)],3)
[[[[]]]] => [1,1,1,0,0,0] => [3,2,1] => ([],3)
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [2,3,4,1] => ([(1,2),(2,3)],4)
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [2,4,3,1] => ([(1,2),(1,3)],4)
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [3,2,4,1] => ([(1,3),(2,3)],4)
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [4,2,3,1] => ([(2,3)],4)
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [4,3,2,1] => ([],4)
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => ([(2,3),(3,4)],5)
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => ([(2,3),(2,4)],5)
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => ([(2,4),(3,4)],5)
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => ([(3,4)],5)
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => ([],5)
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => ([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => ([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => ([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => ([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)
>>> Load all 1625 entries. <<<
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => ([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => ([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => ([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => ([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => ([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => ([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => ([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => ([(1,4),(4,5),(5,2),(5,3)],6)
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => ([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => ([(1,5),(4,3),(5,2),(5,4)],6)
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => ([(1,5),(5,2),(5,3),(5,4)],6)
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => ([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => ([(1,4),(1,5),(5,2),(5,3)],6)
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => ([(1,3),(1,4),(1,5),(5,2)],6)
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5)],6)
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => ([(1,5),(2,5),(5,3),(5,4)],6)
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6)
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6)
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6)
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6)
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6)
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6)
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => ([(2,3),(3,4),(3,5)],6)
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => ([(2,3),(2,4),(3,5),(4,5)],6)
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => ([(2,3),(2,4),(4,5)],6)
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => ([(2,3),(2,4),(2,5)],6)
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6)
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6)
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6)
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6)
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6)
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => ([(3,4),(3,5)],6)
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6)
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => ([(4,5)],6)
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => ([],6)
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,7,6] => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,6,7,5] => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,5,4,6,7] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,5,4,7,6] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,5,6,4,7] => ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => ([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,5,6,7,4] => ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,6,5,7,4] => ([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,7,5,6,4] => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7] => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,4,3,5,7,6] => ([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,4,3,6,5,7] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,3,6,7,5] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,4,5,3,6,7] => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => ([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,5,4,3,7,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => ([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,5,4,6,3,7] => ([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,6,4,5,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => ([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,3] => ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => ([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,7,5,6,3] => ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => ([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,6,4,5,7,3] => ([(0,5),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,6,5,4,7,3] => ([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,7,4,5,6,3] => ([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,7,4,6,5,3] => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,7,5,4,6,3] => ([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,7,5,6,4,3] => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,7,6] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,2,4,6,5,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,3,2,4,6,7,5] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => ([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,4,6,7] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4,7,6] => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,2,5,6,4,7] => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,3,2,5,6,7,4] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => ([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,5,7,4] => ([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,7,5,6,4] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7] => ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,4,3,2,5,7,6] => ([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,4,3,2,6,5,7] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3,2,6,7,5] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => ([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,3,5,2,6,7] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,5,3,4,2,6,7] => ([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,5,3,4,2,7,6] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,4,3,2,7,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,6,4,5,2,7] => ([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,3,4,6,2,7] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,4,3,6,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,6,3,4,5,2,7] => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,6,3,5,4,2,7] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,6,4,3,5,2,7] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,6,4,5,3,2,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => ([(0,3),(0,4),(1,6),(2,6),(4,5),(5,1),(5,2)],7)
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,7,5,6,2] => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => ([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7)
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,6,4,5,7,2] => ([(0,3),(0,5),(1,6),(2,6),(4,2),(5,1),(5,4)],7)
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,7,4,5,6,2] => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,7,4,6,5,2] => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,7,5,4,6,2] => ([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7)
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,7,5,6,4,2] => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => ([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => ([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,7,5,6,2] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,5,3,4,6,7,2] => ([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7)
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => ([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,5,3,4,7,6,2] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(3,5),(3,6),(4,1)],7)
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6,3,4,5,7,2] => ([(0,2),(0,3),(0,5),(1,6),(3,6),(4,1),(5,4)],7)
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6,3,5,4,7,2] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6,4,3,5,7,2] => ([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6,4,5,3,7,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,5,4,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,7,3,4,5,6,2] => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,7,3,4,6,5,2] => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,7,3,5,4,6,2] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7)
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,7,3,5,6,4,2] => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,7,3,6,5,4,2] => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,7,4,3,5,6,2] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,7,4,3,6,5,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,7,4,5,3,6,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,7,5,4,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,7,4,5,6,3,2] => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,7,4,6,5,3,2] => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,7,5,4,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,7,6,4,5,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,7,6] => ([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,6,5,7] => ([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,6,7,5] => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => ([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,5,4,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,5,4,7,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,6,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => ([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,5,6,7,4] => ([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => ([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,6,5,7,4] => ([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,7,5,6,4] => ([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => ([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,3,5,7,6] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,3,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => ([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,5,3,6,7] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,5,4,3,7,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,4,6,3,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,6,4,5,3,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,3] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7)
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7)
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,7,5,6,3] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7)
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => ([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(5,3),(6,3)],7)
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,6,4,5,7,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(5,2),(6,3)],7)
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,6,5,4,7,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,7,4,5,6,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(6,2)],7)
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,7,4,6,5,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,7,5,4,6,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7)
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,7,5,6,4,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => ([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,7,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,2,1,4,6,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => ([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => ([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,2,1,4,6,7,5] => ([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => ([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,5,4,6,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,1,5,4,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,5,6,4,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7)
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => ([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => ([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => ([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,7,5,6,4] => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,5,6,7,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,2,1,6,5,7,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,7,5,6,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => ([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => ([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => ([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => ([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,2,3,1,5,7,6] => ([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,3,2,1,5,7,6] => ([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => ([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => ([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => ([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,3,1,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,3,2,1,6,5,7] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => ([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => ([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => ([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,2,3,1,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,2,3,1,7,6,5] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3,2,1,6,7,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => ([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => ([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,5,3,4,1,6,7] => ([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,2,3,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,2,4,3,1,6,7] => ([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => ([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => ([(0,2),(0,3),(1,4),(1,5),(2,6),(3,6),(6,4),(6,5)],7)
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,5,3,4,1,7,6] => ([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => ([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7)
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,5,4,1,7,6] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,2,3,5,1,7,6] => ([(0,6),(1,4),(1,5),(2,3),(3,6),(6,4),(6,5)],7)
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2,3,4,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2,4,3,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,3,2,4,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,3,4,2,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,4,3,2,1,7,6] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => ([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => ([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,6,4,5,1,7] => ([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => ([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => ([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,5,3,4,6,1,7] => ([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => ([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,6,3,4,5,1,7] => ([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,6,3,5,4,1,7] => ([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,6,4,3,5,1,7] => ([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,6,4,5,3,1,7] => ([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => ([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,5,4,6,1,7] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,6,4,5,1,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,2,3,6,5,1,7] => ([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [5,2,3,4,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [5,2,4,3,6,1,7] => ([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,3,5,4,1,7] => ([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,2,4,3,5,1,7] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,4,5,3,1,7] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,2,5,4,3,1,7] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,3,2,5,4,1,7] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,3,5,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => ([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,7,5,6,1] => ([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => ([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => ([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,6,4,5,7,1] => ([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => ([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,7,4,5,6,1] => ([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,7,4,6,5,1] => ([(1,6),(5,3),(5,4),(6,2),(6,5)],7)
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,7,5,4,6,1] => ([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,7,5,6,4,1] => ([(1,6),(5,4),(6,2),(6,3),(6,5)],7)
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => ([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => ([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => ([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => ([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,7,5,6,1] => ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,5,3,4,6,7,1] => ([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => ([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,5,3,4,7,6,1] => ([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => ([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,6,3,4,5,7,1] => ([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,6,3,5,4,7,1] => ([(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,6,4,3,5,7,1] => ([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,6,4,5,3,7,1] => ([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => ([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,7,3,4,5,6,1] => ([(1,3),(1,6),(4,5),(5,2),(6,4)],7)
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,7,3,4,6,5,1] => ([(1,4),(1,5),(5,6),(6,2),(6,3)],7)
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,7,3,5,4,6,1] => ([(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,7,3,5,6,4,1] => ([(1,4),(1,6),(5,3),(6,2),(6,5)],7)
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,7,3,6,5,4,1] => ([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,7,4,3,5,6,1] => ([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,7,4,3,6,5,1] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,7,4,5,3,6,1] => ([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,7,5,4,3,6,1] => ([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,7,4,5,6,3,1] => ([(1,3),(1,4),(1,6),(5,2),(6,5)],7)
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,7,4,6,5,3,1] => ([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,7,5,4,6,3,1] => ([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,7,6,4,5,3,1] => ([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7)
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => ([(1,6),(2,6),(3,4),(3,5),(6,3)],7)
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => ([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,7,5,6,1] => ([(1,6),(2,6),(4,5),(6,3),(6,4)],7)
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => ([(1,6),(2,6),(6,3),(6,4),(6,5)],7)
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => ([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,6,4,5,7,1] => ([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,7,4,5,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,7,4,6,5,1] => ([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,7,5,4,6,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,7,5,6,4,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,1] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7)
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [4,2,3,5,7,6,1] => ([(1,6),(2,3),(3,6),(6,4),(6,5)],7)
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => ([(1,6),(2,6),(3,6),(6,4),(6,5)],7)
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [4,2,3,6,5,7,1] => ([(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,2,3,7,5,6,1] => ([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,2,3,7,6,5,1] => ([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,7,5,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [5,2,3,4,6,7,1] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,2,4,3,6,7,1] => ([(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [5,3,2,4,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7)
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,3,4,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7)
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7)
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,2,3,4,7,6,1] => ([(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,2,4,3,7,6,1] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,3,2,4,7,6,1] => ([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,3,4,2,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,2,3,4,5,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7)
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,2,3,5,4,7,1] => ([(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,2,4,3,5,7,1] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,2,4,5,3,7,1] => ([(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,5,4,3,7,1] => ([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,3,2,4,5,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7)
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,2,5,4,7,1] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,3,4,2,5,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7)
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,3,5,4,2,7,1] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,4,3,5,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,5,3,4,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7,2,3,4,5,6,1] => ([(2,6),(4,5),(5,3),(6,4)],7)
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7,2,3,4,6,5,1] => ([(2,5),(5,6),(6,3),(6,4)],7)
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7,2,3,5,4,6,1] => ([(2,3),(3,4),(3,5),(4,6),(5,6)],7)
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7,2,3,5,6,4,1] => ([(2,6),(5,4),(6,3),(6,5)],7)
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7,2,3,6,5,4,1] => ([(2,6),(6,3),(6,4),(6,5)],7)
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,2,4,3,5,6,1] => ([(2,3),(2,4),(3,6),(4,6),(6,5)],7)
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,2,4,3,6,5,1] => ([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,2,4,5,3,6,1] => ([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7,2,5,4,3,6,1] => ([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7,2,4,5,6,3,1] => ([(2,4),(2,6),(5,3),(6,5)],7)
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,2,4,6,5,3,1] => ([(2,5),(2,6),(6,3),(6,4)],7)
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7,2,5,4,6,3,1] => ([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7,2,6,4,5,3,1] => ([(2,4),(2,5),(2,6),(6,3)],7)
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7,2,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6)],7)
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7)
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7,3,2,4,6,5,1] => ([(2,6),(3,6),(6,4),(6,5)],7)
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7,3,2,5,4,6,1] => ([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7,3,2,5,6,4,1] => ([(2,5),(2,6),(3,5),(3,6),(6,4)],7)
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7,3,2,6,5,4,1] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7,3,4,2,5,6,1] => ([(2,6),(3,4),(4,6),(6,5)],7)
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7,4,3,2,5,6,1] => ([(2,6),(3,6),(4,6),(6,5)],7)
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,4,2,6,5,1] => ([(2,5),(2,6),(3,4),(4,5),(4,6)],7)
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7,4,3,2,6,5,1] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7,3,4,5,2,6,1] => ([(2,6),(3,4),(4,5),(5,6)],7)
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7,3,5,4,2,6,1] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7,4,3,5,2,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7)
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7,5,3,4,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7)
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7)
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7,3,4,5,6,2,1] => ([(3,4),(4,6),(6,5)],7)
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7,3,4,6,5,2,1] => ([(3,4),(4,5),(4,6)],7)
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7,3,5,4,6,2,1] => ([(3,4),(3,5),(4,6),(5,6)],7)
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7,3,6,4,5,2,1] => ([(3,4),(3,5),(5,6)],7)
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7,3,6,5,4,2,1] => ([(3,4),(3,5),(3,6)],7)
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7,4,3,5,6,2,1] => ([(3,6),(4,6),(6,5)],7)
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7,4,3,6,5,2,1] => ([(3,5),(3,6),(4,5),(4,6)],7)
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7,5,3,4,6,2,1] => ([(3,6),(4,5),(5,6)],7)
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7)
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7)
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7,6,3,5,4,2,1] => ([(4,5),(4,6)],7)
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7)
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7,6,4,5,3,2,1] => ([(5,6)],7)
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => ([],7)
[[],[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[],[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,8,7] => ([(0,6),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],8)
[[],[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,7,6,8] => ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
[[],[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,4,5,7,8,6] => ([(0,6),(3,4),(4,7),(5,1),(6,3),(7,2),(7,5)],8)
[[],[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => ([(0,6),(4,5),(5,7),(6,4),(7,1),(7,2),(7,3)],8)
[[],[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,3,4,6,5,7,8] => ([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)
[[],[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,3,4,6,5,8,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,5),(4,3),(5,1),(5,2)],8)
[[],[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,6,7,5,8] => ([(0,5),(1,7),(2,7),(3,6),(4,1),(5,3),(6,2),(6,4)],8)
[[],[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => ([(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[[],[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,5] => ([(0,6),(3,7),(4,5),(5,1),(6,3),(7,2),(7,4)],8)
[[],[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => ([(0,5),(4,7),(5,4),(6,2),(6,3),(7,1),(7,6)],8)
[[],[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,7,6,8,5] => ([(0,5),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2),(6,3)],8)
[[],[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,8,6,7,5] => ([(0,6),(4,7),(5,3),(6,4),(7,1),(7,2),(7,5)],8)
[[],[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => ([(0,6),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],8)
[[],[],[],[[]],[],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,3,5,4,6,7,8] => ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
[[],[],[],[[]],[],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,3,5,4,6,8,7] => ([(0,5),(1,7),(2,7),(5,6),(6,1),(6,2),(7,3),(7,4)],8)
[[],[],[],[[]],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,3,5,4,7,6,8] => ([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2),(5,7),(6,7)],8)
[[],[],[],[[]],[[],[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3,5,4,7,8,6] => ([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3),(7,1)],8)
[[],[],[],[[]],[[[]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => ([(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,1),(4,2)],8)
[[],[],[],[[],[]],[],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,4,7,8] => ([(0,5),(1,7),(2,7),(4,2),(5,6),(6,1),(6,4),(7,3)],8)
[[],[],[],[[[]]],[],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => ([(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
[[],[],[],[[],[]],[[]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,2),(4,5),(5,1),(5,3)],8)
[[],[],[],[[[]]],[[]]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,6,5,4,8,7] => ([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[[],[],[],[[],[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => ([(0,5),(1,7),(2,7),(3,4),(4,1),(5,6),(6,2),(6,3)],8)
[[],[],[],[[],[[]]],[]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[[],[],[],[[[]],[]],[]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,6,5,7,4,8] => ([(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3),(6,7)],8)
[[],[],[],[[[],[]]],[]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,7,5,6,4,8] => ([(0,5),(1,7),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[[],[],[],[[[[]]]],[]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => ([(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[[],[],[],[[],[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,4] => ([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8)
[[],[],[],[[],[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => ([(0,5),(4,7),(5,6),(6,3),(6,4),(7,1),(7,2)],8)
[[],[],[],[[],[[]],[]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => ([(0,4),(2,7),(3,7),(4,6),(5,2),(5,3),(6,1),(6,5)],8)
[[],[],[],[[],[[],[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,8,6,7,4] => ([(0,5),(4,3),(5,6),(6,2),(6,7),(7,1),(7,4)],8)
[[],[],[],[[],[[[]]]]] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => ([(0,5),(5,6),(6,4),(6,7),(7,1),(7,2),(7,3)],8)
[[],[],[],[[[]],[],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => ([(0,5),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3),(7,4)],8)
[[],[],[],[[[]],[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => ([(0,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3)],8)
[[],[],[],[[[],[]],[]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,7,5,6,8,4] => ([(0,5),(2,7),(3,7),(4,3),(5,6),(6,1),(6,2),(6,4)],8)
[[],[],[],[[[[]]],[]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,2,3,7,6,5,8,4] => ([(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[[],[],[],[[[],[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,8,5,6,7,4] => ([(0,6),(4,5),(5,3),(6,7),(7,1),(7,2),(7,4)],8)
[[],[],[],[[[],[[]]]]] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,8,5,7,6,4] => ([(0,5),(5,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[[],[],[],[[[[]],[]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,8,6,5,7,4] => ([(0,5),(3,7),(4,7),(5,6),(6,1),(6,2),(6,3),(6,4)],8)
[[],[],[],[[[[],[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,8,6,7,5,4] => ([(0,6),(5,4),(6,7),(7,1),(7,2),(7,3),(7,5)],8)
[[],[],[],[[[[[]]]]]] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => ([(0,6),(6,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[[],[],[[]],[],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,3,5,6,7,8] => ([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)
[[],[],[[]],[],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,4,3,5,6,8,7] => ([(0,6),(3,7),(4,7),(5,1),(5,2),(6,3),(6,4),(7,5)],8)
[[],[],[[]],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5,7,6,8] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
[[],[],[[]],[],[[],[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,4,3,5,7,8,6] => ([(0,6),(2,7),(3,7),(5,1),(6,2),(6,3),(7,4),(7,5)],8)
[[],[],[[]],[],[[[]]]] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => ([(0,6),(1,7),(2,7),(6,1),(6,2),(7,3),(7,4),(7,5)],8)
[[],[],[[]],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7),(7,1)],8)
[[],[],[[]],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5,8,7] => ([(0,1),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[],[],[[]],[[],[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,4,3,6,7,5,8] => ([(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(4,3),(5,6),(7,1)],8)
[[],[],[[]],[[],[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4,3,6,7,8,5] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(5,3),(7,4)],8)
[[],[],[[]],[[],[[]]]] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => ([(0,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4),(7,1),(7,2)],8)
[[],[],[[]],[[[]],[]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4,3,7,6,8,5] => ([(0,1),(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[],[[]],[[[],[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,8,6,7,5] => ([(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3),(7,1)],8)
[[],[],[[]],[[[[]]]]] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => ([(0,1),(1,2),(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[],[[[]]],[],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => ([(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(6,3),(6,4),(7,5)],8)
[[],[],[[[]]],[],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,5,4,3,6,8,7] => ([(0,6),(1,7),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4),(7,5)],8)
[[],[],[[],[]],[[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3),(5,7),(6,7)],8)
[[],[],[[],[]],[[],[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4),(7,1)],8)
[[],[],[[],[]],[[[]]]] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,2),(4,1),(4,3)],8)
[[],[],[[[]]],[[],[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[[],[],[[[]]],[[[]]]] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => ([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(4,2),(4,3)],8)
[[],[],[[],[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => ([(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4),(7,3)],8)
[[],[],[[],[[]]],[],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => ([(0,6),(1,7),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5),(7,4)],8)
[[],[],[[[],[]]],[],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,6,4,5,3,7,8] => ([(0,6),(1,7),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
[[],[],[[[[]]]],[],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[[],[],[[],[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,2),(5,1),(5,3)],8)
[[],[],[[],[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => ([(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,2),(6,4)],8)
[[],[],[[[]],[],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,4),(7,3)],8)
[[],[],[[[[]],[]]],[]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,2,7,5,4,6,3,8] => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)
[[],[],[[[[[]]]]],[]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => ([(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[[],[],[[],[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,3] => ([(0,7),(3,4),(4,6),(5,3),(6,1),(7,2),(7,5)],8)
[[],[],[[],[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => ([(0,7),(4,5),(5,6),(6,2),(6,3),(7,1),(7,4)],8)
[[],[],[[],[],[[],[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,8,6,7,3] => ([(0,7),(4,6),(5,3),(6,2),(6,5),(7,1),(7,4)],8)
[[],[],[[],[],[[[]]]]] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => ([(0,6),(5,7),(6,4),(6,5),(7,1),(7,2),(7,3)],8)
[[],[],[[],[[]],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(5,1),(5,4)],8)
[[],[],[[],[[],[]],[]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,4,7,5,6,8,3] => ([(0,6),(2,7),(3,7),(4,3),(5,2),(5,4),(6,1),(6,5)],8)
[[],[],[[],[[[]]],[]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => ([(0,5),(2,7),(3,7),(4,7),(5,1),(5,6),(6,2),(6,3),(6,4)],8)
[[],[],[[],[[],[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,8,5,6,7,3] => ([(0,7),(4,5),(5,3),(6,2),(6,4),(7,1),(7,6)],8)
[[],[],[[],[[[]],[]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,4,8,6,5,7,3] => ([(0,5),(3,7),(4,7),(5,2),(5,6),(6,1),(6,3),(6,4)],8)
[[],[],[[],[[[[]]]]]] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => ([(0,6),(6,5),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[],[[[]],[],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => ([(0,6),(3,7),(4,7),(5,2),(6,1),(6,3),(6,4),(7,5)],8)
[[],[],[[[]],[],[[]]]] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => ([(0,6),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4),(7,5)],8)
[[],[],[[[]],[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3),(5,7),(6,7)],8)
[[],[],[[[]],[[],[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,8,6,7,3] => ([(0,5),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4),(7,1)],8)
[[],[],[[[]],[[[]]]]] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => ([(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(4,2),(4,3)],8)
[[],[],[[[],[]],[],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,6,4,5,7,8,3] => ([(0,6),(2,7),(3,7),(5,3),(6,1),(6,2),(6,5),(7,4)],8)
[[],[],[[[[]]],[],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => ([(0,6),(2,7),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[[],[],[[[[]]],[[]]]] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => ([(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[[],[],[[[],[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,7,4,5,6,8,3] => ([(0,6),(2,7),(3,7),(4,5),(5,3),(6,1),(6,2),(6,4)],8)
[[],[],[[[[]],[]],[]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,7,5,4,6,8,3] => ([(0,5),(2,7),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4),(6,7)],8)
[[],[],[[[[[]]]],[]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,7,6,5,4,8,3] => ([(0,6),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[[],[],[[[],[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,8,4,5,6,7,3] => ([(0,7),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],8)
[[],[],[[[],[[],[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,8,4,6,7,5,3] => ([(0,7),(5,4),(6,3),(6,5),(7,1),(7,2),(7,6)],8)
[[],[],[[[],[[[]]]]]] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,8,4,7,6,5,3] => ([(0,7),(6,3),(6,4),(6,5),(7,1),(7,2),(7,6)],8)
[[],[],[[[[]],[],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,8,5,4,6,7,3] => ([(0,6),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4),(7,5)],8)
[[],[],[[[[]],[[]]]]] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,8,5,4,7,6,3] => ([(0,5),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3),(5,4)],8)
[[],[],[[[[],[]],[]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,8,5,6,4,7,3] => ([(0,6),(3,7),(4,7),(5,4),(6,1),(6,2),(6,3),(6,5)],8)
[[],[],[[[[[]]],[]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,8,6,5,4,7,3] => ([(0,6),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[[],[],[[[[],[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,8,5,6,7,4,3] => ([(0,7),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],8)
[[],[],[[[[[]],[]]]]] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,8,6,5,7,4,3] => ([(0,6),(4,7),(5,7),(6,1),(6,2),(6,3),(6,4),(6,5)],8)
[[],[],[[[[[],[]]]]]] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,8,7,5,6,4,3] => ([(0,7),(6,5),(7,1),(7,2),(7,3),(7,4),(7,6)],8)
[[],[],[[[[[[]]]]]]] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => ([(0,7),(7,1),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[],[[]],[],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7,8] => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[],[[]],[],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,3,2,4,5,6,8,7] => ([(0,3),(0,4),(3,7),(4,7),(5,6),(6,1),(6,2),(7,5)],8)
[[],[[]],[],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,2,4,5,7,6,8] => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
[[],[[]],[],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,3,2,4,5,7,8,6] => ([(0,3),(0,4),(3,7),(4,7),(5,2),(6,1),(6,5),(7,6)],8)
[[],[[]],[],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => ([(0,4),(0,5),(4,7),(5,7),(6,1),(6,2),(6,3),(7,6)],8)
[[],[[]],[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,6,5,7,8] => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
[[],[[]],[],[[]],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,3,2,4,6,5,8,7] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(7,1),(7,2)],8)
[[],[[]],[],[[[]]],[]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
[[],[[]],[],[[],[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,3,2,4,6,7,8,5] => ([(0,3),(0,4),(3,7),(4,7),(5,1),(6,5),(7,2),(7,6)],8)
[[],[[]],[],[[],[[]]]] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => ([(0,4),(0,5),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],8)
[[],[[]],[],[[[]],[]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,3,2,4,7,6,8,5] => ([(0,4),(0,5),(2,6),(3,6),(4,7),(5,7),(7,1),(7,2),(7,3)],8)
[[],[[]],[],[[[],[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,3,2,4,8,6,7,5] => ([(0,4),(0,5),(4,7),(5,7),(6,1),(7,2),(7,3),(7,6)],8)
[[],[[]],[],[[[[]]]]] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => ([(0,5),(0,6),(5,7),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[[]],[[]],[],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,5,4,6,7,8] => ([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7),(7,4)],8)
[[],[[]],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,7,6,8] => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[],[[]],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => ([(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(5,1),(6,4),(6,5),(7,4),(7,5)],8)
[[],[[]],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[[],[[]],[[],[]],[],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,3,2,5,6,4,7,8] => ([(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,2),(7,1)],8)
[[],[[]],[[[]]],[],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7),(7,1)],8)
[[],[[]],[[],[]],[[]]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => ([(0,2),(0,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(6,1),(7,4),(7,5)],8)
[[],[[]],[[[]]],[[]]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2,6,5,4,8,7] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[],[[]],[[],[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => ([(0,2),(0,3),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,4)],8)
[[],[[]],[[],[[]]],[]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => ([(0,3),(0,4),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,1),(6,2)],8)
[[],[[]],[[[]],[]],[]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,2,6,5,7,4,8] => ([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[[],[[]],[[[[]]]],[]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[],[[]],[[],[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,6,7,8,4] => ([(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(4,1),(5,4),(7,5)],8)
[[],[[]],[[],[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => ([(0,3),(0,4),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(7,5)],8)
[[],[[]],[[],[[[]]]]] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => ([(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1),(7,2),(7,3)],8)
[[],[[]],[[[]],[],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => ([(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1),(6,4),(7,4)],8)
[[],[[]],[[[]],[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => ([(0,1),(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[],[[]],[[[],[]],[]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,7,5,6,8,4] => ([(0,2),(0,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,1),(7,4)],8)
[[],[[]],[[[[]]],[]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,3,2,7,6,5,8,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[],[[]],[[[],[[]]]]] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,8,5,7,6,4] => ([(0,3),(0,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1),(7,2)],8)
[[],[[]],[[[[]],[]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,8,6,5,7,4] => ([(0,1),(0,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[[],[[]],[[[[],[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,3,2,8,6,7,5,4] => ([(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(7,1)],8)
[[],[[]],[[[[[]]]]]] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => ([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[],[[],[]],[],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8] => ([(0,3),(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(7,5)],8)
[[],[[[]]],[],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => ([(0,2),(0,3),(0,4),(2,7),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[[],[[],[]],[],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => ([(0,4),(0,5),(3,7),(4,7),(5,3),(6,1),(6,2),(7,6)],8)
[[],[[[]]],[],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,4,3,2,5,6,8,7] => ([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(6,2),(7,6)],8)
[[],[[],[]],[],[[]],[]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
[[],[[[]]],[],[[]],[]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,4,3,2,5,7,6,8] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
[[],[[],[]],[],[[],[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => ([(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,3),(7,5)],8)
[[],[[[]]],[],[[],[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,4,3,2,5,7,8,6] => ([(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,2),(7,6)],8)
[[],[[[]]],[],[[[]]]] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => ([(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1),(7,2),(7,3)],8)
[[],[[],[]],[[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => ([(0,1),(0,3),(1,2),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[],[[],[]],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => ([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8)
[[],[[[]]],[[],[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => ([(0,2),(0,3),(0,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,1)],8)
[[],[[[]]],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[[],[[],[]],[[],[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => ([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,1),(5,2),(7,4)],8)
[[],[[],[]],[[],[[]]]] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => ([(0,4),(0,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,1),(7,2)],8)
[[],[[],[]],[[[]],[]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => ([(0,1),(0,3),(1,2),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[[],[]],[[[],[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,8,6,7,5] => ([(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(7,1)],8)
[[],[[],[]],[[[[]]]]] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => ([(0,1),(0,3),(1,2),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[[[]]],[[],[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,4,3,2,6,7,8,5] => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(7,5)],8)
[[],[[[]]],[[],[[]]]] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => ([(0,3),(0,4),(0,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,1),(7,2)],8)
[[],[[[]]],[[[]],[]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,4,3,2,7,6,8,5] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[[[]]],[[[],[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,4,3,2,8,6,7,5] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1)],8)
[[],[[[]]],[[[[]]]]] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => ([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[[],[],[]],[],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => ([(0,3),(0,6),(2,7),(3,7),(4,2),(5,1),(6,4),(7,5)],8)
[[],[[[],[]]],[],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,5,3,4,2,6,7,8] => ([(0,3),(0,4),(0,6),(2,7),(3,7),(4,7),(5,1),(6,2),(7,5)],8)
[[],[[[[]]]],[],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
[[],[[],[[]]],[],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => ([(0,5),(0,6),(1,7),(2,7),(5,7),(6,1),(6,2),(7,3),(7,4)],8)
[[],[[],[],[]],[[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => ([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3),(5,7),(6,7)],8)
[[],[[],[[]]],[[]],[]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => ([(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,1),(4,2),(6,5),(7,5)],8)
[[],[[[]],[]],[[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => ([(0,1),(0,2),(0,3),(1,7),(2,7),(3,5),(3,6),(5,4),(6,4),(7,5),(7,6)],8)
[[],[[[[]]]],[[]],[]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,5,4,3,2,7,6,8] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[],[[],[],[]],[[],[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => ([(0,3),(0,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4),(7,1)],8)
[[],[[],[],[]],[[[]]]] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => ([(0,2),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,1),(4,3)],8)
[[],[[],[[]]],[[],[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => ([(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(7,1)],8)
[[],[[[],[]]],[[],[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,5,3,4,2,7,8,6] => ([(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(7,1)],8)
[[],[[[],[]]],[[[]]]] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3,4,2,8,7,6] => ([(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,1)],8)
[[],[[[[]]]],[[],[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,4,3,2,7,8,6] => ([(0,2),(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,1)],8)
[[],[[[[]]]],[[[]]]] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[],[[],[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => ([(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4),(7,2)],8)
[[],[[[]],[],[]],[],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => ([(0,3),(0,4),(0,5),(2,7),(3,6),(4,6),(5,7),(6,2),(7,1)],8)
[[],[[[]],[[]]],[],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => ([(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[[],[[[[]]],[]],[],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,4,3,6,2,7,8] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(6,1),(7,6)],8)
[[],[[[],[],[]]],[],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,3,4,5,2,7,8] => ([(0,3),(0,4),(0,6),(1,7),(3,7),(4,7),(5,1),(6,5),(7,2)],8)
[[],[[[],[[]]]],[],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,3,5,4,2,7,8] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(4,7),(5,7),(6,1),(6,2),(7,3)],8)
[[],[[[[]],[]]],[],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,6,4,3,5,2,7,8] => ([(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,6),(5,6),(6,7),(7,1)],8)
[[],[[[[],[]]]],[],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,6,4,5,3,2,7,8] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(3,7),(4,7),(5,7),(6,1),(7,2)],8)
[[],[[[[[]]]]],[],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7),(7,1)],8)
[[],[[],[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => ([(0,2),(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,1),(5,3)],8)
[[],[[],[[],[]]],[[]]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,3,6,4,5,2,8,7] => ([(0,3),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,2),(5,1),(5,4)],8)
[[],[[],[[[]]]],[[]]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => ([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1),(5,2),(5,3)],8)
[[],[[[],[]],[]],[[]]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,3,4,6,2,8,7] => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(3,7),(4,1),(5,6),(5,7)],8)
[[],[[[[],[]]]],[[]]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,6,4,5,3,2,8,7] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,1)],8)
[[],[[[[[]]]]],[[]]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,5,4,3,2,8,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[],[[],[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => ([(0,2),(0,6),(1,7),(2,7),(3,5),(4,3),(5,1),(6,4)],8)
[[],[[],[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => ([(0,3),(0,5),(1,7),(2,7),(3,7),(4,6),(5,4),(6,1),(6,2)],8)
[[],[[],[[]],[[]]],[]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,7),(4,1),(4,2),(5,7),(6,7)],8)
[[],[[],[[],[]],[]],[]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,6,4,5,7,2,8] => ([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)
[[],[[],[[[]]],[]],[]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,2),(5,3),(7,6)],8)
[[],[[],[[],[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,7,4,5,6,2,8] => ([(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,2),(6,1),(6,4)],8)
[[],[[[]],[],[[]]],[]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
[[],[[[]],[[]],[]],[]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,4,3,6,5,7,2,8] => ([(0,1),(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[],[[[],[]],[],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,5,3,4,6,7,2,8] => ([(0,3),(0,4),(0,5),(1,7),(2,6),(3,7),(4,6),(5,1),(7,2)],8)
[[],[[[[]]],[],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(3,7),(4,7),(5,6),(7,1)],8)
[[],[[[],[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,3,4,5,6,2,8] => ([(0,2),(0,3),(0,6),(1,7),(2,7),(3,7),(4,5),(5,1),(6,4)],8)
[[],[[[],[[]],[]]],[]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,7,3,5,4,6,2,8] => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(6,7)],8)
[[],[[[],[[[]]]]],[]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,7,3,6,5,4,2,8] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2),(6,3)],8)
[[],[[[[[]]],[]]],[]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,7,5,4,3,6,2,8] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[],[[[[],[[]]]]],[]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,7,4,6,5,3,2,8] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1),(6,2)],8)
[[],[[[[[],[]]]]],[]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,7,6,4,5,3,2,8] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,1)],8)
[[],[[[[[[]]]]]],[]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[],[[],[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,2] => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8)
[[],[[],[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => ([(0,3),(0,6),(4,5),(5,7),(6,4),(7,1),(7,2)],8)
[[],[[],[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => ([(0,3),(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2)],8)
[[],[[],[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,8,6,7,2] => ([(0,3),(0,6),(4,7),(5,2),(6,4),(7,1),(7,5)],8)
[[],[[],[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => ([(0,4),(0,6),(5,7),(6,5),(7,1),(7,2),(7,3)],8)
[[],[[],[],[[]],[],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => ([(0,4),(0,5),(1,7),(2,7),(5,6),(6,1),(6,2),(7,3)],8)
[[],[[],[],[[[]]],[]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => ([(0,4),(0,5),(1,7),(2,7),(3,7),(5,6),(6,1),(6,2),(6,3)],8)
[[],[[],[],[[],[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,8,5,6,7,2] => ([(0,3),(0,6),(4,5),(5,2),(6,7),(7,1),(7,4)],8)
[[],[[],[],[[[[]]]]]] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => ([(0,5),(0,6),(6,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[[],[[]],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2),(5,7),(6,7)],8)
[[],[[],[[]],[[[]]]]] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => ([(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,1),(4,2)],8)
[[],[[],[[],[]],[],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,6,4,5,7,8,2] => ([(0,4),(0,6),(1,7),(2,7),(5,2),(6,1),(6,5),(7,3)],8)
[[],[[],[[],[]],[[]]]] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,4,5,8,7,2] => ([(0,3),(0,5),(1,6),(1,7),(2,6),(2,7),(4,2),(5,1),(5,4)],8)
[[],[[],[[[]]],[[]]]] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => ([(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,1),(5,2),(5,3)],8)
[[],[[],[[],[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,7,4,5,6,8,2] => ([(0,3),(0,6),(1,7),(2,7),(4,5),(5,2),(6,1),(6,4)],8)
[[],[[],[[],[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,8,4,5,6,7,2] => ([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8)
[[],[[],[[],[[]],[]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,8,4,6,5,7,2] => ([(0,4),(0,6),(2,7),(3,7),(5,2),(5,3),(6,1),(6,5)],8)
[[],[[],[[],[[],[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,8,4,6,7,5,2] => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8)
[[],[[],[[[]],[],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,8,5,4,6,7,2] => ([(0,5),(0,6),(2,7),(3,7),(6,1),(6,2),(6,3),(7,4)],8)
[[],[[],[[[]],[[]]]]] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,8,5,4,7,6,2] => ([(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(5,1),(5,2),(5,3)],8)
[[],[[],[[[],[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,8,5,6,7,4,2] => ([(0,4),(0,7),(5,6),(6,3),(7,1),(7,2),(7,5)],8)
[[],[[],[[[],[[]]]]]] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,8,5,7,6,4,2] => ([(0,5),(0,7),(6,3),(6,4),(7,1),(7,2),(7,6)],8)
[[],[[],[[[[]],[]]]]] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,8,6,5,7,4,2] => ([(0,5),(0,6),(3,7),(4,7),(6,1),(6,2),(6,3),(6,4)],8)
[[],[[],[[[[],[]]]]]] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,8,7,5,6,4,2] => ([(0,5),(0,7),(6,4),(7,1),(7,2),(7,3),(7,6)],8)
[[],[[],[[[[[]]]]]]] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => ([(0,6),(0,7),(7,1),(7,2),(7,3),(7,4),(7,5)],8)
[[],[[[]],[],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => ([(0,2),(0,3),(0,4),(3,7),(4,7),(5,1),(6,5),(7,6)],8)
[[],[[[]],[],[[],[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,8,6,7,2] => ([(0,3),(0,4),(0,5),(4,7),(5,7),(6,1),(7,2),(7,6)],8)
[[],[[[]],[],[[[]]]]] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => ([(0,4),(0,5),(0,6),(5,7),(6,7),(7,1),(7,2),(7,3)],8)
[[],[[[]],[[]],[],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,1)],8)
[[],[[[]],[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => ([(0,1),(0,2),(0,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[],[[[]],[[],[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,8,5,6,7,2] => ([(0,2),(0,3),(0,4),(3,6),(3,7),(4,6),(4,7),(5,1),(7,5)],8)
[[],[[[]],[[],[[]]]]] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,8,5,7,6,2] => ([(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1),(7,2)],8)
[[],[[[]],[[[]],[]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,8,6,5,7,2] => ([(0,1),(0,2),(0,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[],[[[]],[[[],[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,8,6,7,5,2] => ([(0,2),(0,3),(0,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(7,1)],8)
[[],[[[]],[[[[]]]]]] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => ([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[],[[[],[]],[],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,5,3,4,6,7,8,2] => ([(0,3),(0,4),(0,6),(2,7),(4,7),(5,1),(6,2),(7,5)],8)
[[],[[[[]]],[],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => ([(0,2),(0,3),(0,4),(0,5),(3,7),(4,7),(5,7),(6,1),(7,6)],8)
[[],[[[[]]],[],[[]]]] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => ([(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1),(7,2)],8)
[[],[[[],[]],[[],[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,5,3,4,8,6,7,2] => ([(0,3),(0,4),(0,5),(2,6),(2,7),(4,6),(4,7),(5,2),(7,1)],8)
[[],[[[[]]],[[[]]]]] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[],[[[],[],[]],[[]]]] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,6,3,4,5,8,7,2] => ([(0,2),(0,3),(0,5),(1,6),(1,7),(3,6),(3,7),(4,1),(5,4)],8)
[[],[[[],[[]]],[[]]]] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,6,3,5,4,8,7,2] => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(4,6),(4,7),(5,1),(5,2)],8)
[[],[[[[]],[]],[[]]]] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,6,4,3,5,8,7,2] => ([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[],[[[[],[]]],[[]]]] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,6,4,5,3,8,7,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(3,6),(3,7),(4,6),(4,7),(5,1)],8)
[[],[[[[[]]]],[[]]]] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[],[[[],[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7,3,4,5,6,8,2] => ([(0,2),(0,3),(0,6),(1,7),(3,7),(4,5),(5,1),(6,4)],8)
[[],[[[],[[[]]]],[]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7,3,6,5,4,8,2] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(5,7),(6,1),(6,2),(6,3)],8)
[[],[[[[]],[[]]],[]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,7,4,3,6,5,8,2] => ([(0,1),(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[],[[[[],[]],[]],[]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,7,4,5,3,6,8,2] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(3,7),(4,6),(5,1),(6,7)],8)
[[],[[[[[]]],[]],[]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,7,5,4,3,6,8,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[],[[[[],[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7,4,5,6,3,8,2] => ([(0,2),(0,3),(0,4),(0,6),(1,7),(3,7),(4,7),(5,1),(6,5)],8)
[[],[[[[[[]]]]],[]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,6,5,4,3,8,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[],[[[],[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8,3,4,5,6,7,2] => ([(0,2),(0,3),(0,7),(4,6),(5,4),(6,1),(7,5)],8)
[[],[[[],[],[[],[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,8,3,4,6,7,5,2] => ([(0,3),(0,4),(0,6),(5,2),(6,7),(7,1),(7,5)],8)
[[],[[[],[],[[[]]]]]] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,8,3,4,7,6,5,2] => ([(0,4),(0,5),(0,6),(6,7),(7,1),(7,2),(7,3)],8)
[[],[[[],[[]],[],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,8,3,5,4,6,7,2] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(6,1),(6,2),(7,3)],8)
[[],[[[],[[]],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,8,3,5,4,7,6,2] => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,6),(2,7),(5,1),(5,2)],8)
[[],[[[],[[],[]],[]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,8,3,5,6,4,7,2] => ([(0,3),(0,4),(0,6),(1,7),(2,7),(5,2),(6,1),(6,5)],8)
[[],[[[],[[[]]],[]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,8,3,6,5,4,7,2] => ([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(6,1),(6,2),(6,3)],8)
[[],[[[],[[],[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,8,3,5,6,7,4,2] => ([(0,3),(0,4),(0,7),(5,6),(6,2),(7,1),(7,5)],8)
[[],[[[],[[],[[]]]]]] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,8,3,5,7,6,4,2] => ([(0,4),(0,5),(0,7),(6,2),(6,3),(7,1),(7,6)],8)
[[],[[[],[[[],[]]]]]] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,8,3,7,5,6,4,2] => ([(0,4),(0,5),(0,7),(6,3),(7,1),(7,2),(7,6)],8)
[[],[[[],[[[[]]]]]]] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8,3,7,6,5,4,2] => ([(0,5),(0,6),(0,7),(7,1),(7,2),(7,3),(7,4)],8)
[[],[[[[]],[],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,8,4,3,5,6,7,2] => ([(0,2),(0,3),(0,4),(0,5),(4,7),(5,7),(6,1),(7,6)],8)
[[],[[[[]],[],[[]]]]] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,8,4,3,5,7,6,2] => ([(0,3),(0,4),(0,5),(0,6),(5,7),(6,7),(7,1),(7,2)],8)
[[],[[[[]],[[]],[]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,8,4,3,6,5,7,2] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[],[[[[]],[[],[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,8,4,3,6,7,5,2] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7),(7,1)],8)
[[],[[[[],[]],[],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,8,4,5,3,6,7,2] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(5,7),(6,1),(7,2)],8)
[[],[[[[[]]],[],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,8,5,4,3,6,7,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7),(7,1)],8)
[[],[[[[[]]],[[]]]]] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,8,5,4,3,7,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[],[[[[],[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,8,4,5,6,3,7,2] => ([(0,2),(0,3),(0,4),(0,6),(1,7),(4,7),(5,1),(6,5)],8)
[[],[[[[],[[]]],[]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,8,4,6,5,3,7,2] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(5,7),(6,1),(6,2)],8)
[[],[[[[[]],[]],[]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,8,5,4,6,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(3,7),(4,6),(5,6),(6,7)],8)
[[],[[[[[],[]]],[]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,8,6,4,5,3,7,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(4,7),(5,7),(6,1)],8)
[[],[[[[[[]]]],[]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,8,6,5,4,3,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(3,7),(4,7),(5,7),(6,7)],8)
[[],[[[[],[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,8,4,5,6,7,3,2] => ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8)
[[],[[[[],[[]],[]]]]] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,8,4,6,5,7,3,2] => ([(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(6,1),(6,2)],8)
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,8,4,7,6,5,3,2] => ([(0,4),(0,5),(0,6),(0,7),(7,1),(7,2),(7,3)],8)
[[],[[[[[]],[],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,8,5,4,6,7,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(5,7),(6,7),(7,1)],8)
[[],[[[[[]],[[]]]]]] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,8,5,4,7,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(4,7),(5,6),(5,7)],8)
[[],[[[[[],[]],[]]]]] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,8,6,4,5,7,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(5,7),(6,1)],8)
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,8,6,5,4,7,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(4,7),(5,7),(6,7)],8)
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8,7,4,5,6,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8)
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,8,7,4,6,5,3,2] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(7,1),(7,2)],8)
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,8,7,5,4,6,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(5,7),(6,7)],8)
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,8,7,5,6,4,3,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8)
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)],8)
[[[]],[],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[[[]],[],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => ([(0,7),(1,7),(4,6),(5,4),(6,2),(6,3),(7,5)],8)
[[[]],[],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,3,4,5,7,6,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,2),(5,3),(7,4)],8)
[[[]],[],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,3,4,5,7,8,6] => ([(0,7),(1,7),(4,3),(5,6),(6,2),(6,4),(7,5)],8)
[[[]],[],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => ([(0,7),(1,7),(5,6),(6,2),(6,3),(6,4),(7,5)],8)
[[[]],[],[],[[]],[],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,3,4,6,5,7,8] => ([(0,6),(1,6),(3,7),(4,7),(5,3),(5,4),(6,5),(7,2)],8)
[[[]],[],[],[[]],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,3,4,6,5,8,7] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(7,4)],8)
[[[]],[],[],[[],[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,3,4,6,7,8,5] => ([(0,7),(1,7),(4,5),(5,3),(6,2),(6,4),(7,6)],8)
[[[]],[],[],[[[]],[]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,4,7,6,8,5] => ([(0,7),(1,7),(3,6),(4,6),(5,2),(5,3),(5,4),(7,5)],8)
[[[]],[],[],[[[],[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,8,6,7,5] => ([(0,7),(1,7),(5,4),(6,2),(6,3),(6,5),(7,6)],8)
[[[]],[],[],[[[[]]]]] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => ([(0,7),(1,7),(6,2),(6,3),(6,4),(6,5),(7,6)],8)
[[[]],[],[[]],[],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,3,5,4,6,7,8] => ([(0,7),(1,7),(3,6),(4,6),(5,2),(6,5),(7,3),(7,4)],8)
[[[]],[],[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4,6,8,7] => ([(0,7),(1,7),(2,6),(3,6),(6,4),(6,5),(7,2),(7,3)],8)
[[[]],[],[[]],[[],[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => ([(0,7),(1,7),(3,5),(3,6),(4,5),(4,6),(6,2),(7,3),(7,4)],8)
[[[]],[],[[]],[[[]]]] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(7,2),(7,3)],8)
[[[]],[],[[],[]],[[]]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,3),(7,2),(7,4)],8)
[[[]],[],[[[]]],[[]]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => ([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[[]],[],[[],[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,3,5,6,7,8,4] => ([(0,7),(1,7),(4,5),(5,2),(6,4),(7,3),(7,6)],8)
[[[]],[],[[],[[],[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,3,5,8,6,7,4] => ([(0,7),(1,7),(5,3),(6,2),(6,5),(7,4),(7,6)],8)
[[[]],[],[[[]],[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => ([(0,7),(1,7),(3,5),(3,6),(4,5),(4,6),(7,2),(7,3),(7,4)],8)
[[[]],[],[[[],[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,8,5,6,7,4] => ([(0,7),(1,7),(5,2),(6,5),(7,3),(7,4),(7,6)],8)
[[[]],[],[[[],[[]]]]] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,8,5,7,6,4] => ([(0,7),(1,7),(6,2),(6,3),(7,4),(7,5),(7,6)],8)
[[[]],[],[[[[]],[]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,3,8,6,5,7,4] => ([(0,7),(1,7),(4,6),(5,6),(7,2),(7,3),(7,4),(7,5)],8)
[[[]],[],[[[[],[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,8,6,7,5,4] => ([(0,7),(1,7),(6,2),(7,3),(7,4),(7,5),(7,6)],8)
[[[]],[],[[[[[]]]]]] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => ([(0,7),(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[[]],[[]],[],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5,6,7,8] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,7),(6,7),(7,3)],8)
[[[]],[[]],[],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,4,3,5,6,8,7] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,4),(6,5),(7,5)],8)
[[[]],[[]],[],[[],[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => ([(0,5),(0,6),(1,5),(1,6),(4,3),(5,7),(6,7),(7,2),(7,4)],8)
[[[]],[[]],[],[[[]]]] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => ([(0,5),(0,6),(1,5),(1,6),(5,7),(6,7),(7,2),(7,3),(7,4)],8)
[[[]],[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,5,7,8] => ([(0,6),(0,7),(1,6),(1,7),(3,2),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[],[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,3,6,7,5,8] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,2),(5,4),(6,3),(6,5),(7,3),(7,5)],8)
[[[]],[[]],[[],[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,3,6,7,8,5] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[],[[]]]] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => ([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[]],[[[]],[]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,4,3,7,6,8,5] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,3),(6,2),(6,4),(6,5),(7,2),(7,4),(7,5)],8)
[[[]],[[]],[[[],[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,8,6,7,5] => ([(0,6),(0,7),(1,6),(1,7),(5,2),(6,3),(6,4),(6,5),(7,3),(7,4),(7,5)],8)
[[[]],[[]],[[[[]]]]] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => ([(0,6),(0,7),(1,6),(1,7),(6,2),(6,3),(6,4),(6,5),(7,2),(7,3),(7,4),(7,5)],8)
[[[]],[[],[]],[],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,4,5,3,6,7,8] => ([(0,6),(0,7),(1,6),(1,7),(3,5),(4,2),(5,4),(6,5),(7,3)],8)
[[[]],[[[]]],[],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(4,7),(5,7),(6,7),(7,2)],8)
[[[]],[[],[]],[],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => ([(0,5),(0,6),(1,5),(1,6),(4,7),(5,7),(6,4),(7,2),(7,3)],8)
[[[]],[[[]]],[],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,1,5,4,3,6,8,7] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7),(7,2),(7,3)],8)
[[[]],[[[]]],[[]],[]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,5,4,3,7,6,8] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,2),(7,2)],8)
[[[]],[[],[]],[[[]]]] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(6,2),(7,3),(7,4),(7,5)],8)
[[[]],[[[]]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[]],[[],[[]]],[],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(6,3),(7,4)],8)
[[[]],[[],[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,4),(3,5),(6,2),(7,4),(7,5)],8)
[[[]],[[],[[]]],[[]]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => ([(0,4),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[[]],[[[]],[]],[[]]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => ([(0,4),(0,5),(0,7),(1,4),(1,5),(1,7),(4,6),(5,6),(6,2),(6,3),(7,2),(7,3)],8)
[[[]],[[[],[]]],[[]]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,1,6,4,5,3,8,7] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2)],8)
[[[]],[[[[]]]],[[]]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,1,6,5,4,3,8,7] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[]],[[],[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,2),(6,5),(7,3)],8)
[[[]],[[[]],[],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,2),(5,4),(6,3),(7,3)],8)
[[[]],[[[[[]]]]],[]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[]],[[],[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,4,5,6,7,8,3] => ([(0,6),(0,7),(1,6),(1,7),(3,5),(4,3),(5,2),(7,4)],8)
[[[]],[[],[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => ([(0,6),(0,7),(1,6),(1,7),(4,5),(5,2),(5,3),(7,4)],8)
[[[]],[[],[],[[],[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,8,6,7,3] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(5,4),(7,5)],8)
[[[]],[[],[],[[[]]]]] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => ([(0,6),(0,7),(1,6),(1,7),(5,2),(5,3),(5,4),(7,5)],8)
[[[]],[[],[[]],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(7,2),(7,3)],8)
[[[]],[[],[[[]]],[]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => ([(0,5),(0,6),(1,5),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4)],8)
[[[]],[[],[[],[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,8,5,6,7,3] => ([(0,6),(0,7),(1,6),(1,7),(4,5),(5,3),(7,2),(7,4)],8)
[[[]],[[],[[],[[]]]]] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,8,5,7,6,3] => ([(0,6),(0,7),(1,6),(1,7),(5,3),(5,4),(7,2),(7,5)],8)
[[[]],[[],[[[]],[]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,1,4,8,6,5,7,3] => ([(0,6),(0,7),(1,6),(1,7),(3,5),(4,5),(7,2),(7,3),(7,4)],8)
[[[]],[[],[[[],[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,8,6,7,5,3] => ([(0,6),(0,7),(1,6),(1,7),(5,4),(7,2),(7,3),(7,5)],8)
[[[]],[[],[[[[]]]]]] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => ([(0,6),(0,7),(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[[[]],[[[]],[],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(4,2),(6,4),(7,4)],8)
[[[]],[[[]],[],[[]]]] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(4,3),(6,4),(7,4)],8)
[[[]],[[[]],[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => ([(0,3),(0,6),(0,7),(1,3),(1,6),(1,7),(4,2),(5,2),(6,4),(6,5),(7,4),(7,5)],8)
[[[]],[[[]],[[],[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,8,6,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(6,3),(6,4),(7,3),(7,4)],8)
[[[]],[[[]],[[[]]]]] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(6,2),(6,3),(6,4),(7,2),(7,3),(7,4)],8)
[[[]],[[[],[]],[],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,6,4,5,7,8,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(6,3),(7,4)],8)
[[[]],[[[],[]],[[]]]] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,6,4,5,8,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(6,2),(7,3),(7,4)],8)
[[[]],[[[[]]],[[]]]] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[]],[[[],[[]]],[]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,7,4,6,5,8,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,7),(3,7),(5,7),(6,2),(6,3)],8)
[[[]],[[[[],[]]],[]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,7,5,6,4,8,3] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,7),(4,7),(5,7),(6,2)],8)
[[[]],[[[[[]]]],[]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,1,7,6,5,4,8,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[]],[[[],[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,8,4,5,6,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(3,4),(4,2),(7,3)],8)
[[[]],[[[],[],[[]]]]] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,8,4,5,7,6,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,2),(4,3),(7,4)],8)
[[[]],[[[],[[]],[]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,8,4,6,5,7,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,4),(7,2),(7,3)],8)
[[[]],[[[],[[],[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,8,4,6,7,5,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(4,3),(7,2),(7,4)],8)
[[[]],[[[],[[[]]]]]] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,8,4,7,6,5,3] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[[[]],[[[[]],[],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,8,5,4,6,7,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(3,2),(6,3),(7,3)],8)
[[[]],[[[[]],[[]]]]] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,8,5,4,7,6,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(6,2),(6,3),(7,2),(7,3)],8)
[[[]],[[[[],[]],[]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,8,5,6,4,7,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(6,2),(7,3)],8)
[[[]],[[[[[]]],[]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,8,6,5,4,7,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(4,7),(5,7),(6,7)],8)
[[[]],[[[[],[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,8,5,6,7,4,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(7,2)],8)
[[[]],[[[[],[[]]]]]] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,8,5,7,6,4,3] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8)
[[[]],[[[[[]],[]]]]] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,8,6,5,7,4,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(6,2),(7,2)],8)
[[[]],[[[[[],[]]]]]] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,8,7,5,6,4,3] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[[]],[[[[[[]]]]]]] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[[],[]],[],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[[[[]]],[],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => ([(0,7),(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[],[]],[],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => ([(0,7),(1,4),(4,7),(5,6),(6,2),(6,3),(7,5)],8)
[[[[]]],[],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,2,1,4,5,6,8,7] => ([(0,7),(1,7),(2,7),(5,6),(6,3),(6,4),(7,5)],8)
[[[],[]],[],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => ([(0,7),(1,2),(2,7),(3,6),(4,6),(5,3),(5,4),(7,5)],8)
[[[[]]],[],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,2,1,4,5,7,6,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(7,3)],8)
[[[],[]],[],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => ([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8)
[[[[]]],[],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,2,1,4,5,7,8,6] => ([(0,7),(1,7),(2,7),(5,4),(6,3),(6,5),(7,6)],8)
[[[[]]],[],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => ([(0,7),(1,7),(2,7),(6,3),(6,4),(6,5),(7,6)],8)
[[[],[]],[],[[]],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => ([(0,7),(1,2),(2,7),(3,5),(3,6),(4,5),(4,6),(7,3),(7,4)],8)
[[[],[]],[],[[],[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => ([(0,7),(1,2),(2,7),(3,6),(4,6),(5,4),(7,3),(7,5)],8)
[[[[]]],[],[[[]]],[]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => ([(0,6),(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[],[]],[],[[],[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => ([(0,7),(1,3),(3,7),(5,2),(6,5),(7,4),(7,6)],8)
[[[],[]],[],[[[]],[]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => ([(0,7),(1,3),(3,7),(4,6),(5,6),(7,2),(7,4),(7,5)],8)
[[[],[]],[],[[[[]]]]] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => ([(0,7),(1,2),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[[]]],[],[[],[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => ([(0,7),(1,7),(2,7),(5,3),(6,5),(7,4),(7,6)],8)
[[[[]]],[],[[],[[]]]] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => ([(0,7),(1,7),(2,7),(6,3),(6,4),(7,5),(7,6)],8)
[[[[]]],[],[[[]],[]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,2,1,4,7,6,8,5] => ([(0,7),(1,7),(2,7),(4,6),(5,6),(7,3),(7,4),(7,5)],8)
[[[[]]],[],[[[],[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,8,6,7,5] => ([(0,7),(1,7),(2,7),(6,3),(7,4),(7,5),(7,6)],8)
[[[[]]],[],[[[[]]]]] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => ([(0,7),(1,7),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[],[]],[[]],[],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => ([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(6,5),(7,5)],8)
[[[[]]],[[]],[],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,5,4,6,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(5,3),(6,5),(7,5)],8)
[[[],[]],[[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => ([(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[[]]],[[]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,1,5,4,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(6,3),(6,4),(7,3),(7,4)],8)
[[[],[]],[[],[]],[],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => ([(0,5),(0,7),(1,2),(2,5),(2,7),(3,6),(5,6),(6,4),(7,3)],8)
[[[],[]],[[[]]],[],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => ([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7),(7,2)],8)
[[[[]]],[[],[]],[],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(6,5),(7,3)],8)
[[[[]]],[[[]]],[],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,4)],8)
[[[],[]],[[[]]],[[]]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[]]],[[[]]],[[]]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,2,1,6,5,4,8,7] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(5,3),(5,4),(6,3),(6,4),(7,3),(7,4)],8)
[[[],[]],[[],[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => ([(0,6),(0,7),(1,3),(2,5),(3,6),(3,7),(4,2),(6,5),(7,4)],8)
[[[],[]],[[[]],[]],[]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => ([(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(5,4),(6,4),(7,3)],8)
[[[],[]],[[[],[]]],[]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,7,5,6,4,8] => ([(0,3),(1,4),(1,5),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,2)],8)
[[[[]]],[[],[[]]],[]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[]]],[[[]],[]],[]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,2,1,6,5,7,4,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(5,4),(6,3),(7,3)],8)
[[[[]]],[[[],[]]],[]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,2,1,7,5,6,4,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(5,3),(6,4),(7,4)],8)
[[[[]]],[[[[]]]],[]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[],[]],[[],[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => ([(0,6),(0,7),(1,3),(3,6),(3,7),(4,2),(5,4),(7,5)],8)
[[[],[]],[[],[[]],[]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => ([(0,6),(0,7),(1,2),(2,6),(2,7),(3,5),(4,5),(7,3),(7,4)],8)
[[[],[]],[[[]],[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => ([(0,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[[],[]],[[[[]]],[]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[[],[]],[[[],[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,8,5,6,7,4] => ([(0,5),(0,6),(0,7),(1,3),(3,5),(3,6),(3,7),(4,2),(7,4)],8)
[[[],[]],[[[[],[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,8,6,7,5,4] => ([(0,3),(1,4),(1,5),(1,6),(1,7),(3,4),(3,5),(3,6),(3,7),(7,2)],8)
[[[],[]],[[[[[]]]]]] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[[]]],[[],[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,5,6,7,8,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[[[[]]],[[],[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(7,3)],8)
[[[[]]],[[],[[]],[]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(7,3),(7,4)],8)
[[[[]]],[[],[[],[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,8,6,7,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(4,5),(7,3),(7,4)],8)
[[[[]]],[[],[[[]]]]] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[[[[]]],[[[]],[],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(6,4),(7,4)],8)
[[[[]]],[[[]],[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[[[]]],[[[],[]],[]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,7,5,6,8,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(6,4),(7,3)],8)
[[[[]]],[[[[]]],[]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,2,1,7,6,5,8,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(5,3),(6,3),(7,3)],8)
[[[[]]],[[[],[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,8,5,6,7,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(7,3)],8)
[[[[]]],[[[],[[]]]]] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,8,5,7,6,4] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[[[[]]],[[[[]],[]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,8,6,5,7,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[[[[]]],[[[[],[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,8,6,7,5,4] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[[[[]]],[[[[[]]]]]] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[],[],[]],[],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[[[],[[]]],[],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => ([(0,7),(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[[[]],[]],[],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[[[[],[]]],[],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,2,3,1,5,6,7,8] => ([(0,7),(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[]]]],[],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[],[],[]],[],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => ([(0,7),(1,5),(4,7),(5,4),(6,2),(6,3),(7,6)],8)
[[[[]],[]],[],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => ([(0,7),(1,6),(2,6),(3,4),(3,5),(6,7),(7,3)],8)
[[[[[]]]],[],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,3,2,1,5,6,8,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[],[],[]],[],[[]],[]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => ([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(7,3),(7,4)],8)
[[[[]],[]],[],[[]],[]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => ([(0,6),(1,5),(2,5),(3,7),(4,7),(5,6),(6,3),(6,4)],8)
[[[[],[]]],[],[[]],[]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,2,3,1,5,7,6,8] => ([(0,7),(1,7),(2,3),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[[[]]]],[],[[]],[]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,3,2,1,5,7,6,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[],[],[]],[],[[],[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => ([(0,7),(1,5),(3,7),(5,3),(6,2),(7,4),(7,6)],8)
[[[],[],[]],[],[[[]]]] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => ([(0,7),(1,6),(2,7),(6,2),(7,3),(7,4),(7,5)],8)
[[[],[[]]],[],[[[]]]] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => ([(0,7),(1,2),(1,3),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[[]],[]],[],[[],[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => ([(0,7),(1,6),(2,6),(4,5),(6,7),(7,3),(7,4)],8)
[[[[]],[]],[],[[[]]]] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => ([(0,7),(1,6),(2,6),(6,7),(7,3),(7,4),(7,5)],8)
[[[[],[]]],[],[[],[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,2,3,1,5,7,8,6] => ([(0,7),(1,7),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[[[[],[]]],[],[[[]]]] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,2,3,1,5,8,7,6] => ([(0,7),(1,7),(2,3),(3,7),(7,4),(7,5),(7,6)],8)
[[[[[]]]],[],[[],[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,3,2,1,5,7,8,6] => ([(0,7),(1,7),(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[[[[[]]]],[],[[[]]]] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => ([(0,7),(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[],[],[]],[[]],[],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => ([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(5,7),(6,7),(7,2)],8)
[[[],[[]]],[[]],[],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => ([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[]],[]],[[]],[],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => ([(0,7),(1,7),(2,5),(2,6),(4,3),(5,4),(6,4),(7,5),(7,6)],8)
[[[[],[]]],[[]],[],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,3,1,6,5,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[[]]]],[[]],[],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,3,2,1,6,5,7,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[],[],[]],[[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => ([(0,2),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[],[[]]],[[]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => ([(0,6),(0,7),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[]],[]],[[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => ([(0,7),(1,7),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6)],8)
[[[[],[]]],[[]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,3,1,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[[]]]],[[]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,3,2,1,6,5,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[],[],[]],[[],[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => ([(0,6),(0,7),(1,4),(2,6),(2,7),(3,5),(4,2),(6,5),(7,3)],8)
[[[],[],[]],[[[]]],[]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => ([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[]],[]],[[],[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => ([(0,7),(1,7),(2,4),(2,6),(3,5),(4,3),(6,5),(7,4),(7,6)],8)
[[[[]],[]],[[[]]],[]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[],[]]],[[[]]],[]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,2,3,1,7,6,5,8] => ([(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[[[[[]]]],[[],[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,2,1,6,7,5,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[[[[[]]]],[[[]]],[]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8)
[[[],[],[]],[[],[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => ([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8)
[[[],[],[]],[[],[[]]]] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => ([(0,6),(0,7),(1,5),(4,6),(4,7),(5,4),(7,2),(7,3)],8)
[[[],[],[]],[[[]],[]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => ([(0,2),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[],[],[]],[[[],[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,8,6,7,5] => ([(0,5),(0,6),(0,7),(1,4),(3,5),(3,6),(3,7),(4,3),(7,2)],8)
[[[],[],[]],[[[[]]]]] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => ([(0,2),(1,4),(1,5),(1,6),(1,7),(2,3),(3,4),(3,5),(3,6),(3,7)],8)
[[[],[[]]],[[],[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => ([(0,6),(0,7),(1,3),(1,4),(3,6),(3,7),(4,6),(4,7),(5,2),(7,5)],8)
[[[],[[]]],[[],[[]]]] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => ([(0,6),(0,7),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2),(7,3)],8)
[[[],[[]]],[[[]],[]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => ([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[],[[]]],[[[[]]]]] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[]],[]],[[],[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => ([(0,6),(0,7),(1,5),(2,5),(3,4),(5,6),(5,7),(7,3)],8)
[[[[]],[]],[[],[[]]]] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => ([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[[[[]],[]],[[[]],[]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(5,3),(6,3),(7,4),(7,5),(7,6)],8)
[[[[]],[]],[[[],[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,8,6,7,5] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(6,3),(7,4),(7,5),(7,6)],8)
[[[[]],[]],[[[[]]]]] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(7,3),(7,4),(7,5),(7,6)],8)
[[[[],[]]],[[],[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,2,3,1,6,7,8,5] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[[[[],[]]],[[],[[]]]] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,2,3,1,6,8,7,5] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[[[[],[]]],[[[]],[]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,2,3,1,7,6,8,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[[],[]]],[[[],[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,2,3,1,8,6,7,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8)
[[[[],[]]],[[[[]]]]] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,2,3,1,8,7,6,5] => ([(0,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[[]]]],[[],[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,3,2,1,6,7,8,5] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[[]]]],[[],[[]]]] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[[[]]]],[[[]],[]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,2,1,7,6,8,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[[[]]]],[[[],[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,8,6,7,5] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[[[]]]],[[[[]]]]] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[],[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[[[],[],[[]]],[],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => ([(0,7),(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[[],[[]],[]],[],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => ([(0,7),(1,3),(1,4),(3,6),(4,6),(5,2),(6,7),(7,5)],8)
[[[],[[],[]]],[],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,5,3,4,1,6,7,8] => ([(0,7),(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[[],[[[]]]],[],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => ([(0,7),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[[[]],[],[]],[],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[[[[]],[[]]],[],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[[[[],[]],[]],[],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [4,2,3,5,1,6,7,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[[[[[]]],[]],[],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(6,4),(7,6)],8)
[[[[],[],[]]],[],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,2,3,4,1,6,7,8] => ([(0,7),(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[],[[]]]],[],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,2,4,3,1,6,7,8] => ([(0,7),(1,7),(2,4),(2,5),(4,7),(5,7),(6,3),(7,6)],8)
[[[[[]],[]]],[],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,3,2,4,1,6,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[[],[]]]],[],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,3,4,2,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[[]]]]],[],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[],[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => ([(0,7),(1,6),(2,7),(5,2),(6,5),(7,3),(7,4)],8)
[[[],[],[[]]],[],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => ([(0,7),(1,6),(2,7),(3,7),(6,2),(6,3),(7,4),(7,5)],8)
[[[],[[]],[]],[],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => ([(0,7),(1,4),(1,5),(4,6),(5,6),(6,7),(7,2),(7,3)],8)
[[[],[[[]]]],[],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => ([(0,7),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[]],[[]]],[],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[[[[],[]],[]],[],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [4,2,3,5,1,6,8,7] => ([(0,7),(1,6),(2,3),(3,7),(6,4),(6,5),(7,6)],8)
[[[[],[],[]]],[],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,2,3,4,1,6,8,7] => ([(0,7),(1,7),(2,6),(3,7),(6,3),(7,4),(7,5)],8)
[[[[],[[]]]],[],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,2,4,3,1,6,8,7] => ([(0,7),(1,7),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[]],[]]],[],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,3,2,4,1,6,8,7] => ([(0,7),(1,7),(2,6),(3,6),(6,7),(7,4),(7,5)],8)
[[[[[],[]]]],[],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,3,4,2,1,6,8,7] => ([(0,7),(1,7),(2,7),(3,4),(4,7),(7,5),(7,6)],8)
[[[[[[]]]]],[],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,4,3,2,1,6,8,7] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[],[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => ([(0,6),(0,7),(1,4),(2,6),(2,7),(3,2),(4,3),(6,5),(7,5)],8)
[[[],[],[[]]],[[]],[]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => ([(0,6),(0,7),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(4,3),(6,5),(7,5)],8)
[[[],[[]],[]],[[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => ([(0,2),(0,3),(1,5),(1,6),(2,7),(3,7),(5,4),(6,4),(7,5),(7,6)],8)
[[[],[[[]]]],[[]],[]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[]],[[]]],[[]],[]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => ([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[],[[]]]],[[]],[]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,4,3,1,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[]],[]]],[[]],[]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,3,2,4,1,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[[]]]]],[[]],[]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,4,3,2,1,7,6,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[],[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => ([(0,6),(0,7),(1,5),(3,6),(3,7),(4,3),(5,4),(7,2)],8)
[[[],[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,4),(2,5),(2,6),(2,7),(3,2),(4,3)],8)
[[[],[],[[]]],[[[]]]] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3)],8)
[[[],[[]],[]],[[],[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => ([(0,6),(0,7),(1,3),(1,4),(3,5),(4,5),(5,6),(5,7),(7,2)],8)
[[[],[[]],[]],[[[]]]] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => ([(0,2),(0,3),(1,4),(1,5),(1,6),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[],[[],[]]],[[[]]]] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,5,3,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[[[],[[[]]]],[[],[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[[[],[[[]]]],[[[]]]] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[]],[],[]],[[[]]]] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(7,3)],8)
[[[[]],[[]]],[[],[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[[[[]],[[]]],[[[]]]] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[],[]],[]],[[],[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [4,2,3,5,1,7,8,6] => ([(0,7),(1,5),(1,6),(2,4),(4,7),(6,3),(7,5),(7,6)],8)
[[[[],[]],[]],[[[]]]] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [4,2,3,5,1,8,7,6] => ([(0,3),(1,7),(2,4),(2,5),(2,6),(3,7),(7,4),(7,5),(7,6)],8)
[[[[[]]],[]],[[],[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(6,4),(7,5),(7,6)],8)
[[[[[]]],[]],[[[]]]] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(7,4),(7,5),(7,6)],8)
[[[[],[],[]]],[[],[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [5,2,3,4,1,7,8,6] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(4,5),(5,6),(5,7),(7,3)],8)
[[[[],[],[]]],[[[]]]] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [5,2,3,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(3,4),(4,5),(4,6),(4,7)],8)
[[[[],[[]]]],[[[]]]] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [5,2,4,3,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[[]],[]]],[[[]]]] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,3,2,4,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(3,4),(4,5),(4,6),(4,7)],8)
[[[[[],[]]]],[[],[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,3,4,2,1,7,8,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[[[[[],[]]]],[[[]]]] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,3,4,2,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7)],8)
[[[[[[]]]]],[[],[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,4,3,2,1,7,8,6] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[[]]]]],[[[]]]] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[],[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[[[],[],[],[[]]],[],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => ([(0,7),(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[[],[],[[]],[]],[],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => ([(0,7),(1,5),(3,6),(4,6),(5,3),(5,4),(6,7),(7,2)],8)
[[[],[],[[],[]]],[],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,6,4,5,1,7,8] => ([(0,7),(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[[[],[],[[[]]]],[],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => ([(0,7),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[[[],[[]],[[]]],[],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => ([(0,7),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[[[],[[],[],[]]],[],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,6,3,4,5,1,7,8] => ([(0,7),(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[[[],[[[],[]]]],[],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,6,4,5,3,1,7,8] => ([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[[[]],[],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[[[[],[]],[],[]],[],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [4,2,3,5,6,1,7,8] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[[[[[]]],[],[]],[],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(6,5),(7,4)],8)
[[[[[]]],[[]]],[],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[[],[],[]],[]],[],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [5,2,3,4,6,1,7,8] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[[[[],[[]]],[]],[],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [5,2,4,3,6,1,7,8] => ([(0,7),(1,6),(2,3),(2,4),(3,7),(4,7),(6,5),(7,6)],8)
[[[[[]],[]],[]],[],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [5,3,2,4,6,1,7,8] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[[[[[[]]]],[]],[],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,4,3,2,6,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,6)],8)
[[[[],[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [6,2,3,4,5,1,7,8] => ([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[],[],[[]]]],[],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [6,2,3,5,4,1,7,8] => ([(0,7),(1,7),(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[[[[],[[],[]]]],[],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [6,2,4,5,3,1,7,8] => ([(0,7),(1,7),(2,4),(2,6),(3,7),(4,7),(6,3),(7,5)],8)
[[[[],[[[]]]]],[],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [6,2,5,4,3,1,7,8] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[]],[[]]]],[],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [6,3,2,5,4,1,7,8] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[[[[]]],[]]],[],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,4,3,2,5,1,7,8] => ([(0,7),(1,7),(2,6),(3,6),(4,6),(6,7),(7,5)],8)
[[[[[[],[]]]]],[],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,5,3,4,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[[[[[]]]]]],[],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[],[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => ([(0,6),(0,7),(1,5),(2,6),(2,7),(3,4),(4,2),(5,3)],8)
[[[],[],[[],[]]],[[]]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,6,4,5,1,8,7] => ([(0,6),(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4)],8)
[[[],[],[[[]]]],[[]]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => ([(0,6),(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3),(5,4)],8)
[[[],[[]],[],[]],[[]]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => ([(0,5),(0,6),(1,2),(1,3),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[],[[]],[[]]],[[]]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => ([(0,6),(0,7),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[[[]]],[]],[[]]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[],[[],[[]]]],[[]]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,3,5,4,1,8,7] => ([(0,6),(0,7),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[[],[[[]],[]]],[[]]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,6,4,3,5,1,8,7] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[[],[[[[]]]]],[[]]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[]],[[]],[]],[[]]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[[[[]],[[],[]]],[[]]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,6,4,5,1,8,7] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,3)],8)
[[[[]],[[[]]]],[[]]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[]],[],[]],[[]]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [4,2,3,5,6,1,8,7] => ([(0,7),(1,5),(1,6),(2,3),(3,7),(4,5),(4,6),(7,4)],8)
[[[[[]]],[],[]],[[]]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(7,4)],8)
[[[[[]]],[[]]],[[]]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => ([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[],[]],[]],[[]]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2,3,4,6,1,8,7] => ([(0,5),(1,6),(1,7),(2,3),(3,4),(4,5),(5,6),(5,7)],8)
[[[[],[[]]],[]],[[]]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2,4,3,6,1,8,7] => ([(0,7),(1,5),(1,6),(2,3),(2,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[]],[]],[]],[[]]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [5,3,2,4,6,1,8,7] => ([(0,4),(1,4),(2,7),(3,5),(3,6),(4,7),(7,5),(7,6)],8)
[[[[[],[]]],[]],[[]]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,3,4,2,6,1,8,7] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(4,7),(7,5),(7,6)],8)
[[[[[[]]]],[]],[[]]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[[[[],[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [6,2,3,4,5,1,8,7] => ([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[[[[],[],[[]]]],[[]]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [6,2,3,5,4,1,8,7] => ([(0,3),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[[]],[]]],[[]]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [6,2,4,3,5,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,5),(4,5),(5,6),(5,7)],8)
[[[[],[[[]]]]],[[]]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,2,5,4,3,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[]],[[]]]],[[]]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [6,3,2,5,4,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[],[]],[]]],[[]]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [6,3,4,2,5,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[[]]],[]]],[[]]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,4,3,2,5,1,8,7] => ([(0,5),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[],[],[]]]],[[]]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [6,3,4,5,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[],[[]]]]],[[]]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,3,5,4,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[]],[]]]],[[]]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,4,3,5,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(4,5),(5,6),(5,7)],8)
[[[[[[],[]]]]],[[]]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,5,3,4,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[[[[[]]]]]],[[]]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,5,4,3,2,1,8,7] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[[[],[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => ([(0,7),(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[[[],[],[],[[]],[]],[]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => ([(0,7),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
[[[],[],[],[[],[]]],[]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,7,5,6,1,8] => ([(0,7),(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[[[],[],[],[[[]]]],[]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => ([(0,7),(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[],[],[[]],[],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => ([(0,6),(1,5),(2,7),(3,7),(4,6),(5,2),(5,3),(7,4)],8)
[[[],[],[[[]],[]]],[]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,7,5,4,6,1,8] => ([(0,7),(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[[],[],[[[],[]]]],[]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,7,5,6,4,1,8] => ([(0,7),(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[[],[],[[[[]]]]],[]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => ([(0,7),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[],[[]],[[]],[]],[]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => ([(0,2),(0,3),(1,4),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[],[[],[]],[],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,5,3,4,6,7,1,8] => ([(0,6),(1,3),(1,5),(2,7),(3,7),(4,6),(5,2),(7,4)],8)
[[[],[[[]]],[],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => ([(0,6),(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[],[[],[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,7,3,4,5,6,1,8] => ([(0,7),(1,3),(1,6),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[[[],[[],[[[]]]]],[]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,7,3,6,5,4,1,8] => ([(0,7),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4)],8)
[[[],[[[],[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,7,4,5,6,3,1,8] => ([(0,7),(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[[[],[[[],[[]]]]],[]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,7,4,6,5,3,1,8] => ([(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[[[],[[[[[]]]]]],[]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[[]],[],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[[[[]],[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,3),(5,4),(6,3),(6,4)],8)
[[[[]],[[[]]],[]],[]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => ([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7),(7,3)],8)
[[[[]],[[],[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,7,4,5,6,1,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,4),(4,7),(5,7),(6,3)],8)
[[[[]],[[],[[]]]],[]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,7,4,6,5,1,8] => ([(0,7),(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[]],[[[]],[]]],[]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,7,5,4,6,1,8] => ([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,3),(6,3)],8)
[[[[]],[[[],[]]]],[]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,7,5,6,4,1,8] => ([(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[]],[[[[]]]]],[]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[[],[]],[],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,2,3,5,6,7,1,8] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[[[[[]]],[],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[[[[[]]],[],[[]]],[]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => ([(0,7),(1,6),(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[[[]]],[[]],[]],[]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,4),(7,4)],8)
[[[[],[]],[[],[]]],[]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [4,2,3,7,5,6,1,8] => ([(0,7),(1,5),(1,6),(2,4),(3,7),(4,5),(4,6),(5,7),(6,3)],8)
[[[[],[],[]],[],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [5,2,3,4,6,7,1,8] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[[[[],[[]]],[],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [5,2,4,3,6,7,1,8] => ([(0,7),(1,6),(2,3),(2,4),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[[]]]],[],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[[[],[],[]],[[]]],[]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [5,2,3,4,7,6,1,8] => ([(0,7),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[[[[],[[]]],[[]]],[]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [5,2,4,3,7,6,1,8] => ([(0,5),(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[]],[]],[[]]],[]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,3,2,4,7,6,1,8] => ([(0,4),(1,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[],[]]],[[]]],[]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,3,4,2,7,6,1,8] => ([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[[]]]],[[]]],[]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,5)],8)
[[[[],[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [6,2,3,4,5,7,1,8] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[[[[],[],[[]]],[]],[]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [6,2,3,5,4,7,1,8] => ([(0,3),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[],[[[]]]],[]],[]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [6,2,5,4,3,7,1,8] => ([(0,7),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[]],[],[]],[]],[]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [6,3,2,4,5,7,1,8] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[[[[[]],[[]]],[]],[]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [6,3,2,5,4,7,1,8] => ([(0,7),(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[],[],[]]],[]],[]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [6,3,4,5,2,7,1,8] => ([(0,7),(1,7),(2,6),(3,4),(4,5),(5,7),(7,6)],8)
[[[[[],[[]]]],[]],[]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [6,3,5,4,2,7,1,8] => ([(0,7),(1,7),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[[[]]]]],[]],[]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,5,4,3,2,7,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[[],[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [7,2,3,4,5,6,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[[[],[],[],[[]]]],[]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [7,2,3,4,6,5,1,8] => ([(0,7),(1,7),(2,5),(3,7),(4,7),(5,6),(6,3),(6,4)],8)
[[[[],[],[[]],[]]],[]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [7,2,3,5,4,6,1,8] => ([(0,3),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[],[],[[],[]]]],[]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [7,2,3,5,6,4,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,7),(5,4),(6,3),(6,5)],8)
[[[[],[],[[[]]]]],[]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,6,5,4,1,8] => ([(0,7),(1,7),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[],[[]],[[]]]],[]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [7,2,4,3,6,5,1,8] => ([(0,7),(1,7),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[],[[],[]],[]]],[]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [7,2,4,5,3,6,1,8] => ([(0,7),(1,7),(2,3),(2,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[],[[[]]],[]]],[]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [7,2,5,4,3,6,1,8] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[],[[],[[]]]]],[]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,4,6,5,3,1,8] => ([(0,7),(1,7),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[],[[[],[]]]]],[]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,6,4,5,3,1,8] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[],[[[[]]]]]],[]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,2,6,5,4,3,1,8] => ([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[[[]],[[]],[]]],[]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [7,3,2,5,4,6,1,8] => ([(0,7),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[[],[]],[[]]]],[]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,2,6,5,1,8] => ([(0,7),(1,7),(2,5),(2,6),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[]]],[[]]]],[]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,4,3,2,6,5,1,8] => ([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[]]],[]]],[]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [7,3,5,4,2,6,1,8] => ([(0,7),(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[[]],[]],[]]],[]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1,8] => ([(0,6),(1,7),(2,7),(3,5),(4,5),(5,6),(6,7)],8)
[[[[[[],[]]],[]]],[]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [7,5,3,4,2,6,1,8] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(7,6)],8)
[[[[[[[]]]],[]]],[]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,5,4,3,2,6,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(7,6)],8)
[[[[[],[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[],[],[[]]]]],[]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,3,4,6,5,2,1,8] => ([(0,4),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[]],[]]]],[]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [7,3,5,4,6,2,1,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[[],[[],[]]]]],[]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,3,6,4,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,3,6,5,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[[]],[[]]]]],[]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,4,3,6,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,5,4,3,6,2,1,8] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,6,3,4,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,6,3,5,4,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,6,4,3,5,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,6,4,5,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[],[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8)
[[[],[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => ([(1,6),(4,5),(5,7),(6,4),(7,2),(7,3)],8)
[[[],[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => ([(1,5),(2,7),(3,7),(4,6),(5,4),(6,2),(6,3)],8)
[[[],[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,8,6,7,1] => ([(1,6),(4,7),(5,2),(6,4),(7,3),(7,5)],8)
[[[],[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => ([(1,6),(5,7),(6,5),(7,2),(7,3),(7,4)],8)
[[[],[],[],[[]],[],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => ([(1,5),(2,7),(3,7),(5,6),(6,2),(6,3),(7,4)],8)
[[[],[],[],[[]],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => ([(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,2),(5,3)],8)
[[[],[],[],[[],[]],[]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,7,5,6,8,1] => ([(1,5),(2,7),(3,7),(4,3),(5,6),(6,2),(6,4)],8)
[[[],[],[],[[[]]],[]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => ([(1,5),(2,7),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[],[],[],[[],[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,8,5,6,7,1] => ([(1,6),(4,5),(5,2),(6,7),(7,3),(7,4)],8)
[[[],[],[],[[],[[]]]]] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,8,5,7,6,1] => ([(1,5),(5,7),(6,3),(6,4),(7,2),(7,6)],8)
[[[],[],[],[[[]],[]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,8,6,5,7,1] => ([(1,5),(3,7),(4,7),(5,6),(6,2),(6,3),(6,4)],8)
[[[],[],[],[[[],[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,8,6,7,5,1] => ([(1,6),(5,4),(6,7),(7,2),(7,3),(7,5)],8)
[[[],[],[],[[[[]]]]]] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => ([(1,6),(6,7),(7,2),(7,3),(7,4),(7,5)],8)
[[[],[],[[]],[],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => ([(1,6),(3,7),(4,7),(5,2),(6,3),(6,4),(7,5)],8)
[[[],[],[[]],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7)],8)
[[[],[],[[]],[[],[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,8,6,7,1] => ([(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4),(7,2)],8)
[[[],[],[[]],[[[]]]]] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => ([(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2),(4,3)],8)
[[[],[],[[],[]],[],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,6,4,5,7,8,1] => ([(1,6),(2,7),(3,7),(5,3),(6,2),(6,5),(7,4)],8)
[[[],[],[[[]]],[],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => ([(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[[[],[],[[],[]],[[]]]] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,4,5,8,7,1] => ([(1,5),(2,6),(2,7),(3,6),(3,7),(4,3),(5,2),(5,4)],8)
[[[],[],[[],[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,7,4,5,6,8,1] => ([(1,6),(2,7),(3,7),(4,5),(5,3),(6,2),(6,4)],8)
[[[],[],[[],[[]]],[]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,7,4,6,5,8,1] => ([(1,6),(2,7),(3,7),(4,7),(5,3),(5,4),(6,2),(6,5)],8)
[[[],[],[[[]],[]],[]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,7,5,4,6,8,1] => ([(1,5),(2,7),(3,6),(4,6),(5,2),(5,3),(5,4),(6,7)],8)
[[[],[],[[[],[]]],[]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,7,5,6,4,8,1] => ([(1,6),(2,7),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[[],[],[[[[]]]],[]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => ([(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[],[],[[],[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,8,4,5,6,7,1] => ([(1,7),(4,6),(5,4),(6,2),(7,3),(7,5)],8)
[[[],[],[[],[[],[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,8,4,6,7,5,1] => ([(1,7),(5,4),(6,3),(6,5),(7,2),(7,6)],8)
[[[],[],[[[]],[],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,8,5,4,6,7,1] => ([(1,6),(3,7),(4,7),(6,2),(6,3),(6,4),(7,5)],8)
[[[],[],[[[],[]],[]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,8,5,6,4,7,1] => ([(1,6),(3,7),(4,7),(5,4),(6,2),(6,3),(6,5)],8)
[[[],[],[[[[]]],[]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,8,6,5,4,7,1] => ([(1,6),(3,7),(4,7),(5,7),(6,2),(6,3),(6,4),(6,5)],8)
[[[],[],[[[],[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,8,5,6,7,4,1] => ([(1,7),(5,6),(6,4),(7,2),(7,3),(7,5)],8)
[[[],[],[[[],[[]]]]]] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,8,5,7,6,4,1] => ([(1,7),(6,4),(6,5),(7,2),(7,3),(7,6)],8)
[[[],[],[[[[[]]]]]]] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => ([(1,7),(7,2),(7,3),(7,4),(7,5),(7,6)],8)
[[[],[[]],[],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => ([(1,3),(1,4),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[[[],[[]],[],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => ([(1,4),(1,5),(4,7),(5,7),(6,2),(6,3),(7,6)],8)
[[[],[[]],[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => ([(1,2),(1,3),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[],[[]],[],[[],[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,4,3,5,8,6,7,1] => ([(1,3),(1,4),(3,7),(4,7),(6,2),(7,5),(7,6)],8)
[[[],[[]],[[]],[],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => ([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7),(7,2)],8)
[[[],[[]],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => ([(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[],[[]],[[],[]],[]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,7,5,6,8,1] => ([(1,3),(1,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(7,2)],8)
[[[],[[]],[[[]]],[]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => ([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[],[[]],[[],[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,8,5,6,7,1] => ([(1,3),(1,4),(3,6),(3,7),(4,6),(4,7),(5,2),(7,5)],8)
[[[],[[]],[[],[[]]]]] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,8,5,7,6,1] => ([(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2),(7,3)],8)
[[[],[[]],[[[]],[]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,4,3,8,6,5,7,1] => ([(1,2),(1,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8)
[[[],[[]],[[[[]]]]]] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[],[[],[]],[],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,5,3,4,6,7,8,1] => ([(1,4),(1,5),(3,7),(4,7),(5,3),(6,2),(7,6)],8)
[[[],[[[]]],[],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => ([(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(6,2),(7,6)],8)
[[[],[[],[]],[],[[]]]] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,5,3,4,6,8,7,1] => ([(1,3),(1,6),(2,7),(3,7),(6,2),(7,4),(7,5)],8)
[[[],[[[]]],[],[[]]]] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => ([(1,2),(1,3),(1,4),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[],[[],[]],[[]],[]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,5,3,4,7,6,8,1] => ([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(5,7),(6,7)],8)
[[[],[[[]]],[[]],[]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => ([(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[],[[],[]],[[],[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,5,3,4,8,6,7,1] => ([(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(7,2)],8)
[[[],[[],[]],[[[]]]]] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,5,3,4,8,7,6,1] => ([(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,2)],8)
[[[],[[[]]],[[],[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,8,6,7,1] => ([(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[[[],[[[]]],[[[]]]]] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => ([(1,2),(1,3),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[],[[],[],[]],[],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,6,3,4,5,7,8,1] => ([(1,3),(1,6),(2,7),(3,7),(5,2),(6,5),(7,4)],8)
[[[],[[],[[]]],[],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,6,3,5,4,7,8,1] => ([(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(6,3),(7,5)],8)
[[[],[[[]],[]],[],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,6,4,3,5,7,8,1] => ([(1,3),(1,4),(1,5),(3,7),(4,6),(5,6),(6,7),(7,2)],8)
[[[],[[[],[]]],[],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,6,4,5,3,7,8,1] => ([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(6,2),(7,5)],8)
[[[],[[[[]]]],[],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => ([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[],[[],[],[]],[[]]]] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,6,3,4,5,8,7,1] => ([(1,3),(1,5),(2,6),(2,7),(3,6),(3,7),(4,2),(5,4)],8)
[[[],[[],[[]]],[[]]]] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,6,3,5,4,8,7,1] => ([(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,2),(5,3)],8)
[[[],[[[]],[]],[[]]]] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,6,4,3,5,8,7,1] => ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[[[[]]]],[[]]]] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => ([(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[[],[[]],[]],[]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,7,3,5,4,6,8,1] => ([(1,2),(1,5),(2,7),(3,6),(4,6),(5,3),(5,4),(6,7)],8)
[[[],[[],[[],[]]],[]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,7,3,5,6,4,8,1] => ([(1,4),(1,6),(2,7),(3,7),(4,7),(5,3),(6,2),(6,5)],8)
[[[],[[[]],[],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,4,3,5,6,8,1] => ([(1,2),(1,3),(1,5),(2,7),(3,7),(4,6),(5,6),(7,4)],8)
[[[],[[[]],[[]]],[]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,7,4,3,6,5,8,1] => ([(1,2),(1,3),(1,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[],[[[[]]],[]],[]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,7,5,4,3,6,8,1] => ([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[],[[[],[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,7,4,5,6,3,8,1] => ([(1,3),(1,4),(1,6),(2,7),(3,7),(4,7),(5,2),(6,5)],8)
[[[],[[[],[[]]]],[]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,7,4,6,5,3,8,1] => ([(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2),(6,3)],8)
[[[],[[[[]],[]]],[]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,7,5,4,6,3,8,1] => ([(1,2),(1,3),(1,4),(1,5),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[],[[[[],[]]]],[]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,7,6,4,5,3,8,1] => ([(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,2)],8)
[[[],[[[[[]]]]],[]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[],[[],[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,8,3,4,5,6,7,1] => ([(1,3),(1,7),(4,6),(5,4),(6,2),(7,5)],8)
[[[],[[],[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,8,3,4,5,7,6,1] => ([(1,4),(1,6),(5,7),(6,5),(7,2),(7,3)],8)
[[[],[[],[[]],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,8,3,5,4,7,6,1] => ([(1,2),(1,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4)],8)
[[[],[[],[[],[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,8,3,5,6,7,4,1] => ([(1,4),(1,7),(5,6),(6,3),(7,2),(7,5)],8)
[[[],[[],[[],[[]]]]]] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,8,3,5,7,6,4,1] => ([(1,5),(1,7),(6,3),(6,4),(7,2),(7,6)],8)
[[[],[[],[[[],[]]]]]] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,8,3,7,5,6,4,1] => ([(1,5),(1,7),(6,4),(7,2),(7,3),(7,6)],8)
[[[],[[],[[[[]]]]]]] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,8,3,7,6,5,4,1] => ([(1,6),(1,7),(7,2),(7,3),(7,4),(7,5)],8)
[[[],[[[]],[],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,8,4,3,5,6,7,1] => ([(1,3),(1,4),(1,5),(4,7),(5,7),(6,2),(7,6)],8)
[[[],[[[]],[],[[]]]]] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,8,4,3,5,7,6,1] => ([(1,2),(1,3),(1,4),(3,7),(4,7),(7,5),(7,6)],8)
[[[],[[[]],[[]],[]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,3,6,5,7,1] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[],[[[]],[[],[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,4,3,6,7,5,1] => ([(1,3),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7),(7,2)],8)
[[[],[[[]],[[[]]]]]] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,8,4,3,7,6,5,1] => ([(1,2),(1,3),(1,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[],[[[],[]],[],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,8,4,5,3,6,7,1] => ([(1,2),(1,4),(1,6),(3,7),(4,7),(6,3),(7,5)],8)
[[[],[[[[]]],[],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,8,5,4,3,6,7,1] => ([(1,2),(1,3),(1,4),(1,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[],[[[[]]],[[]]]]] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,8,5,4,3,7,6,1] => ([(1,2),(1,3),(1,4),(1,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[[[],[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,8,4,5,6,3,7,1] => ([(1,2),(1,4),(1,6),(3,7),(4,7),(5,3),(6,5)],8)
[[[],[[[],[[]]],[]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,8,4,6,5,3,7,1] => ([(1,2),(1,5),(1,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[],[[[],[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,8,4,5,6,7,3,1] => ([(1,3),(1,4),(1,7),(5,6),(6,2),(7,5)],8)
[[[],[[[],[[[]]]]]]] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,8,4,7,6,5,3,1] => ([(1,5),(1,6),(1,7),(7,2),(7,3),(7,4)],8)
[[[],[[[[]],[],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,5,4,6,7,3,1] => ([(1,2),(1,3),(1,4),(1,5),(4,7),(5,7),(7,6)],8)
[[[],[[[[]],[[]]]]]] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,8,5,4,7,6,3,1] => ([(1,2),(1,3),(1,4),(1,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[],[[[[],[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,8,7,4,5,6,3,1] => ([(1,3),(1,4),(1,5),(1,7),(6,2),(7,6)],8)
[[[],[[[[],[[]]]]]]] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,8,7,4,6,5,3,1] => ([(1,4),(1,5),(1,6),(1,7),(7,2),(7,3)],8)
[[[],[[[[[]],[]]]]]] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,8,7,5,4,6,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(5,7),(6,7)],8)
[[[],[[[[[],[]]]]]]] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,8,7,5,6,4,3,1] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(7,2)],8)
[[[],[[[[[[]]]]]]]] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7)],8)
[[[[]],[],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => ([(1,7),(2,7),(4,5),(5,3),(6,4),(7,6)],8)
[[[[]],[],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => ([(1,7),(2,7),(5,6),(6,3),(6,4),(7,5)],8)
[[[[]],[],[],[[]],[]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => ([(1,6),(2,6),(3,4),(3,5),(4,7),(5,7),(6,3)],8)
[[[[]],[],[],[[],[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,8,6,7,1] => ([(1,7),(2,7),(5,4),(6,3),(6,5),(7,6)],8)
[[[[]],[],[[]],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => ([(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,3),(5,4)],8)
[[[[]],[],[[],[]],[]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,2,4,7,5,6,8,1] => ([(1,6),(2,6),(3,7),(4,5),(5,7),(6,3),(6,4)],8)
[[[[]],[],[[[]]],[]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => ([(1,6),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[]],[],[[],[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,2,4,8,5,6,7,1] => ([(1,7),(2,7),(5,3),(6,5),(7,4),(7,6)],8)
[[[[]],[],[[[],[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,8,6,7,5,1] => ([(1,7),(2,7),(6,3),(7,4),(7,5),(7,6)],8)
[[[[]],[],[[[[]]]]]] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => ([(1,7),(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[[]],[[]],[],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(5,7),(6,7),(7,3)],8)
[[[[]],[[]],[],[[]]]] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => ([(1,5),(1,6),(2,5),(2,6),(5,7),(6,7),(7,3),(7,4)],8)
[[[[]],[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[[]],[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,8,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
[[[[]],[[[]]],[[]]]] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[]],[[],[[]]],[]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,7,4,6,5,8,1] => ([(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[]],[[[],[]]],[]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,7,5,6,4,8,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[]],[[[[]]]],[]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[[]],[[],[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,8,4,5,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(5,4),(7,3)],8)
[[[[]],[[],[[]],[]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,8,4,6,5,7,1] => ([(1,5),(1,6),(2,5),(2,6),(3,7),(4,7),(6,3),(6,4)],8)
[[[[]],[[[]],[],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,2,8,5,4,6,7,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(4,3),(6,4),(7,4)],8)
[[[[]],[[[]],[[]]]]] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,2,8,5,4,7,6,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8)
[[[[]],[[[],[]],[]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,8,5,6,4,7,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(6,3),(7,4)],8)
[[[[]],[[[],[[]]]]]] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,8,5,7,6,4,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[[[[]],[[[[]],[]]]]] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,2,8,6,5,7,4,1] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(6,3),(7,3)],8)
[[[[]],[[[[],[]]]]]] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,8,7,5,6,4,1] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[[[[]],[[[[[]]]]]]] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[[],[]],[],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [4,2,3,5,6,7,8,1] => ([(1,7),(2,4),(4,7),(5,3),(6,5),(7,6)],8)
[[[[[]]],[],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => ([(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[],[]],[],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [4,2,3,5,6,8,7,1] => ([(1,7),(2,5),(5,7),(6,3),(6,4),(7,6)],8)
[[[[[]]],[],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(7,4)],8)
[[[[[]]],[],[[]],[]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(7,4),(7,5)],8)
[[[[],[]],[],[[[]]]]] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [4,2,3,5,8,7,6,1] => ([(1,7),(2,3),(3,7),(7,4),(7,5),(7,6)],8)
[[[[[]]],[],[[[]]]]] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => ([(1,7),(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[[[]]],[[]],[],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(5,4),(6,5),(7,5)],8)
[[[[],[]],[[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [4,2,3,6,5,8,7,1] => ([(1,3),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[[]]],[[]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(6,4),(6,5),(7,4),(7,5)],8)
[[[[],[]],[[],[]],[]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [4,2,3,7,5,6,8,1] => ([(1,5),(1,7),(2,4),(3,6),(4,5),(4,7),(5,6),(7,3)],8)
[[[[],[]],[[[]]],[]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [4,2,3,7,6,5,8,1] => ([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[]]],[[],[]],[]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,7,5,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(6,5),(7,4)],8)
[[[[[]]],[[[]]],[]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[],[]],[[],[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [4,2,3,8,5,6,7,1] => ([(1,6),(1,7),(2,4),(3,5),(4,6),(4,7),(7,3)],8)
[[[[],[]],[[],[[]]]]] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [4,2,3,8,5,7,6,1] => ([(1,6),(1,7),(2,5),(5,6),(5,7),(7,3),(7,4)],8)
[[[[],[]],[[[[]]]]]] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,2,3,8,7,6,5,1] => ([(1,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[[]]],[[],[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,3,2,8,5,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[[]]],[[],[[]]]]] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,8,5,7,6,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[[[]]],[[[],[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,8,6,7,5,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[[[]]],[[[[]]]]]] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[],[],[]],[],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [5,2,3,4,6,7,8,1] => ([(1,7),(2,5),(4,7),(5,4),(6,3),(7,6)],8)
[[[[[]],[]],[],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [5,3,2,4,6,7,8,1] => ([(1,7),(2,6),(3,6),(4,5),(6,7),(7,4)],8)
[[[[[],[]]],[],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [5,3,4,2,6,7,8,1] => ([(1,7),(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[[]]]],[],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[[]]]],[],[[]]]] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => ([(1,7),(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[],[[]]],[[]],[]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [5,2,4,3,7,6,8,1] => ([(1,6),(1,7),(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[],[]]],[[]],[]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [5,3,4,2,7,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[[]]]],[[]],[]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[],[],[]],[[],[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [5,2,3,4,8,6,7,1] => ([(1,6),(1,7),(2,4),(4,5),(5,6),(5,7),(7,3)],8)
[[[[],[],[]],[[[]]]]] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [5,2,3,4,8,7,6,1] => ([(1,5),(1,6),(1,7),(2,3),(3,4),(4,5),(4,6),(4,7)],8)
[[[[],[[]]],[[[]]]]] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,2,4,3,8,7,6,1] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[[],[]]],[[],[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [5,3,4,2,8,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(5,6),(5,7),(7,4)],8)
[[[[[[]]]],[[],[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,8,6,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[[]]]],[[[]]]]] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[],[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [6,2,3,4,5,7,8,1] => ([(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8)
[[[[],[],[[]]],[],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [6,2,3,5,4,7,8,1] => ([(1,7),(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[[[[],[[[]]]],[],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [6,2,5,4,3,7,8,1] => ([(1,7),(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[]],[[]]],[],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [6,3,2,5,4,7,8,1] => ([(1,7),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7),(7,4)],8)
[[[[[],[],[]]],[],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [6,3,4,5,2,7,8,1] => ([(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[[[],[[]]]],[],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [6,3,5,4,2,7,8,1] => ([(1,7),(2,7),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[[],[]]]],[],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [6,5,3,4,2,7,8,1] => ([(1,7),(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[[[[[]]]]],[],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[[],[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,2,3,4,5,8,7,1] => ([(1,3),(2,6),(2,7),(3,5),(4,6),(4,7),(5,4)],8)
[[[[[]],[[]]],[[]]]] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,3,2,5,4,8,7,1] => ([(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[]]],[]],[[]]]] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [6,4,3,2,5,8,7,1] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(7,5),(7,6)],8)
[[[[[],[],[]]],[[]]]] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,3,4,5,2,8,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[],[[]]]],[[]]]] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,3,5,4,2,8,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[[]]]]],[[]]]] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => ([(1,7),(2,6),(3,7),(4,5),(5,3),(6,4)],8)
[[[[],[[]],[[]]],[]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [7,2,4,3,6,5,8,1] => ([(1,7),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[],[[],[]],[]],[]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,2,4,5,3,6,8,1] => ([(1,6),(2,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[[[[],[[],[[]]]],[]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [7,2,4,6,5,3,8,1] => ([(1,7),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3),(6,4)],8)
[[[[],[[[]],[]]],[]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,2,5,4,6,3,8,1] => ([(1,7),(2,3),(2,4),(2,5),(3,7),(4,6),(5,6),(6,7)],8)
[[[[],[[[],[]]]],[]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,2,6,4,5,3,8,1] => ([(1,7),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[],[[[[]]]]],[]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,6,5,4,3,8,1] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[[[]],[],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(7,4)],8)
[[[[[]],[[],[]]],[]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [7,3,2,5,6,4,8,1] => ([(1,7),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[[[[[]]],[],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(7,5)],8)
[[[[[],[]],[[]]],[]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,3,4,2,6,5,8,1] => ([(1,7),(2,5),(2,6),(3,4),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[]]],[[]]],[]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,3,2,6,5,8,1] => ([(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[]],[]],[]],[]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => ([(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
[[[[[[[]]]],[]],[]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[[[],[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[],[[]],[]]],[]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [7,3,5,4,6,2,8,1] => ([(1,7),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)
[[[[[],[[],[]]]],[]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [7,3,6,4,5,2,8,1] => ([(1,7),(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[[]]]]],[]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,3,6,5,4,2,8,1] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[[]],[[]]]],[]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,4,3,6,5,2,8,1] => ([(1,7),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[],[]],[]]],[]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => ([(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
[[[[[[[]]],[]]],[]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => ([(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
[[[[[[],[],[]]]],[]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,6,3,4,5,2,8,1] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[[[[[],[[]]]]],[]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,6,3,5,4,2,8,1] => ([(1,7),(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[]],[]]]],[]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,6,4,3,5,2,8,1] => ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[[],[]]]]],[]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,6,4,5,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[[[[[[]]]]]],[]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,6,5,4,3,2,8,1] => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[[],[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,2,3,4,5,6,7,1] => ([(2,7),(4,6),(5,4),(6,3),(7,5)],8)
[[[[],[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8,2,3,4,5,7,6,1] => ([(2,6),(5,7),(6,5),(7,3),(7,4)],8)
[[[[],[],[],[[[]]]]]] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8,2,3,4,7,6,5,1] => ([(2,6),(6,7),(7,3),(7,4),(7,5)],8)
[[[[],[],[[]],[],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8,2,3,5,4,6,7,1] => ([(2,6),(3,7),(4,7),(6,3),(6,4),(7,5)],8)
[[[[],[],[[]],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8,2,3,5,4,7,6,1] => ([(2,3),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[],[[[]]],[]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8,2,3,6,5,4,7,1] => ([(2,6),(3,7),(4,7),(5,7),(6,3),(6,4),(6,5)],8)
[[[[],[],[[],[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8,2,3,5,6,7,4,1] => ([(2,7),(5,6),(6,4),(7,3),(7,5)],8)
[[[[],[],[[],[[]]]]]] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8,2,3,5,7,6,4,1] => ([(2,7),(6,4),(6,5),(7,3),(7,6)],8)
[[[[],[],[[[],[]]]]]] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8,2,3,7,5,6,4,1] => ([(2,7),(6,5),(7,3),(7,4),(7,6)],8)
[[[[],[],[[[[]]]]]]] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8,2,3,7,6,5,4,1] => ([(2,7),(7,3),(7,4),(7,5),(7,6)],8)
[[[[],[[]],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8,2,4,3,6,5,7,1] => ([(2,3),(2,4),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[],[[]],[[],[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8,2,4,3,6,7,5,1] => ([(2,4),(2,5),(4,6),(4,7),(5,6),(5,7),(7,3)],8)
[[[[],[[]],[[[]]]]]] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8,2,4,3,7,6,5,1] => ([(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[],[[[]]],[],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8,2,5,4,3,6,7,1] => ([(2,3),(2,4),(2,5),(3,7),(4,7),(5,7),(7,6)],8)
[[[[],[[],[]],[[]]]]] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8,2,4,5,3,7,6,1] => ([(2,3),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[[[]]],[[]]]]] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8,2,5,4,3,7,6,1] => ([(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[[[],[]]],[]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8,2,6,4,5,3,7,1] => ([(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,3)],8)
[[[[],[[[[]]]],[]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8,2,6,5,4,3,7,1] => ([(2,3),(2,4),(2,5),(2,6),(3,7),(4,7),(5,7),(6,7)],8)
[[[[],[[],[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8,2,4,5,6,7,3,1] => ([(2,4),(2,7),(5,6),(6,3),(7,5)],8)
[[[[],[[],[],[[]]]]]] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8,2,4,5,7,6,3,1] => ([(2,5),(2,6),(6,7),(7,3),(7,4)],8)
[[[[],[[],[[],[]]]]]] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8,2,4,7,5,6,3,1] => ([(2,5),(2,7),(6,4),(7,3),(7,6)],8)
[[[[],[[],[[[]]]]]]] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8,2,4,7,6,5,3,1] => ([(2,6),(2,7),(7,3),(7,4),(7,5)],8)
[[[[],[[[]],[[]]]]]] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8,2,5,4,7,6,3,1] => ([(2,3),(2,4),(2,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[],[[[],[]],[]]]]] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8,2,6,4,5,7,3,1] => ([(2,3),(2,5),(2,6),(4,7),(5,7),(6,4)],8)
[[[[],[[[[]]],[]]]]] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8,2,6,5,4,7,3,1] => ([(2,3),(2,4),(2,5),(2,6),(4,7),(5,7),(6,7)],8)
[[[[],[[[],[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8,2,7,4,5,6,3,1] => ([(2,4),(2,5),(2,7),(6,3),(7,6)],8)
[[[[],[[[],[[]]]]]]] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,2,7,4,6,5,3,1] => ([(2,5),(2,6),(2,7),(7,3),(7,4)],8)
[[[[],[[[[]],[]]]]]] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8,2,7,5,4,6,3,1] => ([(2,3),(2,4),(2,5),(2,6),(5,7),(6,7)],8)
[[[[],[[[[],[]]]]]]] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8,2,7,5,6,4,3,1] => ([(2,4),(2,5),(2,6),(2,7),(7,3)],8)
[[[[],[[[[[]]]]]]]] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8,2,7,6,5,4,3,1] => ([(2,3),(2,4),(2,5),(2,6),(2,7)],8)
[[[[[]],[],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8,3,2,4,5,6,7,1] => ([(2,7),(3,7),(4,6),(6,5),(7,4)],8)
[[[[[]],[],[[]],[]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8,3,2,4,6,5,7,1] => ([(2,6),(3,6),(4,7),(5,7),(6,4),(6,5)],8)
[[[[[]],[],[[],[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8,3,2,4,6,7,5,1] => ([(2,7),(3,7),(5,6),(7,4),(7,5)],8)
[[[[[]],[],[[[]]]]]] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8,3,2,4,7,6,5,1] => ([(2,7),(3,7),(7,4),(7,5),(7,6)],8)
[[[[[]],[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8,3,2,5,4,7,6,1] => ([(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[]],[[],[]],[]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8,3,2,5,6,4,7,1] => ([(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,4)],8)
[[[[[]],[[],[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8,3,2,5,6,7,4,1] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(7,4)],8)
[[[[[]],[[],[[]]]]]] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8,3,2,5,7,6,4,1] => ([(2,6),(2,7),(3,6),(3,7),(7,4),(7,5)],8)
[[[[[]],[[[]],[]]]]] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8,3,2,6,5,7,4,1] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[[[[[]],[[[],[]]]]]] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8,3,2,7,5,6,4,1] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(7,4)],8)
[[[[[]],[[[[]]]]]]] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8,3,2,7,6,5,4,1] => ([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)
[[[[[],[]],[],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8,3,4,2,5,6,7,1] => ([(2,7),(3,4),(4,7),(5,6),(7,5)],8)
[[[[[[]]],[],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8,4,3,2,5,6,7,1] => ([(2,7),(3,7),(4,7),(5,6),(7,5)],8)
[[[[[[]]],[],[[]]]]] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8,4,3,2,5,7,6,1] => ([(2,7),(3,7),(4,7),(7,5),(7,6)],8)
[[[[[],[]],[[]],[]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8,3,4,2,6,5,7,1] => ([(2,6),(2,7),(3,4),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[[]]],[[]],[]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8,4,3,2,6,5,7,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,5),(7,5)],8)
[[[[[[]]],[[],[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8,4,3,2,6,7,5,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[[]]],[[[]]]]]] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8,4,3,2,7,6,5,1] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[[],[],[]],[],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8,3,4,5,2,6,7,1] => ([(2,7),(3,4),(4,6),(6,7),(7,5)],8)
[[[[[],[[]]],[],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8,3,5,4,2,6,7,1] => ([(2,7),(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[[],[]]],[],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8,5,3,4,2,6,7,1] => ([(2,7),(3,7),(4,5),(5,7),(7,6)],8)
[[[[[[[]]]],[],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8,5,4,3,2,6,7,1] => ([(2,7),(3,7),(4,7),(5,7),(7,6)],8)
[[[[[],[],[]],[[]]]]] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8,3,4,5,2,7,6,1] => ([(2,6),(2,7),(3,4),(4,5),(5,6),(5,7)],8)
[[[[[],[[]]],[[]]]]] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8,3,5,4,2,7,6,1] => ([(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[]],[]],[[]]]]] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8,4,3,5,2,7,6,1] => ([(2,5),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[],[]]],[[]]]]] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,5,3,4,2,7,6,1] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[[[[[]]]],[[]]]]] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8,5,4,3,2,7,6,1] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[],[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8,3,4,5,6,2,7,1] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[[[[[],[[],[]]],[]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8,3,6,4,5,2,7,1] => ([(2,7),(3,4),(3,5),(4,6),(5,7),(6,7)],8)
[[[[[],[[[]]]],[]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8,3,6,5,4,2,7,1] => ([(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[[]],[],[]],[]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8,4,3,5,6,2,7,1] => ([(2,7),(3,6),(4,6),(5,7),(6,5)],8)
[[[[[[[]]],[]],[]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8,5,4,3,6,2,7,1] => ([(2,7),(3,7),(4,7),(5,6),(7,6)],8)
[[[[[[],[],[]]],[]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8,6,3,4,5,2,7,1] => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
[[[[[[],[[]]]],[]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8,6,3,5,4,2,7,1] => ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[]],[]]],[]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8,6,4,3,5,2,7,1] => ([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[[],[]]]],[]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8,6,4,5,3,2,7,1] => ([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
[[[[[[[[]]]]],[]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8,6,5,4,3,2,7,1] => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
[[[[[],[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8,3,4,5,6,7,2,1] => ([(3,4),(4,7),(6,5),(7,6)],8)
[[[[[],[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8,3,4,5,7,6,2,1] => ([(3,4),(4,7),(7,5),(7,6)],8)
[[[[[],[],[[[]]]]]]] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8,3,4,7,6,5,2,1] => ([(3,4),(4,5),(4,6),(4,7)],8)
[[[[[],[[]],[],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8,3,5,4,6,7,2,1] => ([(3,4),(3,5),(4,7),(5,7),(7,6)],8)
[[[[[],[[]],[[]]]]]] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,5,4,7,6,2,1] => ([(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[],[[[]]],[]]]]] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8,3,6,5,4,7,2,1] => ([(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)
[[[[[],[[],[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8,3,7,4,5,6,2,1] => ([(3,4),(3,5),(5,6),(6,7)],8)
[[[[[],[[],[[]]]]]]] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8,3,7,4,6,5,2,1] => ([(3,4),(3,5),(5,6),(5,7)],8)
[[[[[],[[[]],[]]]]]] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8,3,7,5,4,6,2,1] => ([(3,4),(3,5),(3,6),(5,7),(6,7)],8)
[[[[[],[[[],[]]]]]]] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8,3,7,5,6,4,2,1] => ([(3,4),(3,5),(3,6),(6,7)],8)
[[[[[],[[[[]]]]]]]] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8,3,7,6,5,4,2,1] => ([(3,4),(3,5),(3,6),(3,7)],8)
[[[[[[]],[],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8,4,3,5,6,7,2,1] => ([(3,7),(4,7),(5,6),(7,5)],8)
[[[[[[]],[],[[]]]]]] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8,4,3,5,7,6,2,1] => ([(3,7),(4,7),(7,5),(7,6)],8)
[[[[[[]],[[],[]]]]]] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8,4,3,7,5,6,2,1] => ([(3,6),(3,7),(4,6),(4,7),(7,5)],8)
[[[[[[]],[[[]]]]]]] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8,4,3,7,6,5,2,1] => ([(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)
[[[[[[],[]],[],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8,5,3,4,6,7,2,1] => ([(3,7),(4,5),(5,7),(7,6)],8)
[[[[[[[]]],[],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8,5,4,3,6,7,2,1] => ([(3,7),(4,7),(5,7),(7,6)],8)
[[[[[[],[]],[[]]]]]] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8,5,3,4,7,6,2,1] => ([(3,6),(3,7),(4,5),(5,6),(5,7)],8)
[[[[[[[]]],[[]]]]]] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8,5,4,3,7,6,2,1] => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[],[[]]],[]]]]] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8,6,3,5,4,7,2,1] => ([(3,7),(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[[]],[]],[]]]]] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8,6,4,3,5,7,2,1] => ([(3,7),(4,6),(5,6),(6,7)],8)
[[[[[[[[]]]],[]]]]] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8,6,5,4,3,7,2,1] => ([(3,7),(4,7),(5,7),(6,7)],8)
[[[[[[],[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8,7,3,4,5,6,2,1] => ([(4,5),(5,7),(7,6)],8)
[[[[[[],[],[[]]]]]]] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8,7,3,4,6,5,2,1] => ([(4,5),(5,6),(5,7)],8)
[[[[[[],[[]],[]]]]]] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8,7,3,5,4,6,2,1] => ([(4,5),(4,6),(5,7),(6,7)],8)
[[[[[[],[[],[]]]]]]] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8,7,3,5,6,4,2,1] => ([(4,5),(4,6),(6,7)],8)
[[[[[[],[[[]]]]]]]] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8,7,3,6,5,4,2,1] => ([(4,5),(4,6),(4,7)],8)
[[[[[[[]],[],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8,7,4,3,5,6,2,1] => ([(4,7),(5,7),(7,6)],8)
[[[[[[[]],[[]]]]]]] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8,7,4,3,6,5,2,1] => ([(4,6),(4,7),(5,6),(5,7)],8)
[[[[[[[],[]],[]]]]]] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8,7,4,5,3,6,2,1] => ([(4,7),(5,6),(6,7)],8)
[[[[[[[[]]],[]]]]]] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8,7,5,4,3,6,2,1] => ([(4,7),(5,7),(6,7)],8)
[[[[[[[],[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8,7,4,5,6,3,2,1] => ([(5,6),(6,7)],8)
[[[[[[[],[[]]]]]]]] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8,7,4,6,5,3,2,1] => ([(5,6),(5,7)],8)
[[[[[[[[]],[]]]]]]] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8,7,5,4,6,3,2,1] => ([(5,7),(6,7)],8)
[[[[[[[[],[]]]]]]]] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8,7,6,4,5,3,2,1] => ([(6,7)],8)
[[[[[[[[[]]]]]]]]] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => ([],8)
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.
This sends the maximal height of the Dyck path to the depth of the tree.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
searching the database
Sorry, this map was not found in the database.