Identifier
Values
[[]] => [1,0] => [1] => ([],1) => 0
[[],[]] => [1,0,1,0] => [2,1] => ([(0,1)],2) => 1
[[[]]] => [1,1,0,0] => [1,2] => ([],2) => 0
[[],[],[]] => [1,0,1,0,1,0] => [2,1,3] => ([(1,2)],3) => 1
[[],[[]]] => [1,0,1,1,0,0] => [2,3,1] => ([(0,2),(1,2)],3) => 1
[[[]],[]] => [1,1,0,0,1,0] => [3,1,2] => ([(0,2),(1,2)],3) => 1
[[[],[]]] => [1,1,0,1,0,0] => [1,3,2] => ([(1,2)],3) => 1
[[[[]]]] => [1,1,1,0,0,0] => [1,2,3] => ([],3) => 0
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => ([(0,3),(1,2)],4) => 1
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => 1
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [2,1,3,4] => ([(2,3)],4) => 1
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => ([(1,3),(2,3)],4) => 1
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 1
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => 1
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 1
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [3,1,2,4] => ([(1,3),(2,3)],4) => 1
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => 1
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => ([(2,3)],4) => 1
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [1,3,4,2] => ([(1,3),(2,3)],4) => 1
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => ([(1,3),(2,3)],4) => 1
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => ([(2,3)],4) => 1
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => ([],4) => 0
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => 1
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => 1
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => 1
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => 1
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => 1
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => ([(3,4)],5) => 1
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => 1
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => 1
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => 1
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5) => 1
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => 1
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 1
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 1
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 1
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => 1
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => 1
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => 1
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => 1
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 1
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => ([(3,4)],5) => 1
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => 1
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => 1
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => 1
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 1
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => ([(2,4),(3,4)],5) => 1
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => 1
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => ([(3,4)],5) => 1
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => 1
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => ([(2,4),(3,4)],5) => 1
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => ([(3,4)],5) => 1
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([],5) => 0
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => 1
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => 1
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => 1
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => 1
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6) => 1
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 1
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 1
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => 1
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 1
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6) => 1
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => 1
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => ([(4,5)],6) => 1
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => 1
>>> Load all 625 entries. <<<
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 1
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => 1
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 1
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6) => 1
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 1
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 1
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 2
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => 1
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => 1
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6) => 1
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => 1
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => 1
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6) => 1
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 1
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6) => 1
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => 1
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => ([(4,5)],6) => 1
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => 1
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => 1
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6) => 1
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 1
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => ([(3,5),(4,5)],6) => 1
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6) => 1
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => 1
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6) => 1
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => ([(4,5)],6) => 1
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => 1
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => 1
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6) => 1
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 1
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6) => 1
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6) => 1
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => ([(4,5)],6) => 1
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => 1
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => ([(3,5),(4,5)],6) => 1
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => ([(4,5)],6) => 1
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([],6) => 0
[[],[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => ([(1,6),(2,5),(3,4)],7) => 1
[[],[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[],[],[],[],[[]],[]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[],[],[],[],[[],[]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 1
[[],[],[],[],[[[]]]] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[],[],[],[[]],[],[]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => ([(0,3),(1,2),(4,6),(5,6)],7) => 1
[[],[],[],[[]],[[]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[],[],[],[[],[]],[]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[],[],[[[]]],[]] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[],[],[[],[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 1
[[],[],[],[[],[[]]]] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[],[],[],[[[]],[]]] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 1
[[],[],[],[[[],[]]]] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[],[],[],[[[[]]]]] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[],[],[[]],[],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => 1
[[],[],[[]],[],[[]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[],[],[[]],[[]],[]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[],[[]],[[],[]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 1
[[],[],[[]],[[[]]]] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 1
[[],[],[[],[]],[],[]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => ([(1,6),(2,5),(3,4)],7) => 1
[[],[],[[[]]],[],[]] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => ([(3,6),(4,5)],7) => 1
[[],[],[[],[]],[[]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[],[],[[[]]],[[]]] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => ([(3,6),(4,5),(5,6)],7) => 1
[[],[],[[],[],[]],[]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => 1
[[],[],[[],[[]]],[]] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[],[[[]],[]],[]] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[],[[[],[]]],[]] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[],[],[[[[]]]],[]] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[],[],[[],[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[],[[],[],[[]]]] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[],[[],[[]],[]]] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
[[],[],[[],[[],[]]]] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 1
[[],[],[[],[[[]]]]] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[],[[[]],[],[]]] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => 1
[[],[],[[[]],[[]]]] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[],[],[[[],[]],[]]] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[],[],[[[[]]],[]]] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[],[],[[[],[],[]]]] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[],[[[],[[]]]]] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[],[[[[]],[]]]] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[],[[[[],[]]]]] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[],[[[[[]]]]]] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[]],[],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[],[[]],[],[],[[]]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[]],[],[[]],[]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[]],[],[[],[]]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[],[[]],[],[[[]]]] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[],[[]],[[]],[],[]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[]],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[]],[[],[]],[]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[]],[[[]]],[]] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[]],[[],[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[],[[]],[[],[[]]]] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[]],[[[]],[]]] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[],[[]],[[[],[]]]] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
[[],[[]],[[[[]]]]] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[],[[],[]],[],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[[]]],[],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[],[]],[],[[]]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
[[],[[[]]],[],[[]]] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[],[[],[]],[[]],[]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[[]]],[[]],[]] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[],[]],[[],[]]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 1
[[],[[],[]],[[[]]]] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[[]]],[[],[]]] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 1
[[],[[[]]],[[[]]]] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[],[],[]],[],[]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => 1
[[],[[],[[]]],[],[]] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[[]],[]],[],[]] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[[],[]]],[],[]] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[],[[[[]]]],[],[]] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[],[[],[],[]],[[]]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[],[[]]],[[]]] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[[]],[]],[[]]] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[[],[]]],[[]]] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[[[]]]],[[]]] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[],[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => 1
[[],[[],[],[[]]],[]] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[],[[],[[]],[]],[]] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => ([(3,6),(4,5)],7) => 1
[[],[[],[[],[]]],[]] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[],[[[]]]],[]] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[],[[[]],[],[]],[]] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[],[[[]],[[]]],[]] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[[],[]],[]],[]] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[[[]]],[]],[]] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[],[[[],[],[]]],[]] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => ([(3,6),(4,5)],7) => 1
[[],[[[],[[]]]],[]] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[[[]],[]]],[]] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[[[],[]]]],[]] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => ([(3,6),(4,5)],7) => 1
[[],[[[[[]]]]],[]] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => ([(5,6)],7) => 1
[[],[[],[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => 1
[[],[[],[],[],[[]]]] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[],[],[[]],[]]] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[],[[],[],[[],[]]]] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 1
[[],[[],[],[[[]]]]] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 1
[[],[[],[[]],[],[]]] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[],[[]],[[]]]] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[],[[],[]],[]]] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[],[[[]]],[]]] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[],[[],[],[]]]] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[],[[],[[],[[]]]]] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[],[[],[[[]],[]]]] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[],[[],[[[],[]]]]] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[[]],[],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[],[[[]],[],[[]]]] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[],[[[]],[[]],[]]] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 1
[[],[[[]],[[],[]]]] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 1
[[],[[[]],[[[]]]]] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[],[[[],[]],[],[]]] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[[[]]],[],[]]] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[[],[]],[[]]]] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[],[[[[]]],[[]]]] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[],[[[],[],[]],[]]] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[[],[[]]],[]]] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[[[]],[]],[]]] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[[[],[]]],[]]] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => ([(4,6),(5,6)],7) => 1
[[],[[[],[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[],[[[],[],[[]]]]] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[[],[[]],[]]]] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[],[[[[]],[],[]]]] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7) => 1
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 1
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[]],[],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[[]],[],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[],[],[[]],[]] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[]],[],[],[[],[]]] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[]],[],[],[[[]]]] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[]],[],[[]],[],[]] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[[]],[],[[]],[[]]] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 1
[[[]],[],[[],[]],[]] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
[[[]],[],[[[]]],[]] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[]],[],[[],[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 1
[[[]],[],[[],[[]]]] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[[]],[],[[[]],[]]] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[]],[],[[[],[]]]] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[[]],[],[[[[]]]]] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[]],[],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[[]],[[]],[],[[]]] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 1
[[[]],[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[]],[[]],[[],[]]] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 1
[[[]],[[]],[[[]]]] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[]],[[],[]],[],[]] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[[]],[[[]]],[],[]] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => ([(3,6),(4,5),(5,6)],7) => 1
[[[]],[[],[]],[[]]] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[]]],[[]]] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[],[],[]],[]] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[]],[[],[[]]],[]] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[]],[[[]],[]],[]] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[]],[[[],[]]],[]] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[]],[[[[]]]],[]] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[]],[[],[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[],[],[[]]]] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[],[[]],[]]] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[]],[[],[[],[]]]] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 1
[[[]],[[],[[[]]]]] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[]],[],[]]] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[]],[[[]],[[]]]] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[],[]],[]]] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[]],[[[[]]],[]]] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[],[],[]]]] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[],[[]]]]] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[[]],[]]]] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[[],[]]]]] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[]],[],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 1
[[[[]]],[],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[]],[],[],[[]]] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[[]]],[],[],[[]]] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[]],[],[[]],[]] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[[]]],[],[[]],[]] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[]],[],[[],[]]] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 2
[[[],[]],[],[[[]]]] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]]],[],[[],[]]] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]]],[],[[[]]]] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
[[[],[]],[[]],[],[]] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 1
[[[[]]],[[]],[],[]] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 1
[[[],[]],[[]],[[]]] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 1
[[[[]]],[[]],[[]]] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[]],[[],[]],[]] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 1
[[[],[]],[[[]]],[]] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 1
[[[[]]],[[],[]],[]] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]]],[[[]]],[]] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[]],[[],[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[[],[]],[[],[[]]]] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
[[[],[]],[[[]],[]]] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[[],[]],[[[],[]]]] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[[[],[]],[[[[]]]]] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]]],[[],[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[]]],[[],[[]]]] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[[[]]],[[[]],[]]] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]]],[[[],[]]]] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]]],[[[[]]]]] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => ([(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
[[[],[],[]],[],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 1
[[[],[[]]],[],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[]],[],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[[],[]]],[],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[[[[]]]],[],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[],[]],[],[[]]] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 1
[[[],[[]]],[],[[]]] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[]],[]],[],[[]]] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[[[],[]]],[],[[]]] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[[[[]]]],[],[[]]] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[],[]],[[]],[]] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[],[[]]],[[]],[]] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[[[]],[]],[[]],[]] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[]]],[[]],[]] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
[[[[[]]]],[[]],[]] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[[],[],[]],[[],[]]] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[[],[],[]],[[[]]]] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[[]]],[[],[]]] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 2
[[[],[[]]],[[[]]]] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[]],[[],[]]] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => ([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
[[[[]],[]],[[[]]]] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => 1
[[[[],[]]],[[],[]]] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[[[[],[]]],[[[]]]] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[]]]],[[],[]]] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[]]]],[[[]]]] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => ([(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
[[[],[],[],[]],[],[]] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => ([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[],[],[[]]],[],[]] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => 1
[[[],[[]],[]],[],[]] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 1
[[[],[[],[]]],[],[]] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[],[[[]]]],[],[]] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[[]],[],[]],[],[]] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[[]]],[],[]] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[],[]],[]],[],[]] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => 1
[[[[[]]],[]],[],[]] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[],[]]],[],[]] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[[]]]],[],[]] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[]],[]]],[],[]] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[],[]]]],[],[]] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[[]]]]],[],[]] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[],[],[]],[[]]] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[],[[]]],[[]]] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[[]],[]],[[]]] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[],[[],[]]],[[]]] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[[[]]]],[[]]] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[],[]],[[]]] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => ([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[[]]],[[]]] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[]],[]],[[]]] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) => 1
[[[[[]]],[]],[[]]] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[],[]]],[[]]] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[[]]]],[[]]] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[]],[]]],[[]]] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[],[]]]],[[]]] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => ([(0,3),(1,2),(4,6),(5,6)],7) => 1
[[[],[],[],[[]]],[]] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[[],[],[[]],[]],[]] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[],[[],[]]],[]] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[],[[[]]]],[]] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[[]],[],[]],[]] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => ([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => 1
[[[],[[]],[[]]],[]] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => 1
[[[],[[],[]],[]],[]] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[[[]]],[]],[]] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[[],[],[]]],[]] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[[],[[]]]],[]] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[[[]],[]]],[]] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[[[],[]]]],[]] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => 1
[[[[]],[],[],[]],[]] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => ([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[]],[],[[]]],[]] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[]],[[]],[]],[]] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[]],[[],[]]],[]] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[[]],[[[]]]],[]] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[[],[]],[],[]],[]] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 1
[[[[[]]],[],[]],[]] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 1
[[[[],[]],[[]]],[]] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => ([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => 1
[[[[[]]],[[]]],[]] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[],[],[]],[]],[]] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[[],[[]]],[]],[]] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 1
[[[[[]],[]],[]],[]] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[[],[]]],[]],[]] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[],[],[]]],[]] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[[[],[],[[]]]],[]] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[[],[[]],[]]],[]] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => 1
[[[[[]],[],[]]],[]] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[],[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => 1
[[[],[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[[],[],[],[[]],[]]] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[[],[],[],[[],[]]]] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 1
[[[],[],[],[[[]]]]] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[],[[]],[],[]]] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => 1
[[[],[],[[]],[[]]]] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => ([(3,6),(4,5),(5,6)],7) => 1
[[[],[],[[],[]],[]]] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[],[[[]]],[]]] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[[],[],[[],[],[]]]] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => 1
[[[],[],[[],[[]]]]] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[],[[[]],[]]]] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[],[],[[[],[]]]]] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[],[[[[]]]]]] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[[]],[],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[[],[[]],[],[[]]]] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[],[[]],[[]],[]]] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[],[[]],[[],[]]]] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[],[[]],[[[]]]]] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[[],[]],[],[]]] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[[[]]],[],[]]] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[[],[[],[]],[[]]]] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[[[]]],[[]]]] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[[],[],[]],[]]] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => 1
[[[],[[],[[]]],[]]] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[[[]],[]],[]]] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[[[],[]]],[]]] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => 1
[[[],[[[[]]]],[]]] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => ([(5,6)],7) => 1
[[[],[[],[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[[],[],[[]]]]] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[[],[[]],[]]]] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[[],[[],[]]]]] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[],[[],[[[]]]]]] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[],[[[]],[],[]]]] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[],[[[]],[[]]]]] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[],[[[],[]],[]]]] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[[],[[[[]]],[]]]] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => ([(4,6),(5,6)],7) => 1
[[[],[[[],[],[]]]]] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[[],[[[],[[]]]]]] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[],[[[[]],[]]]]] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => ([(3,6),(4,6),(5,6)],7) => 1
[[[],[[[[],[]]]]]] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[],[[[[[]]]]]]] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[]],[],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => ([(1,2),(3,6),(4,5),(5,6)],7) => 1
[[[[]],[],[],[[]]]] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => ([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[],[[]],[]]] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 1
[[[[]],[],[[],[]]]] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[[]],[],[[[]]]]] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[]],[[]],[],[]]] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => ([(3,6),(4,5),(5,6)],7) => 1
[[[[]],[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[[],[]],[]]] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[]],[[[]]],[]]] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[]],[[],[],[]]]] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[]],[[],[[]]]]] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[[[]],[]]]] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[]],[[[],[]]]]] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[]],[[[[]]]]]] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[]],[],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => 1
[[[[[]]],[],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[],[]],[],[[]]]] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[[[]]],[],[[]]]] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[],[]],[[]],[]]] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => 1
[[[[[]]],[[]],[]]] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[],[]],[[],[]]]] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => ([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => 2
[[[[],[]],[[[]]]]] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[]]],[[],[]]]] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[]]],[[[]]]]] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 1
[[[[],[],[]],[],[]]] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => ([(2,6),(3,5),(4,5),(4,6)],7) => 1
[[[[],[[]]],[],[]]] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[[[]],[]],[],[]]] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[[],[]]],[],[]]] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[[]]]],[],[]]] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[],[]],[[]]]] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[],[[]]],[[]]]] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[[]],[]],[[]]]] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[],[]]],[[]]]] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[[]]]],[[]]]] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[],[],[],[]],[]]] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => ([(2,3),(4,6),(5,6)],7) => 1
[[[[],[],[[]]],[]]] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[[],[[]],[]],[]]] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => ([(1,6),(2,6),(3,5),(4,5)],7) => 1
[[[[],[[],[]]],[]]] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[[[],[[[]]]],[]]] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => ([(4,6),(5,6)],7) => 1
[[[[[]],[],[]],[]]] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[[]],[[]]],[]]] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 1
[[[[[],[]],[]],[]]] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 1
[[[[[[]]],[]],[]]] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[[],[],[]]],[]]] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7) => 1
[[[[[],[[]]]],[]]] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => ([(3,6),(4,6),(5,6)],7) => 1
[[[[[[]],[]]],[]]] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[[[],[]]]],[]]] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => ([(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[[[[]]]]],[]]] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[],[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => 1
[[[[],[],[],[[]]]]] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => ([(3,6),(4,5),(5,6)],7) => 1
[[[[],[],[[]],[]]]] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7) => 1
[[[[],[],[[],[]]]]] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => ([(2,6),(3,5),(4,5),(4,6)],7) => 1
[[[[],[],[[[]]]]]] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[],[[]],[],[]]]] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[[[],[[]],[[]]]]] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[],[[],[]],[]]]] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => 1
[[[[],[[[]]],[]]]] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => ([(5,6)],7) => 1
[[[[],[[],[],[]]]]] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[[[],[[],[[]]]]]] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[],[[[]],[]]]]] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => ([(4,6),(5,6)],7) => 1
[[[[],[[[],[]]]]]] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => ([(3,6),(4,6),(5,6)],7) => 1
[[[[],[[[[]]]]]]] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[[]],[],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => ([(3,6),(4,5),(5,6)],7) => 1
[[[[[]],[],[[]]]]] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => ([(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[]],[[]],[]]]] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[[]],[[],[]]]]] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[[]],[[[]]]]]] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[],[]],[],[]]]] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => ([(2,6),(3,5),(4,5),(4,6)],7) => 1
[[[[[[]]],[],[]]]] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[[],[]],[[]]]]] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => 1
[[[[[[]]],[[]]]]] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[],[],[]],[]]]] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => ([(2,3),(4,6),(5,6)],7) => 1
[[[[[],[[]]],[]]]] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => ([(4,6),(5,6)],7) => 1
[[[[[[]],[]],[]]]] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 1
[[[[[[],[]]],[]]]] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => ([(3,6),(4,6),(5,6)],7) => 1
[[[[[[[]]]],[]]]] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => ([(2,6),(3,6),(4,6),(5,6)],7) => 1
[[[[[],[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => 1
[[[[[],[],[[]]]]]] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => ([(3,6),(4,5),(5,6)],7) => 1
[[[[[],[[]],[]]]]] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => ([(5,6)],7) => 1
[[[[[],[[],[]]]]]] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => ([(4,6),(5,6)],7) => 1
[[[[[],[[[]]]]]]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7) => 1
[[[[[[]],[],[]]]]] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => ([(3,6),(4,5),(5,6)],7) => 1
[[[[[[]],[[]]]]]] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7) => 1
[[[[[[],[]],[]]]]] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7) => 1
[[[[[[[]]],[]]]]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => ([(3,6),(4,6),(5,6)],7) => 1
[[[[[[],[],[]]]]]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => ([(5,6)],7) => 1
[[[[[[],[[]]]]]]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7) => 1
[[[[[[[]],[]]]]]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => ([(4,6),(5,6)],7) => 1
[[[[[[[],[]]]]]]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => ([(5,6)],7) => 1
[[[[[[[[]]]]]]]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => ([],7) => 0
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Description
The rank-width of a graph.
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.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.