Identifier
Values
[1,0] => [1,0] => [[]] => ([(0,1)],2) => 2
[1,0,1,0] => [1,1,0,0] => [[[]]] => ([(0,2),(1,2)],3) => 2
[1,1,0,0] => [1,0,1,0] => [[],[]] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [[[[]]]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,1,0,0] => [1,1,0,1,0,0] => [[[],[]]] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0] => [1,0,1,0,1,0] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0] => [1,0,1,1,0,0] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,1,0,0,0] => [1,1,0,0,1,0] => [[[]],[]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 3
[1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 4
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 4
[1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 4
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 4
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 4
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 4
[1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 3
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [[[[[],[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [[[[],[[[]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [[[[],[],[[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[],[[[]]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [[[],[[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[[],[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [[[],[[],[[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[[[]]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[[],[[]],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[[[],[[]]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[[[]],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[[[],[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[[[]],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[[[]],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [[[[]],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [[[[],[]],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
>>> Load all 478 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[[[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[],[[],[[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[],[[[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[[[]],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[],[],[[],[[]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[],[[]]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[[],[]],[[[]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[[],[[]]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[[]],[]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[[]],[]],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[[]]],[[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[[]]],[[[]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[[[],[]]],[[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[[],[]]]],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[[]],[]]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[[]]],[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[[]]]],[[]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[[],[]]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[[],[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[[[[],[[[]]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[[[[]]],[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[[],[[[],[]]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[[],[],[[[]]],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[],[[[]]],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[[],[[[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[[],[],[[[],[]]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[],[[[]]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[[],[],[]]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[[],[]]],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[[]]],[[[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[[[[[]]]]],[]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[],[[[],[],[]]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 7
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[],[],[[[],[]]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[],[[[],[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[],[],[[[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[[[[[]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[],[[[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[[[]]],[[[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[]],[[],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[[]],[[[[]]],[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[[]],[[[[],[]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[[]],[[],[[[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[],[],[],[]],[[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[],[]],[[],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[],[],[]],[[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[],[]],[[[[]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[],[[[]]]],[[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[[[]]]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[],[]]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => 5
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[],[],[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[],[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8) => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[[]]],[[[],[]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[[],[]]],[[[]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[[]]],[]],[[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[[]]]],[[],[]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[[],[]]]],[[]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[]]]]],[]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[[]]],[]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8) => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[[]]]]],[],[]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[[]]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[[],[],[]]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [[[[[],[[[]]],[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [[[[[],[[[],[]]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [[[[[],[],[[[]]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [[[[[[[],[]]],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [[[[[[[]]],[],[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[],[[[],[]],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[],[[],[[],[]]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [[[[[],[[],[]]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[[[[],[]],[[],[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [[[[[[],[]],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[],[[[[[]]]]],[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[[],[[[[],[]]],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[],[[[],[[]]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[],[[[[]],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[],[[[[[]]],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[],[[[[],[]],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[],[[[[[],[]]]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[],[[[],[[],[]]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[[],[[[],[[[]]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[],[[],[[[]],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[],[[],[[],[[]]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[],[[],[[[],[]]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[],[[[],[]],[[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[],[[[]],[[],[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[],[[[[[]]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[],[[[]]],[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[],[[[],[]]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[],[[],[[]]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[],[[[]],[]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[[]],[[[],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[[]],[[],[[],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [[[[],[]],[[[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [[[[],[]],[[],[[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [[[[],[]],[[[],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[],[[],[]]],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[],[[]]],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [[[[[],[[[]]]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[[[],[[],[]]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[[[]],[[],[]]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [[[[[],[]],[[]]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [[[[[],[[]]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [[[[[]]],[[[]]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[[[[]],[]],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [[[[[]]],[],[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [[[[[]]],[[[],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[[],[]],[]],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[[[[],[]]],[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [[[[[],[]]],[[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[[[[],[]],[]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[]],[]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[[[[[],[]]],[]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [[[[[[[],[]]]]],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [[[[[[[]]],[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [[[[[[[]]]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[],[[[[[],[]]]]],[]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[],[[[],[[],[]]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[],[[[],[[[]]]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[],[[[[],[]],[]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[],[[[[[]]],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[],[[],[[[]],[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[],[[],[[[],[]]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[],[[],[[],[[]]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[],[[[],[[]]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[],[[[]],[[],[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[],[[[],[]],[[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[],[[[[],[]]],[]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[],[[[[]],[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[],[[[],[[],[]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[],[[[[],[]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[],[[[[[],[]]],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[],[[[],[[[]]],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[],[[[[[]]],[],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[],[[[[[[[]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[],[[[],[[[],[]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[],[[[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[],[[],[[[],[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[],[[],[[],[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[],[[[],[]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[],[],[[[[]],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[],[[[[],[]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[],[],[[[],[[]]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[],[],[[[],[]],[[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[],[[[[],[]],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[],[[[[[]]],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[],[],[[],[[[]],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[],[],[[[]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[],[[[],[[],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[],[[[[[],[]]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[],[[[],[[[]]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[],[],[[],[[],[[]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[],[],[[],[[[],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[],[[[[[]]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[],[[],[[],[]]],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[],[[]],[[[],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[],[[],[]],[[[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[],[[],[[]]],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[],[[]],[[],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[],[[],[]],[[],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[],[[],[]],[[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[],[[[],[]],[]],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[],[[[]],[]],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[],[[[],[]]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[],[[[]]],[[[],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[],[[[],[]]],[[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[],[[],[[],[]]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[],[[[],[]],[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[]],[[[],[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[]],[[],[[],[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[],[]],[[[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[],[]],[[],[[]]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[],[]],[[[],[]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[],[[],[[]]]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[],[[]]],[[],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[],[[],[]]],[[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[],[[[],[]]]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[],[[[]],[]]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[[]],[[[[]]],[],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[]],[[[[],[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[]],[[],[[[]]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[]],[],[[[],[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]],[[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[]],[[[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[[[[[]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[[]],[[],[],[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[[]],[[],[[[],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[]],[],[[],[[],[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[],[],[[[]]]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[],[]],[[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[],[]],[[]],[[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[],[]],[[[],[]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[[],[]],[[[[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[],[]],[],[[[]],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[],[]],[],[[],[[]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[],[]],[[],[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[],[]],[],[[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[[],[]],[[],[[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[[],[]],[[[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[],[],[]],[[[[]]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[],[[],[]]],[],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[],[[]]],[],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[],[[],[]]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[],[[[],[]]]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[],[[[]]],[]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[],[[[]]]],[[],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[],[[[],[]]]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[],[[[]]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[],[[[]]],[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[[[],[]],[[],[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[],[[],[]]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[[]],[[],[]]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[]]],[[[]]],[],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[[]]],[[[],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[]]],[],[[[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[[]],[]],[[],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[],[]],[[]]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9) => 5
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[],[]],[]],[[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[[],[]]],[[],[]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[],[]]],[[[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[],[[],[]]]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[],[[]]],[]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[],[[[]]]]],[],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[[]],[]],[],[[],[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[[[]]],[[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[[]]],[],[[[],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[]]],[[[[[]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [[[[],[]],[]],[],[[]]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[],[]],[]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[],[]]],[],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[],[]]],[],[[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[[[],[]]],[[[],[]]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[[[],[],[]]],[[[]]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[],[]],[]],[]],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [[[[[]],[]],[]],[],[]] => ([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9) => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[[[],[]],[]]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[[[],[]]],[]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9) => 5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [[[[[]]],[],[]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[[]]],[]],[[],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[[[[]]]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[]]]],[[[[]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[[[[],[],[]]]],[[]]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[[[[],[]]],[]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[[[],[]]]],[[],[]]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[[[[[]]],[],[]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,6),(5,7),(6,8),(7,8)],9) => 4
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[[[[[],[]]],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[[[[]]],[]]],[],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,7),(4,8),(5,6),(5,8)],9) => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[]]]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,4),(4,6),(5,7),(5,8),(6,7)],9) => 4
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [[[[[[],[]]]]],[],[]] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9) => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[]]]]],[[[]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[[]]]]]],[[]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9) => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[],[]]]]]]],[]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[]]]]]]],[]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[] => [] => [] => ([],1) => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[],[],[[[[[[[]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[]],[[[[[[],[]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[]],[[],[[[[[]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[],[]]]]],[[[]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[[],[]]]]]],[[]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[[]]]]]]],[],[]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[[],[]]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[],[[[]]]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[],[[[[[]]]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[],[[[[[[[]]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[[]]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[[]]],[]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 3
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [[[[[[[[[]]]]],[]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[],[[[[[[[]]]]]]],[]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10) => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[[]]]]]]]],[[]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[]]],[[[[[[[]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[]],[[[[[[[[]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11) => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[[]]],[[[],[[[]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10) => 3
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Description
The number of leaves in a graph.
That is, the number of vertices of a graph that have degree 1.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
Map
Knuth-Krattenthaler
Description
The map that sends the Dyck path to a 321-avoiding permutation, then applies the Robinson-Schensted correspondence and finally interprets the first row of the insertion tableau and the second row of the recording tableau as up steps.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and $321$-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.