Processing math: 100%

Identifier
Values
[1,0] => [[]] => ([(0,1)],2) => 2
[1,0,1,0] => [[],[]] => ([(0,2),(1,2)],3) => 2
[1,1,0,0] => [[[]]] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,0,1,0] => [[[]],[]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,1,0,1,0,0] => [[[],[]]] => ([(0,3),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0] => [[[[]]]] => ([(0,3),(1,2),(2,3)],4) => 2
[1,0,1,0,1,0,1,0] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0] => [[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,0,0,1,0] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,0,1,0,0] => [[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,0,1,1,1,0,0,0] => [[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,0,1,0,1,0] => [[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,0,0,1,1,0,0] => [[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,0,1,0,0,1,0] => [[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,0,1,0,1,0,0] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,1,0,1,1,0,0,0] => [[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,0,0,1,0] => [[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,1,1,0,0,1,0,0] => [[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,1,0,1,0,0,0] => [[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => 2
[1,1,1,1,0,0,0,0] => [[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 2
[1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 2
[1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 2
[1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
>>> Load all 738 entries. <<<
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[[]],[]],[],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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
[1,1,1,1,0,0,0,1,0,0,1,0] => [[[[[]]],[]],[]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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
[1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 2
[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) => 2
[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) => 2
[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) => 2
[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
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[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) => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[[]],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[],[],[],[[],[]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[],[[],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[],[],[],[[],[[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[],[[[]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[[[[]]]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[],[],[[]],[[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[[]],[[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[],[],[[],[]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[],[],[[],[]],[[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[],[],[[],[],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[],[],[[],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[],[],[[],[],[[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[],[],[[],[[]]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[],[],[[],[[]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[],[],[[],[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[],[],[[],[[[]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[],[],[[[]],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[],[],[[[]],[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[],[],[[[]],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[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) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[],[],[[[],[]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[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) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[],[],[[[],[[]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[],[],[[[[]]],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[],[],[[[[]],[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[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) => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[],[[]],[],[[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[],[[]],[[],[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[],[[]],[[],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[],[[]],[[],[[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[],[[]],[[[]],[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[],[[]],[[[],[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[[]],[[[[]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[],[[],[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[],[[],[]],[],[[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[],[[],[]],[[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[],[[],[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[],[[],[]],[[[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[],[[],[],[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[],[[],[],[]],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[],[[],[],[],[]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[],[[],[],[],[[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[],[[],[],[[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[],[[],[],[[]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[],[[],[],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[],[[],[],[[[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[],[[],[[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[],[[],[[]]],[[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[],[[],[[]],[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[],[[],[[]],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[],[[],[[]],[[]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[],[[],[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[],[[],[[],[]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[],[[],[[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[],[[],[[],[[]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[],[[],[[[]]]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[],[[],[[[]]],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[],[[],[[[]],[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[],[[],[[[],[]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[],[[[]]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[],[[[]],[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[],[[[]],[]],[[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[],[[[]],[],[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[],[[[]],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[],[[[]],[],[[]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[],[[[]],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[],[[[]],[[]],[]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[],[[[]],[[],[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[],[[[]],[[[]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[],[[[],[]]],[[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[],[[[],[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[],[[[],[]],[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[],[[[],[]],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[],[[[],[],[]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[],[[[],[],[[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[],[[[],[[]]]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[],[[[],[[]]],[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[],[[[],[[]],[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[[[[]]]],[[]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[],[[[[]]],[]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[],[[[[]]],[],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[],[[[[]]],[[]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[],[[[[]],[]]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[],[[[[]],[]],[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[],[[[[]],[],[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[],[[[[],[]]]],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[[],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[]],[],[[],[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[]],[],[[],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[]],[],[[],[[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[]],[],[[[]],[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[]],[],[[[],[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[[[[]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[]],[[]],[[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[]],[[],[]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[]],[[],[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[]],[[],[],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[[]],[[],[],[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[]],[[],[[]]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[]],[[],[[]],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[]],[[],[[],[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[]],[[[]],[]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[[]],[[[]],[],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[]],[[[]],[[]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[]],[[[],[]]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[]],[[[],[]],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[[]],[[[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[[]],[[[],[[]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[[[[]]]],[]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[]],[[[[]],[]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[[[[[]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[],[]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[],[]],[],[],[[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[],[]],[],[[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[],[]],[],[[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[],[]],[],[[[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[],[]],[[]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[],[]],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[],[]],[[],[]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[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) => 2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[[],[]],[[],[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[],[]],[[[]]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[[],[]],[[[]],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[[],[]],[[[],[]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[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) => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[],[],[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[],[],[]],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[],[],[]],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[[],[],[]],[[[]]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[],[]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[],[]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[],[[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[],[[]]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[],[[]],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[],[[],[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[],[],[[]]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[[],[],[[]]],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[[],[],[[]],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[[],[],[[]],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[[],[],[[]],[[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[[],[],[[],[]]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[[],[],[[],[]],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[[],[],[[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[[],[],[[],[[]]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[[],[],[[[]]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[[],[],[[[]],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[[],[],[[[[]]]]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[],[[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[],[[]]],[],[[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[],[[]]],[[]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[[],[[]]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[[],[[]]],[[[]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[],[[]],[]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[[],[[]],[]],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[[],[[]],[],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[[],[[]],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[[],[[]],[],[[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[[],[[]],[[]]],[]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[[],[[]],[[]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[[],[[]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[[],[[]],[[[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[],[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[[],[[],[]]],[[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[[],[[],[]],[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[[],[[],[]],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[[],[[],[]],[[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[[],[[],[],[]]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[[],[[],[],[]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[[],[[],[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[[],[[],[],[[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[],[[],[[]]]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[[],[[],[[]]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[[],[[],[[]],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[],[[],[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[[],[[],[[[]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[],[[[]]]],[],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[[],[[[]]],[]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[[],[[[]]],[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[],[[[]],[]]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[[],[[[]],[]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[[],[[[]],[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[[],[[[]],[[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[],[[[],[]]]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[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) => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[[],[[[],[]],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[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) => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[[],[[[],[[]]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[[],[[[[]]],[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[[],[[[[]],[]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[[],[[[[],[]]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[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) => 2
[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) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[]]],[],[[],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[[]]],[[],[]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[[]]],[[],[],[]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[[]]],[[],[[]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[[]]],[[[]],[]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[]]],[[[[]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[]],[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[[]],[]],[],[[]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[]],[]],[[]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[]],[]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[[]],[]],[[[]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[[]],[],[]],[],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[[]],[],[]],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[[]],[],[],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[[]],[],[],[[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[[]],[],[[]]],[]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[[]],[],[[]],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[[]],[],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[[]],[],[[[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[]],[[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[[]],[[]]],[[]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[[]],[[]],[]],[]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[[]],[[]],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[[]],[[]],[[]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[[]],[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[[[]],[[],[]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[[[]],[[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[[[]],[[],[[]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[[]],[[[]]]],[]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[]],[[[]]],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[[]],[[[]],[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[[]],[[[],[]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[]],[[[[]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[[],[]]],[],[[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[],[]]],[[]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[],[]]],[[],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[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) => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[[],[]],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[[],[]],[]],[[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[[],[]],[],[]],[]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[[],[]],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[[[],[]],[],[[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[[],[]],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[[],[]],[[]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[[],[]],[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[[],[]],[[[]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[[],[],[]]],[[]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[[],[],[]],[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[[],[],[]],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[[[],[],[]],[[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[],[]],[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[[],[],[],[[]]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[[],[],[[]]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[[],[],[[]]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[[],[],[[]],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[[],[],[[],[]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[[],[],[[[]]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[],[[]]]],[],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[[],[[]]]],[[]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[[],[[]]],[]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[[],[[]]],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[[],[[]]],[[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[[],[[]],[]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[[],[[]],[]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[[],[[]],[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[[[],[[]],[[]]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[[],[[],[]]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[[],[[],[]],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[[],[[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[[],[[],[[]]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[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) => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[[],[[[]]]],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[[],[[[]]],[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[[],[[[]],[]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[[],[[[],[]]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[[],[[[[]]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[[]]]],[],[[]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[[]]]],[[]],[]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[[]]]],[[[]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[[]]],[]],[],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[[]]],[],[]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[[]]],[],[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[[]]],[[]]],[]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[[]]],[[]],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[[]]],[[],[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[[]],[]]],[],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[[]],[]]],[[]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[[]],[]],[]],[]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[[]],[]],[],[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[[]],[]],[[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[[]],[],[]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[[]],[],[]],[]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[[]],[],[],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[[]],[],[[]]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[[]],[[]]]],[]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[[]],[[]]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[[]],[[]],[]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[[]],[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[[]],[[[]]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[[],[]]]],[],[]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[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) => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[[],[]]],[]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[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) => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[[],[]]],[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[[],[]],[]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[[],[]],[],[]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[[],[]],[[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[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) => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[[],[],[]],[]]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8) => 2
[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) => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[[[[],[],[[]]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[[],[[]]]]],[]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[[],[[]]]],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[[],[[]]],[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[[],[[]],[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[[],[[],[]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[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) => 2
[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) => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[[]]]]],[[]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[[]]]],[]],[]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[[]]]],[],[]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[[]]]],[[]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[[[[[]]],[]],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[[[[[]]],[],[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[[[[[]]],[[]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[[]],[]]]],[]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[[[]],[]]],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[[[]],[]],[]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[[]],[],[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,7),(5,6),(6,7)],8) => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[[[[[]],[[]]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) => 2
[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) => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[[[],[]]]],[]]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[[[],[]]],[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[[[],[]],[]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8) => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[[[],[],[]]]]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(5,6),(5,7)],8) => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[[[],[[]]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[[]]]]]],[]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[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) => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[[[[[]]]],[]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[[[[]],[]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) => 2
[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) => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[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) => 2
[] => [] => ([],1) => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of q possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number HG(G) of a graph G is the largest integer q such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of q possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
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 D1,…,Dk of respective semilengths n1,…,nk (so one has n=n1+…nk) each of which has no returns.
Denote by ˜Di the path of semilength ni−1 obtained from Di 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 T1,…,Tk which are again ordered trees computed from D1,…,Dk respectively.
The unique path of semilength 1 is sent to the tree consisting of a single node.