Identifier
Mp00142: Dyck paths —promotion⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00046: Ordered trees —to graph⟶ Graphs
Images
[1,0] => [1,0] => [[]] => ([(0,1)],2)
[1,0,1,0] => [1,1,0,0] => [[[]]] => ([(0,2),(1,2)],3)
[1,1,0,0] => [1,0,1,0] => [[],[]] => ([(0,2),(1,2)],3)
[1,0,1,0,1,0] => [1,1,0,1,0,0] => [[[],[]]] => ([(0,3),(1,3),(2,3)],4)
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [[[]],[]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,0] => [1,1,1,0,0,0] => [[[[]]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0] => [1,0,1,0,1,0] => [[],[],[]] => ([(0,3),(1,3),(2,3)],4)
[1,1,1,0,0,0] => [1,0,1,1,0,0] => [[],[[]]] => ([(0,3),(1,2),(2,3)],4)
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => ([(0,4),(1,4),(2,4),(3,4)],5)
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5)
[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)
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[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)
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[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)
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [[[[],[[]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,0,1,0,1,0] => [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)
[1,0,1,0,1,0,1,0,1,1,0,0] => [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)
[1,0,1,0,1,0,1,1,0,0,1,0] => [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)
[1,0,1,0,1,0,1,1,0,1,0,0] => [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)
[1,0,1,0,1,0,1,1,1,0,0,0] => [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)
[1,0,1,0,1,1,0,0,1,0,1,0] => [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)
[1,0,1,0,1,1,0,0,1,1,0,0] => [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)
[1,0,1,0,1,1,0,1,0,0,1,0] => [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)
[1,0,1,0,1,1,0,1,0,1,0,0] => [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)
[1,0,1,0,1,1,0,1,1,0,0,0] => [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)
[1,0,1,0,1,1,1,0,0,0,1,0] => [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)
[1,0,1,0,1,1,1,0,0,1,0,0] => [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)
[1,0,1,0,1,1,1,0,1,0,0,0] => [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)
[1,0,1,0,1,1,1,1,0,0,0,0] => [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)
[1,0,1,1,0,0,1,0,1,0,1,0] => [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)
[1,0,1,1,0,0,1,0,1,1,0,0] => [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)
[1,0,1,1,0,0,1,1,0,0,1,0] => [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)
[1,0,1,1,0,0,1,1,0,1,0,0] => [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)
[1,0,1,1,0,0,1,1,1,0,0,0] => [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)
[1,0,1,1,0,1,0,0,1,0,1,0] => [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)
[1,0,1,1,0,1,0,0,1,1,0,0] => [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)
[1,0,1,1,0,1,0,1,0,0,1,0] => [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)
[1,0,1,1,0,1,0,1,0,1,0,0] => [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)
[1,0,1,1,0,1,0,1,1,0,0,0] => [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)
[1,0,1,1,0,1,1,0,0,0,1,0] => [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)
[1,0,1,1,0,1,1,0,0,1,0,0] => [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)
[1,0,1,1,0,1,1,0,1,0,0,0] => [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)
[1,0,1,1,0,1,1,1,0,0,0,0] => [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)
[1,0,1,1,1,0,0,0,1,0,1,0] => [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)
[1,0,1,1,1,0,0,0,1,1,0,0] => [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)
[1,0,1,1,1,0,0,1,0,0,1,0] => [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)
[1,0,1,1,1,0,0,1,0,1,0,0] => [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)
[1,0,1,1,1,0,0,1,1,0,0,0] => [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)
[1,0,1,1,1,0,1,0,0,0,1,0] => [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)
[1,0,1,1,1,0,1,0,0,1,0,0] => [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)
[1,0,1,1,1,0,1,0,1,0,0,0] => [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)
[1,0,1,1,1,0,1,1,0,0,0,0] => [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)
>>> Load all 2259 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [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)
[1,0,1,1,1,1,0,0,0,1,0,0] => [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)
[1,0,1,1,1,1,0,0,1,0,0,0] => [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)
[1,0,1,1,1,1,0,1,0,0,0,0] => [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)
[1,0,1,1,1,1,1,0,0,0,0,0] => [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)
[1,1,0,0,1,0,1,0,1,0,1,0] => [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)
[1,1,0,0,1,0,1,0,1,1,0,0] => [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)
[1,1,0,0,1,0,1,1,0,0,1,0] => [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)
[1,1,0,0,1,0,1,1,0,1,0,0] => [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)
[1,1,0,0,1,0,1,1,1,0,0,0] => [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)
[1,1,0,0,1,1,0,0,1,0,1,0] => [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)
[1,1,0,0,1,1,0,0,1,1,0,0] => [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)
[1,1,0,0,1,1,0,1,0,0,1,0] => [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)
[1,1,0,0,1,1,0,1,0,1,0,0] => [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)
[1,1,0,0,1,1,0,1,1,0,0,0] => [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)
[1,1,0,0,1,1,1,0,0,0,1,0] => [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)
[1,1,0,0,1,1,1,0,0,1,0,0] => [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)
[1,1,0,0,1,1,1,0,1,0,0,0] => [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)
[1,1,0,0,1,1,1,1,0,0,0,0] => [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)
[1,1,0,1,0,0,1,0,1,0,1,0] => [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)
[1,1,0,1,0,0,1,0,1,1,0,0] => [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)
[1,1,0,1,0,0,1,1,0,0,1,0] => [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)
[1,1,0,1,0,0,1,1,0,1,0,0] => [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)
[1,1,0,1,0,0,1,1,1,0,0,0] => [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)
[1,1,0,1,0,1,0,0,1,0,1,0] => [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)
[1,1,0,1,0,1,0,0,1,1,0,0] => [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)
[1,1,0,1,0,1,0,1,0,0,1,0] => [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)
[1,1,0,1,0,1,0,1,0,1,0,0] => [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)
[1,1,0,1,0,1,0,1,1,0,0,0] => [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)
[1,1,0,1,0,1,1,0,0,0,1,0] => [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)
[1,1,0,1,0,1,1,0,0,1,0,0] => [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)
[1,1,0,1,0,1,1,0,1,0,0,0] => [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)
[1,1,0,1,0,1,1,1,0,0,0,0] => [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)
[1,1,0,1,1,0,0,0,1,0,1,0] => [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)
[1,1,0,1,1,0,0,0,1,1,0,0] => [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)
[1,1,0,1,1,0,0,1,0,0,1,0] => [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)
[1,1,0,1,1,0,0,1,0,1,0,0] => [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)
[1,1,0,1,1,0,0,1,1,0,0,0] => [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)
[1,1,0,1,1,0,1,0,0,0,1,0] => [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)
[1,1,0,1,1,0,1,0,0,1,0,0] => [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)
[1,1,0,1,1,0,1,0,1,0,0,0] => [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)
[1,1,0,1,1,0,1,1,0,0,0,0] => [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)
[1,1,0,1,1,1,0,0,0,0,1,0] => [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)
[1,1,0,1,1,1,0,0,0,1,0,0] => [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)
[1,1,0,1,1,1,0,0,1,0,0,0] => [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)
[1,1,0,1,1,1,0,1,0,0,0,0] => [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)
[1,1,0,1,1,1,1,0,0,0,0,0] => [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)
[1,1,1,0,0,0,1,0,1,0,1,0] => [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)
[1,1,1,0,0,0,1,0,1,1,0,0] => [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)
[1,1,1,0,0,0,1,1,0,0,1,0] => [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)
[1,1,1,0,0,0,1,1,0,1,0,0] => [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)
[1,1,1,0,0,0,1,1,1,0,0,0] => [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)
[1,1,1,0,0,1,0,0,1,0,1,0] => [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)
[1,1,1,0,0,1,0,0,1,1,0,0] => [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)
[1,1,1,0,0,1,0,1,0,0,1,0] => [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)
[1,1,1,0,0,1,0,1,0,1,0,0] => [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)
[1,1,1,0,0,1,0,1,1,0,0,0] => [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)
[1,1,1,0,0,1,1,0,0,0,1,0] => [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)
[1,1,1,0,0,1,1,0,0,1,0,0] => [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)
[1,1,1,0,0,1,1,0,1,0,0,0] => [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)
[1,1,1,0,0,1,1,1,0,0,0,0] => [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)
[1,1,1,0,1,0,0,0,1,0,1,0] => [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)
[1,1,1,0,1,0,0,0,1,1,0,0] => [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)
[1,1,1,0,1,0,0,1,0,0,1,0] => [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)
[1,1,1,0,1,0,0,1,0,1,0,0] => [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)
[1,1,1,0,1,0,0,1,1,0,0,0] => [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)
[1,1,1,0,1,0,1,0,0,0,1,0] => [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)
[1,1,1,0,1,0,1,0,0,1,0,0] => [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)
[1,1,1,0,1,0,1,0,1,0,0,0] => [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)
[1,1,1,0,1,0,1,1,0,0,0,0] => [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)
[1,1,1,0,1,1,0,0,0,0,1,0] => [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)
[1,1,1,0,1,1,0,0,0,1,0,0] => [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)
[1,1,1,0,1,1,0,0,1,0,0,0] => [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)
[1,1,1,0,1,1,0,1,0,0,0,0] => [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)
[1,1,1,0,1,1,1,0,0,0,0,0] => [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)
[1,1,1,1,0,0,0,0,1,0,1,0] => [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)
[1,1,1,1,0,0,0,0,1,1,0,0] => [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)
[1,1,1,1,0,0,0,1,0,0,1,0] => [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)
[1,1,1,1,0,0,0,1,0,1,0,0] => [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)
[1,1,1,1,0,0,0,1,1,0,0,0] => [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)
[1,1,1,1,0,0,1,0,0,0,1,0] => [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)
[1,1,1,1,0,0,1,0,0,1,0,0] => [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)
[1,1,1,1,0,0,1,0,1,0,0,0] => [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)
[1,1,1,1,0,0,1,1,0,0,0,0] => [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)
[1,1,1,1,0,1,0,0,0,0,1,0] => [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)
[1,1,1,1,0,1,0,0,0,1,0,0] => [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)
[1,1,1,1,0,1,0,0,1,0,0,0] => [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)
[1,1,1,1,0,1,0,1,0,0,0,0] => [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)
[1,1,1,1,0,1,1,0,0,0,0,0] => [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)
[1,1,1,1,1,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,0,0,0,0,1,0,0] => [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)
[1,1,1,1,1,0,0,0,1,0,0,0] => [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)
[1,1,1,1,1,0,0,1,0,0,0,0] => [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)
[1,1,1,1,1,0,1,0,0,0,0,0] => [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)
[1,1,1,1,1,1,0,0,0,0,0,0] => [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)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [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)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [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)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [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)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [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)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [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)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [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)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [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)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [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)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [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)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [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)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [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)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [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)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [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)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [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)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [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)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [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)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [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)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [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)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [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)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [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)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [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)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [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)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [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)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [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)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [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)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [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)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [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)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [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)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [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)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [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)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [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)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [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)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [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)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [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)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [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)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [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)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [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)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [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)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [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)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [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)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [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)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [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)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [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)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [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)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [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)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [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)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [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)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [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)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [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)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [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)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [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)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [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)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [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)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [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)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [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)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [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)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [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)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [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)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [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)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [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)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [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)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [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)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [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)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [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)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [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)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [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)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [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)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [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)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [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)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [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)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [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)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [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)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [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)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [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)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [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)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [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)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [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)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [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)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [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)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [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)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [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)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [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)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [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)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [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)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [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)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [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)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [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)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [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)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [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)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [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)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [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)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [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)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [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)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [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)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [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)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [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)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [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)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [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)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [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)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [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)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [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)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [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)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [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)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [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)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [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)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [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)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [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)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [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)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [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)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [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)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [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)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [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)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [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)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [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)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [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)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [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)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [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)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [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)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [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)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [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)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [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)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [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)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [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)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [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)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [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)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [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)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [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)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [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)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [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)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [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)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [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)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [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)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [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)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [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)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [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)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [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)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [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)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [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)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [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)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [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)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [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)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [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)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [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)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [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)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [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)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [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)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [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)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [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)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [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)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [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)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [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)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [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)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [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)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [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)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [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)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [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)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [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)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [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)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [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)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [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)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [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)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [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)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [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)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [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)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [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)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [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)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [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)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [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)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [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)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [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)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [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)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [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)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [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)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [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)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [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)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [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)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [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)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [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)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [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)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [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)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [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)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [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)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [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)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [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)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [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)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [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)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [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)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [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)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [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)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [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)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [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)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [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)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [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)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [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)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [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)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [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)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [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)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [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)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [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)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [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)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [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)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [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)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [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)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [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)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [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)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [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)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [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)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [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)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [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)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [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)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [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)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [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)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [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)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [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)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [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)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [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)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [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)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [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)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [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)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [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)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [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)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [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)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [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)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [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)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [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)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [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)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [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)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [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)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [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)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [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)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [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)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [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)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [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)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [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)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [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)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [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)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [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)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [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)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [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)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [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)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [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)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [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)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [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)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [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)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [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)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [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)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [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)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [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)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [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)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [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)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [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)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [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)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [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)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [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)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [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)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [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)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [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)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [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)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [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)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [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)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [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)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [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)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [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)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [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)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [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)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [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)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [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)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [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)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [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)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [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)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [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)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [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)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [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)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [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)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [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)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [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)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [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)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [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)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [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)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [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)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [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)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [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)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [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)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [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)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [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)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [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)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [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)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [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)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [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)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [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)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [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)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [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)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [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)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [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)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [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)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [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)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [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)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [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)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [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)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [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)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [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)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [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)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [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)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [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)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [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)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [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)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [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)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [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)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [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)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [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)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [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)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [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)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [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)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [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)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [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)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [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)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [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)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [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)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [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)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [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)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [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)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [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)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [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)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [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)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [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)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [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)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [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)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [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)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [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)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [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)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [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)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [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)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [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)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [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)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [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)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [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)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [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)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [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)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [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)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [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)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [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)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [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)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [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)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [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)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [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)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [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)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [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)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [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)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [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)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [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)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [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)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [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)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [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)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [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)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [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)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [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)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [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)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [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)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [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)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [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)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [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)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [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)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [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)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [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)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [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)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [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)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [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)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [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)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [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)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [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)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [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)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [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)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [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)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [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)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [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)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [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)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [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)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [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)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [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)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [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)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [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)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [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)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [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)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [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)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [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)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [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)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [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)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [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)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [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)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [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)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [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)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [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)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [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)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [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)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [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)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [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)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [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)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [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)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [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)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [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)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [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)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [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)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [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)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [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)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [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)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [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)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [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)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [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)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [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)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [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)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [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)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [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)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [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)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [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)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [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)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [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)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [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)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [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)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [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)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [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)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [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)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [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)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [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)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [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)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [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)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[],[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[],[],[],[],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[],[],[[]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[],[],[[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[],[],[],[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[],[],[],[]],[],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[],[],[[[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[],[],[],[]],[[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[],[],[],[]],[[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[[],[],[],[]],[[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[[],[],[],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[[],[],[],[[]],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[[],[],[],[[]],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[],[],[],[[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[[],[],[],[[]]],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[[],[],[],[[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[[],[],[],[[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[[],[],[],[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[],[],[]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[],[],[]],[],[],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[[],[],[],[[],[[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[],[],[]],[],[[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[],[],[]],[],[[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[],[],[]],[],[[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[[],[],[],[[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[[],[],[],[[[]]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[[],[],[],[[[]],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[],[],[]],[[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[],[],[]],[[]],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[[],[],[],[[[],[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[],[],[]],[[],[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[],[],[]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[[],[],[]],[[],[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[[],[],[],[[[[]]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[],[],[]],[[[]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[[],[],[]],[[[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[[],[],[]],[[[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [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)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[[],[],[[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[[],[],[[]],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[[],[],[[]],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[],[],[[]],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[[],[],[[]],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[[],[],[[]],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[[],[],[[]],[[]]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[[],[],[[]],[[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[],[],[[]]],[],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[],[],[[]]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[[],[],[[]],[[[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[],[],[[]]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[[],[],[[]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[[],[],[[]]],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[[],[],[[],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[[],[],[[],[]],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[[],[],[[],[]],[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[],[],[[],[]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[[],[],[[],[]]],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[[],[],[[],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[[],[],[[],[],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[[],[],[[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[],[]],[],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[],[]],[],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[[],[],[[],[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[],[]],[],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[],[]],[],[],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[],[]],[],[],[[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[[],[],[[],[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[],[],[[],[[]]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[[],[],[[],[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[],[]],[],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[],[]],[],[[]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[],[],[[],[[],[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[],[]],[],[[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[],[]],[],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [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)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[[],[],[[],[[[]]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[],[]],[],[[[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [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)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [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)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[],[]],[],[[[[]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[],[],[[[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[[],[],[[[]]],[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[[],[],[[[]]],[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[],[],[[[]]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [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)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[[],[],[[[]],[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[],[],[[[]],[]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[[],[],[[[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[],[]],[[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[],[]],[[]],[],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[[],[],[[[]],[[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[[]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [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)
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[],[]],[[]],[[[]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[[],[],[[[],[]]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[],[],[[[],[]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[[],[],[[[],[]],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[],[]],[[],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [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)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[[],[],[[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[],[]],[[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[],[]],[[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[[],[]],[[],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[[],[],[[[],[[]]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [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)
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[],[]],[[],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [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)
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [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)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[],[[[[]]]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[],[[[[]]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[[],[],[[[[]]],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[],[]],[[[]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[],[]],[[[]]],[[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[[],[],[[[[]],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [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)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[[],[]],[[[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[],[]],[[[]],[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[[],[],[[[[],[]]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [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)
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [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)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[[],[]],[[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[[],[]],[[[],[[]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [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)
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[],[]],[[[[]]]],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [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)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[],[]],[[[[]],[]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [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)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[],[]],[[[[[]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[],[[]],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[],[[]],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[],[[]],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[],[[]],[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[],[[]],[],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[],[[]],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[],[[]],[],[[]]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[],[[]],[],[[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[],[[]],[]],[],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[],[[]],[]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[],[[]],[],[[[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[],[[]],[]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[],[[]],[]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[],[[]],[]],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[],[[]],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[],[[]],[[]],[[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[],[[]],[[]]],[],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[],[[]],[[]]],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[[],[[]],[[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[],[[]],[[],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[[],[[]],[[],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[],[[]]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[],[[]]],[],[],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[[],[[]],[[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[],[[]]],[],[[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [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)
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[],[[]]],[],[[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[],[[]],[[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[],[[]],[[[]]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[],[[]],[[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[],[[]]],[[]],[],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[],[[]]],[[]],[[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[],[[]],[[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [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)
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[],[[]]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[],[[]]],[[],[[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[],[[]],[[[[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[],[[]]],[[[]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[],[[]]],[[[]],[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[],[[]]],[[[],[]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[],[[]]],[[[[]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[],[[],[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[],[[],[]],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[[],[[],[]],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[],[[],[]],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[],[[],[]],[]],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[],[[],[]],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[],[[],[]],[[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[],[[],[]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[],[[],[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [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)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[],[[],[]],[[[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [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)
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [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)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[],[[],[]]],[[[]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[],[[],[],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[],[[],[],[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[[],[[],[],[]],[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[],[[],[],[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[],[[],[],[]]],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[],[[],[],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[],[[],[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[],[[],[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[],[[],[],[],[[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[],[[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[],[[],[],[[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[],[[],[],[[]]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[],[[],[],[[]],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[],[[],[],[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[]],[],[],[[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[]],[],[],[[],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[]],[],[],[[],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[],[[],[],[[[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[],[[[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[]],[],[],[[[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[]],[],[],[[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[],[[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[],[[],[[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[],[[],[[]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[],[[],[[]]],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [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)
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[],[[],[[]]]],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[],[[],[[]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[],[[],[[]],[]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[],[[],[[]],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[[],[[],[[]],[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[]],[],[[]],[[],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[],[[]],[[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[],[[],[[],[]]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [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)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[],[[],[[],[]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[]],[],[[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[]],[],[[],[]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[],[[],[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[]],[],[[],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[]],[],[[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[]],[],[[],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [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)
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[]],[],[[],[[]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[]],[],[[],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [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)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[]],[],[[],[[[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[],[[],[[[]]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[],[[],[[[]]]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[],[[],[[[]]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[],[[[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[],[[[]]],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [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)
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[]],[],[[[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[]],[],[[[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[]],[],[[[]],[[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [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)
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[]],[],[[[],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [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)
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[]],[],[[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[]],[],[[[],[[]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[],[[],[[[[]]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[]],[],[[[[]]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[]],[],[[[[]],[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[]],[],[[[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[],[[[[[]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[],[[[]]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[],[[[]]],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[],[[[]]],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[],[[[]]],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [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)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[],[[[]]],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[],[[[]]],[[]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[],[[[]]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[],[[[]]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[],[[[]]]],[],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [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)
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[],[[[]]]],[[]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [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)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[],[[[]]]],[[[]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[],[[[]],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[],[[[]],[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[],[[[]],[]],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [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)
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[],[[[]],[]]],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[],[[[]],[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[],[[[]],[],[]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[],[[[]],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[[]],[],[],[[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[],[[[]],[],[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[[]],[],[[]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[[]],[],[[],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[[]],[],[[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[],[[[]],[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[],[[[]],[[]]]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[],[[[]],[[]],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[[]],[],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]],[[]]] => ([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [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)
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[]],[[],[]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[]],[[]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[]],[[],[[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[[],[[[]],[[[]]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[]],[[[]],[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[]],[[[],[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[]],[[[[]]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[],[[[],[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[],[[[],[]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[[],[[[],[]]],[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [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)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [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)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[],[[[],[]],[]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [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)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[],[[[],[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[]],[[],[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[]],[[],[]],[],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [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)
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[]],[[],[]],[[]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [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)
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[]],[[],[]],[[[]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[],[[[],[],[]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[],[[[],[],[]]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[],[[[],[],[]],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[]],[[],[],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[]],[[],[],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[],[[[],[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[]],[[],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[]],[[],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[[]],[[],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[[],[[[],[],[[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[]],[[],[],[[]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[[]],[[],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[[]],[[],[],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [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)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[[],[[[],[[]]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[],[[[],[[]]]]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [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)
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[]],[[],[[]]],[],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[]],[[],[[]]],[[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[],[[[],[[]],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[]],[[],[[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[[]],[[],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[[]],[[],[[]],[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [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)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [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)
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[[]],[[],[[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[[]],[[],[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[[]],[[],[[],[[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [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)
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[]],[[],[[[]]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [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)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[[]],[[],[[[]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [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)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[[]],[[],[[[[]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[],[[[[]]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[],[[[[]]]],[]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[],[[[[]]]],[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[],[[[[]]]]],[],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[],[[[[]]]]],[[]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[[],[[[[]]],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[],[[[[]]],[]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[[],[[[[]]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[]],[[[]]],[],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[[],[[[[]]],[[]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[]],[[[]]],[[],[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[]],[[[]]],[[[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[],[[[[]],[]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[],[[[[]],[]]]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [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)
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[]],[[[]],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[]],[[[]],[]],[[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[],[[[[]],[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[]],[[[]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[]],[[[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[[]],[[[]],[],[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[[],[[[[]],[[]]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[]],[[[]],[[]]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[]],[[[]],[[]],[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[[]],[[[]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[[]],[[[]],[[[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[],[[[[],[]]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[],[[[[],[]]]]],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [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)
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[]],[[[],[]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[]],[[[],[]]],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [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)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [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)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[]],[[[],[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[[]],[[[],[]],[[]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[],[[[[],[],[]]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[]],[[[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[[]],[[[],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[[]],[[[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[]],[[[],[],[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[],[[[[],[[]]]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[]],[[[],[[]]]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[[]],[[[],[[]]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[]],[[[],[[]],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[[]],[[[],[[],[]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[]],[[[],[[[]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [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)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[],[[[[[]]]]]],[]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[],[[[[[]]]],[]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[]],[[[[]]]],[[]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [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)
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[]],[[[[]]],[]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [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)
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[[]],[[[[]]],[[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[],[[[[[]],[]]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[]],[[[[]],[]]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[]],[[[[]],[]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[[]],[[[[]],[],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[[]],[[[[]],[[]]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [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)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[]],[[[[],[]]]],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [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)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[[]],[[[[],[]],[]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [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)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[[]],[[[[],[[]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[],[[[[[[]]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[[]],[[[[[]]]],[]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[[]],[[[[[]]],[]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[]],[[[[[]],[]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[]],[[[[[],[]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [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)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[]],[],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [[[[]],[],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[]],[],[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[[[]],[],[],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [[[[]],[],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [[[[]],[],[],[[]]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [[[[]],[],[],[[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[]],[],[]],[],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [[[[]],[],[]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [[[[]],[],[],[[[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[[[]],[],[]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[[[]],[],[]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [[[[]],[],[]],[[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[[[]],[],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[[[]],[],[[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [[[[]],[],[[]],[[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[[]],[],[[]]],[],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[[[]],[],[[]]],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [[[[]],[],[[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[[]],[],[[],[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [[[[]],[],[[],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[]],[]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[]],[]],[],[],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[[]],[],[[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[]],[]],[],[[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [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)
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[[]],[]],[],[[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [[[[]],[],[[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[[[]],[],[[[]]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[[]],[],[[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[]],[]],[[]],[],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[]],[]],[[]],[[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [[[[]],[],[[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [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)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[[[]],[]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[[[]],[]],[[],[[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [[[[]],[],[[[[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[[]],[]],[[[]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[]],[]],[[[]],[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [[[[]],[]],[[[],[]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[[[]],[]],[[[[]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[[]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [[[[]],[[]],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[[[]],[[]],[]],[],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[]],[[]],[]],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[[]],[[]],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]],[[]]],[]] => ([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [[[[]],[[]],[[],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[]],[[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[[]],[[]]],[],[[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [[[[]],[[]],[[[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[]],[[]]],[[]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[[[]],[[]]],[[],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[[[]],[[]]],[[[]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [[[[]],[[],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [[[[]],[[],[]],[]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [[[[]],[[],[]],[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [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)
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [[[[]],[[],[]]],[[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [[[[]],[[],[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[[[]],[[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [[[[]],[[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [[[[]],[[],[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[]]],[],[],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [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)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [[[[]],[[],[[]]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[[]],[[],[[]]]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [[[[]],[[],[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[]]],[],[[]],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [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)
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[]]],[],[[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[[]]],[],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[]]],[],[[],[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [[[[]],[[],[[[]]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [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)
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[[]]],[],[[[]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [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)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[]]],[],[[[[]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [[[[]],[[[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [[[[]],[[[]]],[]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [[[[]],[[[]]],[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[[]],[[[]]]],[],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[[[]],[[[]]]],[[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[[]],[[[]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[[[]],[[[]],[]]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [[[[]],[[[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[]]],[[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[]]],[[]],[],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [[[[]],[[[]],[[]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[[]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[]]],[[]],[[],[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[]]],[[]],[[[]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [[[[]],[[[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [[[[]],[[[],[]]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [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)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[]]],[[],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[[[]]],[[],[]],[[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [[[[]],[[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[[[]]],[[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[[]]],[[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[[[]]],[[],[],[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [[[[]],[[[],[[]]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[[]]],[[],[[]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[[[]]],[[],[[]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[[]]],[[],[[],[]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[[[]]],[[],[[[]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [[[[]],[[[[]]]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[[[]],[[[[]]]]],[]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [[[[]],[[[[]]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [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)
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[[]]],[[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [[[[]],[[[[]],[]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [[[[]]],[[[]],[]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[[[]]],[[[]],[],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [[[[]]],[[[]],[[]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[[[]],[[[[],[]]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [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)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[[]]],[[[],[]],[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [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)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[[[]]],[[[],[[]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[[]],[[[[[]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[]]],[[[[]]]],[]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[[[]]],[[[[]]],[]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[[[]]],[[[[]],[]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[[]]],[[[[],[]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [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)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[[],[]],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[[[],[]],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [[[[],[]],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[[],[]],[],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[[[],[]],[],[]],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [[[[],[]],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [[[[],[]],[],[[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [[[[],[]],[],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[],[]],[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [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)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [[[[],[]],[],[[[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [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)
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [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)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [[[[],[]],[]],[[[]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [[[[],[]],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [[[[],[]],[[]],[]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [[[[],[]],[[]],[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [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)
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [[[[],[]],[[]]],[[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [[[[],[]],[[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [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)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [[[[],[]],[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[],[]]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[],[]]],[],[],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [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)
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[],[]]],[],[[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [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)
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [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)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[],[]],[[[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [[[[],[]],[[[]]]],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [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)
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[],[]]],[[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[],[]]],[[]],[[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [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)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [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)
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [[[[],[]]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [[[[],[]]],[[],[[]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[],[]],[[[[]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [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)
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [[[[],[]]],[[[]],[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [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)
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[],[]]],[[[[]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[[[],[],[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[[[],[],[]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [[[[],[],[]],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[[],[],[]],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[[[],[],[]],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [[[[],[],[]],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [[[[],[],[]],[[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [[[[],[],[]],[[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[],[],[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[[],[],[]]],[],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [[[[],[],[]],[[[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[],[],[]]],[[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[],[],[]]],[[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [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)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[[],[],[],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[[],[],[],[]],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[[[],[],[],[]],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[],[],[],[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[[],[],[],[]]],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[[],[],[],[],[[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[],[[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[],[[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [[[[],[],[],[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[[[],[],[],[[]]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [[[[],[],[],[[]],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[[]],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [[[[],[],[],[[],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[],[],[],[],[[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[],[],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[],[],[],[],[[],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[[],[],[],[[[]]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[],[[[]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[],[],[[[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[],[],[[[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[],[[[[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [[[[],[],[[]]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[[[],[],[[]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [[[[],[],[[]]],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[],[],[[]]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[[[],[],[[]]]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [[[[],[],[[]],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[[[],[],[[]],[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [[[[],[],[[]],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[],[[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[],[[]],[],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [[[[],[],[[]],[[]]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[],[],[],[[]],[[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[],[[]],[[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [[[[],[],[[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[],[[],[]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [[[[],[],[[],[]],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[],[],[],[[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[],[],[],[[],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[[[],[],[[],[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[],[],[],[[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[],[],[],[[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[],[],[],[[],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [[[[],[],[[],[[]]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[],[],[],[[],[[]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[],[],[],[[],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[],[],[],[[],[[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[],[],[],[[],[[[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [[[[],[],[[[]]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [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)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [[[[],[],[[[]]],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[],[[[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[],[[[]]],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [[[[],[],[[[]],[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[],[],[],[[[]],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[],[],[],[[[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[],[],[],[[[]],[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [[[[],[],[[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[],[],[],[[[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[],[],[],[[[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[],[],[],[[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[],[],[],[[[],[[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [[[[],[],[[[[]]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[],[[[[]]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[],[],[],[[[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[],[],[],[[[[]],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[],[[[[],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [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)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[],[[]]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[],[[]]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[],[[]]],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [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)
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[],[[]]],[]],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[],[[]]],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[],[[]]],[[]]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [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)
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[],[[]]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[],[[]]]],[],[[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[],[[]]],[[[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[],[[]]]],[[]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[],[[]]]],[[],[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[],[[]]]],[[[]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[],[[]],[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[],[[]],[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[],[[]],[]],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[],[[]],[]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[],[[]],[]]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[],[[]],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[],[[]],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[],[[]],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[],[[]],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[],[[]],[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[],[],[[]],[],[[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[],[[]],[],[[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[],[[]],[[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[],[[]],[[]]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]],[[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[],[[]],[[],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[],[],[[]],[[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[],[],[[]],[[],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[],[],[[]],[[],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[],[[]],[[[]]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[],[[]],[[[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[],[],[[]],[[[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[],[],[[]],[[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[],[],[[]],[[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[],[[],[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [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)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [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)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [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)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[],[[],[]]]],[[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[],[[],[]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[],[[],[]],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[],[[],[]],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[],[],[[],[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[],[],[[],[]],[],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[],[[],[]],[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[],[],[[],[]],[[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[],[],[[],[]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[],[],[[],[]],[[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[],[[],[],[]]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[],[[],[],[]]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[],[[],[],[]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[],[],[[],[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[],[],[[],[],[]],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[],[[],[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[],[],[[],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[[],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[],[],[[],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[[[],[[],[],[[]]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[],[],[[],[],[[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[],[],[[],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[],[],[[],[],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[],[],[[],[],[[[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [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)
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[],[[],[[]]]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[],[[],[[]]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[],[],[[],[[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[],[],[[],[[]]],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[],[[],[[]],[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[],[],[[],[[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[],[],[[],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[],[],[[],[[]],[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [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)
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[],[],[[],[[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[],[],[[],[[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[],[],[[],[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [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)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [[[[],[[],[[[]]]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[],[],[[],[[[]]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[],[],[[],[[[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [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)
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [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)
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[],[[],[[[[]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[],[[[]]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[],[[[]]]],[]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[],[[[]]]],[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [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)
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[],[[[]]]]],[[]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [[[[],[[[]]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [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)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [[[[],[[[]]],[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[],[[[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[],[[[]]],[],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [[[[],[[[]]],[[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[],[[[]]],[[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[],[],[[[]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [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)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [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)
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[],[[[]],[]]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[],[[[]],[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[],[],[[[]],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[],[],[[[]],[]],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[],[[[]],[],[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[],[],[[[]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[],[],[[[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[],[],[[[]],[],[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [[[[],[[[]],[[]]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[],[],[[[]],[[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[],[],[[[]],[[]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [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)
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[],[],[[[]],[[[]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [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)
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [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)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[],[[[],[]]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[],[],[[[],[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[],[],[[[],[]]],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [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)
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[],[],[[[],[]],[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[],[],[[[],[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [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)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[],[[[],[],[]]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[],[],[[[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[],[],[[[],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[],[],[[[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[],[],[[[],[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[],[[[],[[]]]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[],[],[[[],[[]]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [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)
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[],[],[[[],[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [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)
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [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)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[],[[[[]]]]],[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[],[[[[]]]]]],[]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [[[[],[[[[]]]],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[],[[[[]]]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[],[[[[]]]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[],[[[[]]],[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[],[],[[[[]]],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[],[],[[[[]]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[],[],[[[[]]],[[]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[],[[[[]],[]]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[],[],[[[[]],[]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [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)
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[],[],[[[[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[],[[[[]],[[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[],[[[[],[]]]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[],[],[[[[],[]]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [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)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [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)
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[],[[[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[],[[[[],[[]]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[],[[[[[]]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [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)
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[],[[[[[]]]],[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [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)
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[],[[[[[]],[]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [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)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[],[[[[[[]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[[[[]]],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [[[[[]]],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[[[]]],[],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [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)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[[[[]]],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[[[[]]],[],[[]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [[[[[]]],[],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[[]]],[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [[[[[]]],[]],[],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [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)
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[[]]],[]],[[]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [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)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [[[[[]]],[]],[[[]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [[[[[]]],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [[[[[]]],[[]],[]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [[[[[]]],[[]],[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[[[]]],[[]]],[],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [[[[[]]],[[]]],[[]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [[[[[]]],[[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[[[[]]],[[],[]]],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [[[[[]]],[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[[]]]],[],[],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [[[[[]]],[[],[[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[]]]],[],[[]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[[[]]]],[],[[],[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[[]]]],[],[[[]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [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)
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[[[[]]],[[[]]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [[[[[]]],[[[]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[[]]]],[[]],[],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[[]]]],[[]],[[]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [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)
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[[[]]]],[[],[]],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [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)
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [[[[[]]]],[[],[[]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [[[[[]]],[[[[]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[[]]]],[[[]]],[]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [[[[[]]]],[[[]],[]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[[]]]],[[[],[]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [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)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [[[[[]],[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[[[[]],[]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [[[[[]],[]],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [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)
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[[]],[]],[]],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[]],[]],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[[[[]],[]],[[]]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [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)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[[]],[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[[[]],[]]],[],[[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [[[[[]],[]],[[[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[[]],[]]],[[]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[[[]],[]]],[[],[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[[[[]],[]]],[[[]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [[[[[]],[],[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[[[[]],[],[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [[[[[]],[],[]],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[[[[]],[],[]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[[[[]],[],[]]],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [[[[[]],[],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [[[[[]],[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[[[[]],[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [[[[[]],[],[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[],[[]],[],[],[[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[],[[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [[[[[]],[],[[]]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[[[[]],[],[[]]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [[[[[]],[],[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [[[[[]],[],[[],[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[],[[]],[],[[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[],[[]],[],[[],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[],[[]],[],[[],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [[[[[]],[],[[[]]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[],[[]],[],[[[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[],[[]],[],[[[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[],[[]],[],[[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [[[[[]],[[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[[[[]],[[]]],[]],[]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [[[[[]],[[]]],[[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[[[]],[[]]]],[],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [[[[[]],[[]]]],[[]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[[]],[]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[[[[]],[[]],[]]],[]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[[]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]],[[]]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[]],[[],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[]],[[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [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)
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[[[[]],[[],[]]]],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [[[[[]],[[],[]],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[],[[]],[[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[],[[]],[[],[]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[[[[]],[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[],[[]],[[],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[],[[]],[[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[],[[]],[[],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [[[[[]],[[],[[]]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[],[[]],[[],[[]]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[],[[]],[[],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [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)
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[],[[]],[[],[[[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [[[[[]],[[[]]]],[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [[[[[]],[[[]]]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [[[[[]],[[[]]],[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [[[[[]],[[[]],[]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[],[[]],[[[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[],[[]],[[[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[],[[]],[[[]],[[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [[[[[]],[[[],[]]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[],[[]],[[[],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [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)
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[],[[]],[[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[],[[]],[[[],[[]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [[[[[]],[[[[]]]]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[],[[]],[[[[]]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[],[[]],[[[[]],[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[],[[]],[[[[],[]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[[],[]]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[[[[],[]]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [[[[[],[]]],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [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)
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [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)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [[[[[],[]]],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[[[[],[]]],[[]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [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)
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[[],[]]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[[],[]]]],[],[[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [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)
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[[[],[]]]],[[]],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [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)
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[[],[]]]],[[[]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [[[[[],[]],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [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)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [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)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [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)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[[[[],[]],[]]],[[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [[[[[],[]],[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[[[[],[]],[],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[[],[]],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[],[[],[]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[],[[],[]],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [[[[[],[]],[],[[]]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[],[[],[]],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[],[[],[]],[],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[],[[],[]],[],[[[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [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)
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [[[[[],[]],[[]]]],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [[[[[],[]],[[]],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[],[[],[]],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[],[[],[]],[[]],[[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [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)
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[],[[],[]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [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)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [[[[[],[]],[[[]]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[],[[],[]],[[[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [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)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [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)
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[],[[],[]],[[[[]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[[],[],[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[[[[],[],[]]],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[[[[],[],[]]],[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[[[],[],[]]]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [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)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [[[[[],[],[]],[]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[],[]],[]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[[],[],[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[],[[],[],[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[],[[],[],[]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[[],[],[]],[[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[],[[],[],[]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[],[[],[],[]],[[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[],[[],[],[]],[[[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[[],[],[],[]]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[],[]]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[],[],[],[]],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[],[[],[],[],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[],[[],[],[],[]],[[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[],[],[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[],[[],[],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[],[[],[],[],[],[[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[[],[],[],[[]]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[],[[],[],[],[[]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[],[[],[],[],[[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[],[[],[],[],[[],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[],[[],[],[],[[[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [[[[[],[],[[]]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[[[[],[],[[]]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[[[[],[],[[]]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[],[[],[],[[]]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[],[[],[],[[]]],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [[[[[],[],[[]],[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[],[[],[],[[]],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[],[[],[],[[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[],[[],[],[[]],[[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [[[[[],[],[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[],[[],[],[[],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[],[[],[],[[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[],[[],[],[[],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[],[[],[],[[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [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)
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[],[[],[],[[[]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[],[[],[],[[[]]],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[],[[],[],[[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[],[[],[],[[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[],[[[[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [[[[[],[[]]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[[[[],[[]]]],[]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [[[[[],[[]]]],[[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[[[],[[]]]]],[],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[[[[],[[]]]]],[[]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [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)
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[[[[],[[]]],[]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [[[[[],[[]]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[],[[],[[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[],[[],[[]]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [[[[[],[[]]],[[]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[],[[],[[]]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [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)
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[],[[],[[]]],[[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [[[[[],[[]],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[[[[],[[]],[]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [[[[[],[[]],[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[],[[],[[]],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[],[[],[[]],[]],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [[[[[],[[]],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[],[[],[[]],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[],[[],[[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[],[[],[[]],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [[[[[],[[]],[[]]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[],[[],[[]],[[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[],[[],[[]],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[],[[],[[]],[[],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[],[[],[[]],[[[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [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)
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[[[],[[],[]]]]],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [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)
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[],[[],[[],[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [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)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [[[[[],[[],[]],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[],[[],[[],[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[],[[],[[],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[],[[],[[],[]],[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [[[[[],[[],[],[]]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[],[[],[[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[],[[],[[],[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[],[[],[[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[],[[],[[],[],[[]]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[[[[],[[],[[]]]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [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)
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[],[[],[[],[[]]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[],[[],[[],[[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [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)
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[],[[],[[],[[[]]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [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)
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[[],[[[]]]]]],[]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [[[[[],[[[]]]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[],[[],[[[]]]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[],[[],[[[]]]],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [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)
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[],[[],[[[]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[],[[],[[[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[],[[],[[[]]],[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [[[[[],[[[]],[]]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [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)
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[],[[],[[[]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[],[[],[[[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[],[[],[[[]],[[]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [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)
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [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)
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[],[[],[[[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [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)
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[],[[],[[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[],[[],[[[],[[]]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[[[[],[[[[]]]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[],[[],[[[[]]]]],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[],[[],[[[[]]]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[],[[],[[[[]]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[],[[],[[[[]],[]]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[],[[],[[[[],[]]]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[],[[],[[[[[]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [[[[[[]]]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[[[[[]]]],[],[]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [[[[[[]]]],[],[[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[[[[]]]],[]],[],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[[[[[]]]],[]],[[]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [[[[[[]]]],[[]],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [[[[[[]]]],[[]]],[]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [[[[[[]]]],[[],[]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [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)
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[[[]]]]],[],[[]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [[[[[[]]]],[[[]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[[[]]]]],[[]],[]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[[[[[]]]]],[[],[]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [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)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [[[[[[]]],[]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[[[[]]],[]],[]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [[[[[[]]],[]],[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [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)
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [[[[[[]]],[]]],[[]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [[[[[[]]],[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [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)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [[[[[[]]],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[],[[[]]],[],[],[[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [[[[[[]]],[],[[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[],[[[]]],[],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [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)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [[[[[[]]],[[]]],[]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[[[[[]]],[[]]]],[]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [[[[[[]]],[[]],[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[],[[[]]],[[]],[[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [[[[[[]]],[[],[]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[],[[[]]],[[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[],[[[]]],[[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[],[[[]]],[[],[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [[[[[[]]],[[[]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [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)
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[],[[[]]],[[[]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [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)
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [[[[[[]],[]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[[[[]],[]]],[]],[]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [[[[[[]],[]]],[[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[[[[]],[]]]],[],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[[[[[]],[]]]],[[]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [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)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[[[[]],[]],[]]],[]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [[[[[[]],[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[],[[[]],[]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[],[[[]],[]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [[[[[[]],[]],[[]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[],[[[]],[]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [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)
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[],[[[]],[]],[[[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [[[[[[]],[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[[[[[]],[],[]]]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [[[[[[]],[],[]],[]]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[],[[[]],[],[]],[],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[],[[[]],[],[]],[[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[[[[[]],[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[],[[[]],[],[],[]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[],[[[]],[],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[],[[[]],[],[],[[]]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[[[[[]],[],[[]]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[],[[[]],[],[[]]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[],[[[]],[],[[]],[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[],[[[]],[],[[],[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[],[[[]],[],[[[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [[[[[[]],[[]]]],[]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[[[[[]],[[]]]]],[]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [[[[[[]],[[]]],[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[],[[[]],[[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[],[[[]],[[]]],[[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [[[[[[]],[[]],[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[],[[[]],[[]],[]],[]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[],[[[]],[[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]],[[]]]] => ([(0,7),(1,6),(2,5),(3,4),(4,8),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [[[[[[]],[[],[]]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [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)
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[],[[[]],[[],[]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[],[[[]],[[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[],[[[]],[[],[[]]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [[[[[[]],[[[]]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[],[[[]],[[[]]]],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[],[[[]],[[[]]],[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[],[[[]],[[[]],[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[],[[[]],[[[],[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[],[[[]],[[[[]]]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[[[[[],[]]]],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[[[[[],[]]]],[]],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [[[[[[],[]]]],[[]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [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)
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[[[[[],[]]]]],[[]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [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)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [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)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [[[[[[],[]]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[],[[[],[]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[],[[[],[]]],[],[[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [[[[[[],[]]],[[]]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[],[[[],[]]],[[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [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)
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [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)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [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)
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [[[[[[],[]],[]]]],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [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)
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[],[[[],[]],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [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)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [[[[[[],[]],[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[],[[[],[]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[],[[[],[]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[],[[[],[]],[],[[]]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [[[[[[],[]],[[]]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [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)
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[],[[[],[]],[[]],[]]] => ([(0,8),(1,7),(2,7),(3,6),(4,5),(5,8),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [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)
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[],[[[],[]],[[[]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[[[[[],[],[]]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [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)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [[[[[[],[],[]]],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[],[[[],[],[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[],[[[],[],[]]],[[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [[[[[[],[],[]],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[],[[[],[],[]],[]],[]] => ([(0,8),(1,8),(2,8),(3,6),(4,6),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[],[[[],[],[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,7),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[],[[[],[],[]],[[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,7),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[[],[],[],[]]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[],[[[],[],[],[]]],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[],[[[],[],[],[]],[]]] => ([(0,8),(1,8),(2,8),(3,8),(4,7),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[],[[[],[],[],[[]]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[[],[],[[]]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[],[[[],[],[[]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[],[[[],[],[[]]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[],[[[],[],[[]],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[],[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [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)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [[[[[[],[[]]]]],[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[[],[[]]]]]],[]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [[[[[[],[[]]]],[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[],[[[],[[]]]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[],[[[],[[]]]],[[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[[[[[],[[]]],[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [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)
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[],[[[],[[]]],[],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[],[[[],[[]]],[[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[[[[[],[[]],[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[],[[[],[[]],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[],[[[],[[]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[],[[[],[[]],[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[],[[[],[[]],[[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[[[[],[[],[]]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [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)
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [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)
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[],[[[],[[],[]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[],[[[],[[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[],[[[],[[],[[]]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[[[[[],[[[]]]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [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)
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[],[[[],[[[]]]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [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)
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[],[[[],[[[]],[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [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)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[],[[[],[[[[]]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [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)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[[[[[[]]]]],[]],[]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [[[[[[[]]]]],[[]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[[[[]]]]]],[],[]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [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)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [[[[[[[]]]],[]],[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[[[[[[]]]],[]]],[]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [[[[[[[]]]],[],[]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[],[[[[]]]],[],[],[]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[],[[[[]]]],[],[[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [[[[[[[]]]],[[]]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[],[[[[]]]],[[],[]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [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)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[[]]],[]]]],[]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [[[[[[[]]],[]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[],[[[[]]],[]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[],[[[[]]],[]],[[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [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)
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[],[[[[]]],[],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[],[[[[]]],[],[],[]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[],[[[[]]],[],[[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [[[[[[[]]],[[]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[],[[[[]]],[[]]],[]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[],[[[[]]],[[]],[]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[],[[[[]]],[[],[]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[],[[[[]]],[[[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [[[[[[[]],[]]]],[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[[]],[]]]]],[]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[[[[[[]],[]]],[]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[],[[[[]],[]]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[],[[[[]],[]]],[[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[[[[[[]],[]],[]]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [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)
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[],[[[[]],[]],[],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[],[[[[]],[]],[[]]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[[[[[[]],[],[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[],[[[[]],[],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[],[[[[]],[],[]],[]]] => ([(0,8),(1,8),(2,7),(3,5),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[],[[[[]],[],[],[]]]] => ([(0,8),(1,8),(2,8),(3,6),(4,5),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[],[[[[]],[],[[]]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [[[[[[[]],[[]]]]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[],[[[[]],[[]]]],[]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[],[[[[]],[[]]],[]]] => ([(0,7),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[],[[[[]],[[]],[]]]] => ([(0,8),(1,5),(2,4),(3,6),(4,8),(5,8),(6,7),(7,8)],9)
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[],[[[[]],[[],[]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[],[[[[]],[[[]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [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)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[[],[]]]]]],[]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [[[[[[[],[]]]],[]]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[],[[[[],[]]]],[],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[],[[[[],[]]]],[[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [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)
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [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)
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[],[[[[],[]]],[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[],[[[[],[]]],[[]]]] => ([(0,7),(1,7),(2,5),(3,4),(4,8),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[[],[]],[]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [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)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [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)
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[],[[[[],[]],[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,5),(5,6),(6,8),(7,8)],9)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[],[[[[],[]],[[]]]]] => ([(0,7),(1,7),(2,6),(3,4),(4,8),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[],[[[[],[],[]]]],[]] => ([(0,8),(1,8),(2,8),(3,7),(4,7),(5,6),(5,8),(6,7)],9)
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[],[[[[],[],[]]],[]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[],[[[[],[],[]],[]]]] => ([(0,8),(1,8),(2,8),(3,7),(4,5),(5,6),(6,7),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[],[]]]]] => ([(0,8),(1,8),(2,8),(3,8),(4,5),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[],[[[[],[],[[]]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[[],[[]]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[],[[[[],[[]]]]],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[],[[[[],[[]]]],[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[],[[[[],[[]]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[],[[[[],[[]],[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[[[],[[],[]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[[[[[[[]]]]]],[]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [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)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[[[[[[]]]]],[]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [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)
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[[[[[]]]],[]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[],[[[[[]]]],[]],[]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[],[[[[[]]]],[],[]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[],[[[[[]]]],[[]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[[[[[[[]]],[]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [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)
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[],[[[[[]]],[]],[]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [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)
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[],[[[[[]]],[[]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,8),(4,6),(4,8),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[[[[[[[]],[]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[],[[[[[]],[]]]],[]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[],[[[[[]],[]]],[]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(6,7),(6,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[],[[[[[]],[]],[]]]] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[],[[[[[]],[],[]]]]] => ([(0,8),(1,8),(2,5),(3,4),(4,8),(5,7),(6,7),(6,8)],9)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[],[[[[[]],[[]]]]]] => ([(0,7),(1,6),(2,5),(3,4),(3,5),(4,8),(6,8),(7,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[[[[[[],[]]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [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)
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[],[[[[[],[]]]],[]]] => ([(0,7),(1,7),(2,8),(3,4),(4,8),(5,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [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)
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[],[[[[[],[]],[]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [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)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[],[[[[[[]]]]],[]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[],[[[[[[]]]],[]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[],[[[[[[[]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[]]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[]],[[[[[[[]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [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)
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [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)
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [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)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[],[]]]]]]]]]] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[[]],[]]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[],[[]]]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[[],[]]]]]]]]]]] => ([(0,10),(1,11),(2,11),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[[[]],[]]]]]]]]] => ([(0,9),(1,8),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,10),(9,10)],11)
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[],[[]]]]]]]]]] => ([(0,9),(1,8),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,10),(9,10)],11)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[[],[],[]]]]]]]] => ([(0,8),(1,9),(2,9),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[],[[]]]]]]]]]]] => ([(0,10),(1,9),(2,11),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,11),(10,11)],12)
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[[[]]],[]]]]]]]] => ([(0,8),(1,9),(2,10),(3,4),(3,5),(4,6),(5,9),(6,10),(7,8),(7,10)],11)
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[],[[[]]]]]]]]]] => ([(0,8),(1,9),(2,10),(3,4),(3,5),(4,6),(5,9),(6,10),(7,8),(7,10)],11)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[],[[[[]]]]]]]]] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[[[]]]],[]]]]]]] => ([(0,8),(1,9),(2,10),(3,4),(3,7),(4,8),(5,6),(5,9),(6,10),(7,10)],11)
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[],[[[[]]]]]]]]]] => ([(0,8),(1,9),(2,10),(3,4),(3,7),(4,8),(5,6),(5,9),(6,10),(7,10)],11)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[[],[],[[]]]]]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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)
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [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)
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[],[],[[]]]]]]]]] => ([(0,9),(1,8),(2,10),(3,10),(4,5),(4,6),(5,7),(6,8),(7,10),(9,10)],11)
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[],[[[[[]]]]]]]]]] => ([(0,8),(1,9),(2,10),(3,4),(3,7),(4,8),(5,6),(5,9),(6,10),(7,10)],11)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [[[[[[[[[]]]]]],[]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[],[[],[[]]]]]]]] => ([(0,9),(1,8),(2,6),(3,4),(4,8),(5,7),(5,9),(6,7),(8,9)],10)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[],[[[[[[]]]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[]],[[[[[[]]]]]],[]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[]],[[[[],[],[],[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,7),(6,8),(6,9),(7,8)],10)
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[]]],[[[[[[]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[],[[[[[[]]]]]]]]]] => ([(0,8),(1,9),(2,10),(3,4),(3,5),(4,6),(5,9),(6,10),(7,8),(7,10)],11)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [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)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [[[[[[[],[]],[[]]]]]]] => ([(0,8),(1,8),(2,6),(3,4),(4,9),(5,7),(5,9),(6,7),(8,9)],10)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [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)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [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)
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[[]]],[[[[[],[]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[],[]],[[[[[[]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [[[[[[[[[[]]]]]]],[]]]] => ([(0,9),(1,8),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,10),(9,10)],11)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[],[[[[[[[]]]]]]]]]] => ([(0,9),(1,8),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,10),(9,10)],11)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [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)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [[[[[[[[],[]]]]]],[]]] => ([(0,8),(1,8),(2,9),(3,9),(4,7),(4,9),(5,6),(5,8),(6,7)],10)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[],[[[[[[],[]]]]]]]] => ([(0,8),(1,8),(2,9),(3,9),(4,7),(4,9),(5,6),(5,8),(6,7)],10)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[[]],[]]]]]],[]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[],[[]]]]]]],[]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[[]]]]]]]],[]]] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[],[[[[[[[[]]]]]]]]]] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[],[]]]]]]]],[]] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [[[[[[[[]],[]]]]],[]]] => ([(0,8),(1,8),(2,9),(3,4),(4,9),(5,7),(5,8),(6,7),(6,9)],10)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [[[[[[[],[[]]]]]],[]]] => ([(0,8),(1,8),(2,9),(3,4),(4,9),(5,7),(5,8),(6,7),(6,9)],10)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[[],[],[],[[]]]]]]] => ([(0,9),(1,9),(2,9),(3,6),(4,5),(5,9),(6,8),(7,8),(7,9)],10)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[[],[[[[[[]],[]]]]]]] => ([(0,8),(1,8),(2,9),(3,4),(4,9),(5,7),(5,8),(6,7),(6,9)],10)
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [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)
[] => [] => [] => ([],1)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[],[],[[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[],[],[[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[],[],[[[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[],[[]],[[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[],[],[],[[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[],[],[],[[[]],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[],[],[],[],[[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[],[],[],[],[[[]],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,7),(7,8),(8,9)],10)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[],[[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[],[],[],[[[]],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,8),(4,8),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[[],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[],[],[[[]],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[],[],[[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[[]],[],[],[],[[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[],[[],[],[],[],[],[[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[[[]],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[],[[[],[],[],[],[]],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,8),(8,9)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[],[],[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[],[[[[]],[],[],[],[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(5,6),(6,9),(7,8),(8,9)],10)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[],[],[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[],[[[[[]],[],[],[]]]]] => ([(0,9),(1,9),(2,9),(3,6),(4,5),(5,9),(6,8),(7,8),(7,9)],10)
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[],[]]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,7),(6,8),(6,9),(7,8)],10)
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[],[[[[[[]],[],[]]]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[],[]]]]]]] => ([(0,8),(1,9),(2,9),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [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)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[],[],[],[]],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[],[],[],[]],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[],[]],[],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[],[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[],[],[],[],[]],[]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[],[],[],[],[],[]],[[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[],[],[]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[],[],[]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,10),(9,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[],[],[],[],[]]] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,11),(10,11)],12)
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[[],[],[],[],[]],[[[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[],[],[],[]] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[],[],[],[]],[[[[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,7),(6,8),(6,9),(7,8)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[]],[[],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[[],[],[]],[[[[],[]]]]] => ([(0,9),(1,9),(2,9),(3,8),(4,8),(5,7),(5,9),(6,7),(6,8)],10)
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[]],[[[],[],[],[],[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10)
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[],[]],[[[[],[],[]]]]] => ([(0,9),(1,9),(2,9),(3,8),(4,8),(5,7),(5,9),(6,7),(6,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[],[],[],[[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[],[],[],[[]],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[],[],[],[[[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[[]],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[[],[[[[[[]]]]]],[]]] => ([(0,8),(1,9),(2,9),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[],[[[[[[]]]]]]],[]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[]],[],[],[],[],[]],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[[]]]],[[[[[]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[[]]]]],[[[[]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[[]]]]]],[[[]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[[[[[[[]]]]]],[]],[]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[]]]]]]],[[]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[],[],[],[],[[]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[],[],[],[],[[[]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[],[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[]]]],[[[[[[]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]],[[[[[]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[[[]]]]]],[[[[]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[[[]]]]]]],[[[]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [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)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [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)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[],[]],[],[],[],[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[],[],[],[]],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[],[],[],[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[],[],[],[],[]],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[],[],[],[[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[[]],[]]]]]]]] => ([(0,9),(1,8),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,10),(9,10)],11)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[],[],[],[],[],[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[],[[[[[[[[]]]]]]]],[]] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[[],[],[],[],[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[],[]]],[[[[[]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[],[]]]],[[[[]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [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)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [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)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[],[[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[],[],[],[]]],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[[],[],[],[],[]]],[[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[],[],[],[]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11)
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[[[]]]]],[[[],[]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [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)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[[[[[[]]]]]],[[],[]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[[[]]]],[[[[],[]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[],[],[],[],[],[[],[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9),(9,10)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[],[],[],[[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[],[],[],[],[[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(9,10)],11)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[],[],[[],[],[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,9),(8,9),(9,10)],11)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[],[[],[],[],[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(9,10)],11)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[],[],[],[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,10),(8,9),(9,10)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[],[],[],[],[[]]] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,11),(9,10),(10,11)],12)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[],[],[],[],[[],[]]] => ([(0,11),(1,11),(2,11),(3,11),(4,11),(5,11),(6,11),(7,11),(8,10),(9,10),(10,11)],12)
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[[]]]]]]]]]]] => ([(0,11),(1,10),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[],[],[],[],[],[],[]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[[],[],[],[],[[]]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(5,6),(6,9),(7,8),(8,9)],10)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,6),(6,8),(7,8),(7,9)],10)
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[]]]]],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,5),(5,7),(6,8),(6,9),(7,8)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => ([(0,11),(1,10),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[],[],[],[]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,7),(7,9),(8,9),(8,10)],11)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[[],[],[],[],[[[],[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(7,9)],10)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[],[],[]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,8),(8,9),(9,10)],11)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[],[]]],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(7,9)],10)
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[],[]]]]]]]] => ([(0,9),(1,10),(2,10),(3,10),(4,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[],[],[],[[],[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[],[[],[],[],[],[]]],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,8),(8,9)],10)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[],[]],[],[],[],[],[[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[],[],[]]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,6),(6,8),(7,9),(7,10),(8,9)],11)
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[],[],[]]]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,5),(5,9),(6,8),(6,10),(7,8),(7,9)],11)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[],[[],[],[],[],[],[]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,8),(7,8),(8,9)],10)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]],[]],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,8),(8,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[],[],[],[],[]]],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[[[]]]]]]]]],[]]] => ([(0,10),(1,11),(2,11),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10),(9,11)],12)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[],[[],[],[],[],[],[],[]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,10),(7,9),(8,9),(9,10)],11)
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[[[]]]],[]],[],[],[]] => ([(0,9),(1,9),(2,9),(3,8),(4,5),(5,7),(6,7),(6,8),(8,9)],10)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[],[],[]]],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(7,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[],[],[[],[]]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,7),(7,9),(8,9)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[[],[],[],[],[[]]]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,7),(5,6),(6,10),(7,9),(8,9),(8,10)],11)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[],[]]]]]]],[]]] => ([(0,9),(1,9),(2,10),(3,10),(4,5),(4,6),(5,8),(6,7),(7,9),(8,10)],11)
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[[]]]]]],[],[],[]] => ([(0,8),(1,9),(2,9),(3,9),(4,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[],[[]],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,9),(8,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[],[],[],[[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,8),(8,10),(9,10)],11)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[[[[[[]]]]],[]],[],[]] => ([(0,9),(1,8),(2,8),(3,5),(4,6),(4,9),(5,7),(6,7),(8,9)],10)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[],[[]]],[],[],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,7),(7,8),(8,9)],10)
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[],[[],[[],[[],[]]]]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11)
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[],[[]]]]],[[[]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[]],[],[],[],[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,7),(5,6),(6,9),(7,8),(8,9)],10)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[]],[],[],[],[],[]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,10),(8,9),(9,10)],11)
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[],[[[[[],[]],[]],[]],[]]] => ([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[],[[[],[],[],[],[]]]]] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,8),(6,8),(7,8),(7,9)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[],[[[],[],[],[],[],[]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,10),(6,9),(7,9),(8,9),(8,10)],11)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[],[],[],[]]],[],[],[]] => ([(0,9),(1,9),(2,9),(3,9),(4,8),(5,8),(6,8),(7,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[[[]]]]]]]],[],[]] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[],[],[],[[],[]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,9),(6,9),(7,8),(8,10),(9,10)],11)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[],[]],[],[],[],[[],[]]] => ([(0,9),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[[],[],[],[],[],[[]]]]]] => ([(0,10),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,10),(8,9),(9,10)],11)
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
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
to graph
Description
Return the undirected graph obtained from the tree nodes and edges.