Identifier
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
Images
[1,0] => [.,.] => [[]]
[1,0,1,0] => [[.,.],.] => [[[]]]
[1,1,0,0] => [.,[.,.]] => [[],[]]
[1,0,1,0,1,0] => [[[.,.],.],.] => [[[[]]]]
[1,0,1,1,0,0] => [[.,.],[.,.]] => [[[]],[]]
[1,1,0,0,1,0] => [[.,[.,.]],.] => [[[],[]]]
[1,1,0,1,0,0] => [.,[[.,.],.]] => [[],[[]]]
[1,1,1,0,0,0] => [.,[.,[.,.]]] => [[],[],[]]
[1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => [[[[[]]]]]
[1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => [[[[]]],[]]
[1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],.] => [[[[]],[]]]
[1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => [[[]],[[]]]
[1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => [[[]],[],[]]
[1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],.] => [[[[],[]]]]
[1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,.]] => [[[],[]],[]]
[1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],.] => [[[],[[]]]]
[1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => [[],[[[]]]]
[1,1,0,1,1,0,0,0] => [.,[[.,.],[.,.]]] => [[],[[]],[]]
[1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],.] => [[[],[],[]]]
[1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => [[],[[],[]]]
[1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => [[],[],[[]]]
[1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => [[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => [[[[[[]]]]]]
[1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => [[[[[]]]],[]]
[1,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],.] => [[[[[]]],[]]]
[1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => [[[[]]],[[]]]
[1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => [[[[]]],[],[]]
[1,0,1,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],.] => [[[[[]],[]]]]
[1,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[.,.]] => [[[[]],[]],[]]
[1,0,1,1,0,1,0,0,1,0] => [[[.,.],[[.,.],.]],.] => [[[[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => [[[]],[[[]]]]
[1,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[.,.]]] => [[[]],[[]],[]]
[1,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,[.,.]]],.] => [[[[]],[],[]]]
[1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [[[]],[[],[]]]
[1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => [[[]],[],[[]]]
[1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => [[[]],[],[],[]]
[1,1,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],.] => [[[[[],[]]]]]
[1,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,.]] => [[[[],[]]],[]]
[1,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],.] => [[[[],[]],[]]]
[1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => [[[],[]],[[]]]
[1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,.]]] => [[[],[]],[],[]]
[1,1,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],.] => [[[[],[[]]]]]
[1,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[.,.]] => [[[],[[]]],[]]
[1,1,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],.]],.] => [[[],[[[]]]]]
[1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => [[],[[[[]]]]]
[1,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],.],[.,.]]] => [[],[[[]]],[]]
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,.]]],.] => [[[],[[]],[]]]
[1,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [[],[[[]],[]]]
[1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,.],.]]] => [[],[[]],[[]]]
[1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[.,[.,.]]]] => [[],[[]],[],[]]
[1,1,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => [[[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,.]]],[.,.]] => [[[],[],[]],[]]
[1,1,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => [[[],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => [[],[[[],[]]]]
[1,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,.]],[.,.]]] => [[],[[],[]],[]]
[1,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],.] => [[[],[],[[]]]]
[1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => [[],[[],[[]]]]
[1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [[],[],[[[]]]]
[1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,.]]]],.] => [[[],[],[],[]]]
[1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [[],[[],[],[]]]
[1,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[.,.]],.]]] => [[],[],[[],[]]]
[1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => [[],[],[],[[]]]
[1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => [[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => [[[[[[[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => [[[[[[]]]]],[]]
[1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],.] => [[[[[[]]]],[]]]
[1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [[[[[]]]],[[]]]
[1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[]]]],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],.] => [[[[[[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[]]],[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],.] => [[[[[]]],[[]]]]
[1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => [[[[]]],[[[]]]]
[1,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,.],[.,.]]] => [[[[]]],[[]],[]]
[1,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[]]],[],[]]]
[1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [[[[]]],[[],[]]]
[1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [[[[]]],[],[[]]]
[1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[]]],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],.] => [[[[[[]],[]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[]],[]]],[]]
[1,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[]],[]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [[[[]],[]],[[]]]
[1,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[]],[]],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],.] => [[[[[]],[[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,.]] => [[[[]],[[]]],[]]
[1,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],.]],.] => [[[[]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => [[[]],[[[[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],.],[.,.]]] => [[[]],[[[]]],[]]
[1,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],.] => [[[[]],[[]],[]]]
[1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [[[]],[[[]],[]]]
[1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [[[]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,.],[.,[.,.]]]] => [[[]],[[]],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],.] => [[[[[]],[],[]]]]
[1,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[]],[],[]],[]]
[1,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => [[[[]],[[],[]]]]
[1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [[[]],[[[],[]]]]
[1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[.,.]],[.,.]]] => [[[]],[[],[]],[]]
[1,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],.] => [[[[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [[[]],[[],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [[[]],[],[[[]]]]
[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [[[]],[],[[]],[]]
>>> Load all 2595 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[]],[],[],[]]]
[1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [[[]],[[],[],[]]]
[1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [[[]],[],[[],[]]]
[1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [[[]],[],[],[[]]]
[1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[]],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => [[[[[[],[]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[]]]],[]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],.] => [[[[[],[]]],[]]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[]]],[[]]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[]]],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],.] => [[[[[],[]],[]]]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[]],[]],[]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[]],[[]]]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[]],[[[]]]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[]],[[]],[]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[]],[],[]]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[]],[],[[]]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[]],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],.] => [[[[[],[[]]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[]]]],[]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[]]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[]]],[[]]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[]]],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],.] => [[[[],[[[]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[]]]],[]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],.]],.] => [[[],[[[[]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => [[],[[[[[]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[]]]],[]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[[[]]],[]]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [[],[[[[]]],[]]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[]]],[[]]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[]]],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],.] => [[[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[]],[]],[]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[[]],[]]]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [[],[[[[]],[]]]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[]],[]],[]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [[],[[[]],[[]]]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[]],[[[]]]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[]],[[]],[]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [[],[[[]],[],[]]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[]],[[],[]]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[]],[],[[]]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[]],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => [[[[[],[],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[],[]]],[]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[],[]],[]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[],[]],[[]]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[],[]],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => [[[[],[[],[]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[],[]]],[]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => [[[],[[[],[]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [[],[[[[],[]]]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[],[]]],[]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],.] => [[[],[[],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [[],[[[],[]],[]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[],[]],[[]]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[],[]],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],.] => [[[[],[],[[]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[],[[]]],[]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],.] => [[[],[[],[[]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [[],[[[],[[]]]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[],[[]]],[]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],.] => [[[],[],[[[]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [[],[[],[[[]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [[],[],[[[[]]]]]
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[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [[[]],[[[],[],[]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[[]],[[],[],[]],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [[[[]],[],[[],[]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [[[]],[[],[[],[]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [[[]],[],[[[],[]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[[]],[],[[],[]],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [[[[]],[],[],[[]]]]
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[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [[[]],[],[[],[[]]]]
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[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[[[]],[],[],[],[]]]
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[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => [[[[[[],[]]],[]]]]
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[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => [[[[[],[]]],[[]]]]
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[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [[[[[[],[]],[]]]]]
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[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[[[],[]],[]],[]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [[[[],[]],[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[[],[]],[]],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => [[[[[],[]],[[]]]]]
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[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [[[[],[]],[[[]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => [[[],[]],[[[[]]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [[[],[]],[[[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [[[[],[]],[[]],[]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [[[],[]],[[[]],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[[],[]],[[]],[[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[[],[]],[[]],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [[[[[],[]],[],[]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[[],[]],[],[]],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [[[[],[]],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [[[],[]],[[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[[],[]],[[],[]],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [[[[],[]],[],[[]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [[[],[]],[[],[[]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [[[],[]],[],[[[]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[[],[]],[],[[]],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[[],[]],[],[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[[],[]],[[],[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[[],[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[[],[]],[],[],[[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[],[]],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [[[[[[],[[]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => [[[[[],[[]]]]],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => [[[[[],[[]]]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => [[[[],[[]]]],[[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [[[[],[[]]]],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => [[[[[],[[]]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [[[[],[[]]],[]],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => [[[[],[[]]],[[]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => [[[],[[]]],[[[]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [[[],[[]]],[[]],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [[[[],[[]]],[],[]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [[[],[[]]],[[],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [[[],[[]]],[],[[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [[[],[[]]],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],.] => [[[[[],[[[]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [[[[],[[[]]]]],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [[[[],[[[]]]],[]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => [[[],[[[]]]],[[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [[[],[[[]]]],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [[[[],[[[[]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [[[],[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [[[],[[[[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [[],[[[[[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => [[],[[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [[[],[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [[],[[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => [[],[[[[]]]],[[]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [[],[[[[]]]],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [[[[],[[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [[[],[[[]]],[]],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => [[[],[[[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => [[],[[[[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [[],[[[[]]],[]],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [[[],[[[]]],[[]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => [[],[[[[]]],[[]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => [[],[[[]]],[[[]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [[],[[[]]],[[]],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [[[],[[[]]],[],[]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [[],[[[[]]],[],[]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [[],[[[]]],[[],[]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [[],[[[]]],[],[[]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [[],[[[]]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => [[[[[],[[]],[]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [[[[],[[]],[]]],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [[[[],[[]],[]],[]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [[[],[[]],[]],[[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [[[],[[]],[]],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [[[[],[[[]],[]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [[[],[[[]],[]]],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [[[],[[[[]],[]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => [[],[[[[[]],[]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [[],[[[[]],[]]],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [[[],[[[]],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [[],[[[[]],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [[],[[[]],[]],[[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [[],[[[]],[]],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => [[[[],[[]],[[]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [[[],[[]],[[]]],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => [[[],[[[]],[[]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => [[],[[[[]],[[]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [[],[[[]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => [[[],[[]],[[[]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => [[],[[[]],[[[]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => [[],[[]],[[[[]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [[],[[]],[[[]]],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [[[],[[]],[[]],[]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [[],[[[]],[[]],[]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [[],[[]],[[[]],[]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [[],[[]],[[]],[[]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [[[[],[[]],[],[]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [[[],[[]],[],[]],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [[[],[[[]],[],[]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [[],[[[[]],[],[]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [[],[[[]],[],[]],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [[[],[[]],[[],[]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [[],[[[]],[[],[]]]]
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[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [[[[[],[],[]],[]]]]
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[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [[[[],[],[]],[[]]]]
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[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => [[[[[],[[],[]]]]]]
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[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [[[],[[[[],[]]]]]]
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[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [[[],[[[],[]],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [[],[[[[],[]],[]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [[],[[[],[]],[]],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [[[],[[],[]],[[]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [[],[[[],[]],[[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [[],[[],[]],[[[]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [[],[[],[]],[[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [[[],[[],[]],[],[]]]
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[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [[[[],[],[[]]],[]]]
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[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [[[],[],[[]]],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => [[[[],[[],[[]]]]]]
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[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [[[],[[[],[[]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [[],[[[[],[[]]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [[],[[[],[[]]]],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [[[],[[],[[]]],[]]]
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[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [[[],[[[],[],[]]]]]
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[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [[[],[[],[[],[]]]]]
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[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [[],[[],[[],[]]],[]]
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[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [[],[],[[[],[]]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [[[],[],[[],[]],[]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [[],[[],[[],[]],[]]]
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[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [[],[],[[],[]],[[]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [[],[],[[],[]],[],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [[[[],[],[],[[]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [[[],[],[],[[]]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [[[],[[],[],[[]]]]]
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[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [[[[[]]],[],[[]],[]]]
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[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [[[[[[]]],[],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[[[[]]],[],[],[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [[[[[]]],[[],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [[[[]]],[[[],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [[[[]]],[[],[],[]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [[[[[]]],[],[[],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [[[[]]],[[],[[],[]]]]
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[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [[[[]]],[],[[],[]],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [[[[[]]],[],[],[[]]]]
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[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [[[[]]],[],[[],[[]]]]
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[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [[[[]]],[],[],[[]],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[[[[]]],[],[],[],[]]]
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[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [[[[[[[[]],[]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[[[[[[]],[]]]]],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [[[[[[[]],[]]]],[]]]
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[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [[[[[[[]],[]]],[]]]]
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[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [[[[[]],[]]],[[[]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [[[[[]],[]]],[[]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [[[[[[]],[]]],[],[]]]
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[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [[[[[]],[]],[[],[]]]]
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[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [[[[]],[]],[[],[]],[]]
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[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [[[[]],[]],[],[[]],[]]
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[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => [[[[[[]],[[]]]],[]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [[[[[]],[[]]]],[[]]]
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[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [[[[[[]],[[]]],[]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [[[[[]],[[]]],[]],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [[[[[]],[[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [[[[]],[[]]],[[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [[[[]],[[]]],[[]],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [[[[[]],[[]]],[],[]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [[[[]],[[]]],[[],[]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [[[[]],[[]]],[],[[]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [[[[]],[[]]],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [[[[[[]],[[[]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [[[[[]],[[[]]]]],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [[[[[]],[[[]]]],[]]]
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[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [[[[]],[[[]]]],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [[[[[]],[[[[]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [[[[]],[[[[]]]]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [[[[]],[[[[[]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [[[]],[[[[[[]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [[[]],[[[[[]]]]],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [[[[]],[[[[]]]],[]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [[[]],[[[[[]]]],[]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [[[]],[[[[]]]],[[]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [[[]],[[[[]]]],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [[[[[]],[[[]]],[]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [[[[]],[[[]]],[]],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [[[[]],[[[[]]],[]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [[[]],[[[[[]]],[]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [[[]],[[[[]]],[]],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [[[[]],[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [[[]],[[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [[[]],[[[]]],[[[]]]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [[[]],[[[]]],[[]],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [[[[]],[[[]]],[],[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [[[]],[[[[]]],[],[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [[[]],[[[]]],[[],[]]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [[[]],[[[]]],[],[[]]]
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[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [[[[[[]],[[]],[]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [[[[[]],[[]],[]]],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [[[[[]],[[]],[]],[]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [[[[]],[[]],[]],[[]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [[[[]],[[]],[]],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => [[[[[]],[[[]],[]]]]]
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[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [[[[]],[[[]],[]],[]]]
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[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [[[[]],[[[]],[],[]]]]
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[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [[[[]],[[]],[[],[]]]]
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[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [[[[[[[]],[],[]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[[[[[]],[],[]]]],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [[[[[[]],[],[]]],[]]]
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[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[[[[]],[],[]]],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [[[[[[]],[],[]],[]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[[[[]],[],[]],[]],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [[[[[]],[],[]],[[]]]]
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[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [[[[]],[],[]],[[]],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[[[[]],[],[]],[],[]]]
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[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [[[[[[]],[[],[]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [[[[[]],[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [[[[[]],[[],[]]],[]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [[[[]],[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [[[[]],[[],[]]],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [[[[[]],[[[],[]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [[[[]],[[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [[[[]],[[[[],[]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [[[]],[[[[[],[]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [[[]],[[[[],[]]]],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [[[[]],[[[],[]]],[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [[[]],[[[[],[]]],[]]]
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[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [[[]],[[[],[]]],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [[[[[]],[[],[]],[]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [[[[]],[[],[]],[]],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [[[[]],[[[],[]],[]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [[[]],[[[[],[]],[]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [[[]],[[[],[]],[]],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [[[[]],[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [[[]],[[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [[[]],[[],[]],[[[]]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [[[]],[[],[]],[[]],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [[[[]],[[],[]],[],[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [[[]],[[[],[]],[],[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [[[]],[[],[]],[[],[]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [[[]],[[],[]],[],[[]]]
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[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[[.,.],.]]],.],.],.] => [[[[[[]],[],[[]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [[[[[]],[],[[]]]],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [[[[[]],[],[[]]],[]]]
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[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [[[[]],[],[[]]],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [[[[[]],[[],[[]]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [[[[]],[[],[[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [[[[]],[[[],[[]]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [[[]],[[[[],[[]]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [[[]],[[[],[[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [[[[]],[[],[[]]],[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [[[]],[[[],[[]]],[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [[[]],[[],[[]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [[[]],[[],[[]]],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [[[[[]],[],[[[]]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [[[[]],[],[[[]]]],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [[[[]],[[],[[[]]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [[[]],[[[],[[[]]]]]]
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[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [[[[[[],[]]],[]],[]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [[[[[],[]]],[]],[[]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[[[],[]]],[]],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [[[[[[],[]]],[[]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [[[[[],[]]],[[]]],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [[[[[],[]]],[[[]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [[[[],[]]],[[[[]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [[[[],[]]],[[[]]],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [[[[[],[]]],[[]],[]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [[[[],[]]],[[[]],[]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [[[[],[]]],[[]],[[]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [[[[],[]]],[[]],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [[[[[[],[]]],[],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[[[],[]]],[],[]],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [[[[[],[]]],[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [[[[],[]]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [[[[],[]]],[[],[]],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [[[[[],[]]],[],[[]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [[[[],[]]],[[],[[]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [[[[],[]]],[],[[[]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [[[[],[]]],[],[[]],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [[[[[],[]]],[],[],[]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [[[[],[]]],[[],[],[]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [[[[],[]]],[],[[],[]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [[[[],[]]],[],[],[[]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[[],[]]],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [[[[[[[],[]],[]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[[[[[],[]],[]]]],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [[[[[[],[]],[]]],[]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [[[[[],[]],[]]],[[]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[[[],[]],[]]],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [[[[[[],[]],[]],[]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[],[]],[]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [[[[[],[]],[]],[[]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [[[[],[]],[]],[[[]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[[],[]],[]],[[]],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[[[],[]],[]],[],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[[[],[]],[]],[[],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [[[[],[]],[]],[],[[]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[[],[]],[]],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [[[[[[],[]],[[]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [[[[[],[]],[[]]]],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [[[[[],[]],[[]]],[]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [[[[],[]],[[]]],[[]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [[[[],[]],[[]]],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [[[[[],[]],[[[]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [[[[],[]],[[[]]]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [[[[],[]],[[[[]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[[],[]],[[[[[]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [[[],[]],[[[[]]]],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [[[[],[]],[[[]]],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [[[],[]],[[[[]]],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [[[],[]],[[[]]],[[]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [[[],[]],[[[]]],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [[[[[],[]],[[]],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[[[],[]],[[]],[]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [[[[],[]],[[[]],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [[[],[]],[[[[]],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[[],[]],[[[]],[]],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [[[[],[]],[[]],[[]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [[[],[]],[[[]],[[]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [[[],[]],[[]],[[[]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[[],[]],[[]],[[]],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [[[[],[]],[[]],[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [[[],[]],[[[]],[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[],[]],[[]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [[[],[]],[[]],[],[[]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [[[],[]],[[]],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [[[[[[],[]],[],[]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[[[],[]],[],[]]],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[[[],[]],[],[]],[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [[[[],[]],[],[]],[[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[[],[]],[],[]],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [[[[[],[]],[[],[]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[],[]],[[],[]]],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [[[[],[]],[[[],[]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [[[],[]],[[[[],[]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [[[],[]],[[[],[]]],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [[[[],[]],[[],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [[[],[]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [[[],[]],[[],[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [[[],[]],[[],[]],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [[[[[],[]],[],[[]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [[[[],[]],[],[[]]],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [[[[],[]],[[],[[]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [[[],[]],[[[],[[]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [[[],[]],[[],[[]]],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [[[[],[]],[],[[[]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [[[],[]],[[],[[[]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [[[],[]],[],[[[[]]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [[[],[]],[],[[[]]],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [[[[],[]],[],[[]],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [[[],[]],[[],[[]],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [[[],[]],[],[[[]],[]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [[[],[]],[],[[]],[[]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [[[],[]],[],[[]],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [[[[[],[]],[],[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[[],[]],[],[],[]],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [[[[],[]],[[],[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [[[],[]],[[[],[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [[[],[]],[[],[],[]],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [[[[],[]],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [[[],[]],[[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [[[],[]],[],[[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [[[],[]],[],[[],[]],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [[[[],[]],[],[],[[]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [[[],[]],[[],[],[[]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [[[],[]],[],[[],[[]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [[[],[]],[],[],[[[]]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [[[],[]],[],[],[[]],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[[],[]],[],[],[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[[],[]],[[],[],[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [[[],[]],[],[[],[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [[[],[]],[],[],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[[],[]],[],[],[],[[]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[],[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [[[[[[[],[[]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [[[[[[],[[]]]]]],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [[[[[[],[[]]]]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[[[[],[[]]]]],[[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [[[[[],[[]]]]],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],[.,.]],.],.] => [[[[[[],[[]]]],[]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [[[[[],[[]]]],[]],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [[[[[],[[]]]],[[]]]]
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[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [[[[[],[[]]]],[],[]]]
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[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [[[[[[],[[]]],[]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [[[[[],[[]]],[]]],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [[[[[],[[]]],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [[[[],[[]]],[]],[[]]]
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[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => [[[[[],[[]]],[[]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [[[[],[[]]],[[]]],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => [[[[],[[]]],[[[]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [[[],[[]]],[[[[]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [[[],[[]]],[[[]]],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [[[[],[[]]],[[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [[[],[[]]],[[[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [[[],[[]]],[[]],[[]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [[[],[[]]],[[]],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [[[[[],[[]]],[],[]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [[[[],[[]]],[],[]],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [[[[],[[]]],[[],[]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [[[],[[]]],[[[],[]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [[[],[[]]],[[],[]],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [[[[],[[]]],[],[[]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [[[],[[]]],[[],[[]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [[[],[[]]],[],[[[]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [[[],[[]]],[],[[]],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [[[[],[[]]],[],[],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [[[],[[]]],[[],[],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [[[],[[]]],[],[[],[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [[[],[[]]],[],[],[[]]]
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[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [[[[[[],[[[]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [[[[[],[[[]]]]]],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => [[[[[],[[[]]]]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[[.,.],.],.]],.],[[.,.],.]] => [[[[],[[[]]]]],[[]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [[[[],[[[]]]]],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],[.,.]],.],.] => [[[[[],[[[]]]],[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [[[[],[[[]]]],[]],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => [[[[],[[[]]]],[[]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[[],[[[]]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [[[],[[[]]]],[[]],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [[[[],[[[]]]],[],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [[[],[[[]]]],[[],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [[[],[[[]]]],[],[[]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [[[],[[[]]]],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [[[[[],[[[[]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => [[[[],[[[[]]]]]],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [[[[],[[[[]]]]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [[[],[[[[]]]]],[[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [[[],[[[[]]]]],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [[[[],[[[[[]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [[[],[[[[[]]]]]],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [[[],[[[[[[]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [[],[[[[[[[]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [[],[[[[[[]]]]]],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [[[],[[[[[]]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [[],[[[[[[]]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [[],[[[[[]]]]],[[]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [[],[[[[[]]]]],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [[[[],[[[[]]]],[]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [[[],[[[[]]]],[]],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [[[],[[[[[]]]],[]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [[],[[[[[[]]]],[]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [[],[[[[[]]]],[]],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [[[],[[[[]]]],[[]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [[],[[[[[]]]],[[]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [[],[[[[]]]],[[[]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [[],[[[[]]]],[[]],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [[[],[[[[]]]],[],[]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [[],[[[[[]]]],[],[]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [[],[[[[]]]],[[],[]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [[],[[[[]]]],[],[[]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [[],[[[[]]]],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => [[[[[],[[[]]],[]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [[[[],[[[]]],[]]],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [[[[],[[[]]],[]],[]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [[[],[[[]]],[]],[[]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [[[],[[[]]],[]],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [[[[],[[[[]]],[]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [[[],[[[[]]],[]]],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [[[],[[[[[]]],[]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [[],[[[[[[]]],[]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [[],[[[[[]]],[]]],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [[[],[[[[]]],[]],[]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [[],[[[[[]]],[]],[]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [[],[[[[]]],[]],[[]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [[],[[[[]]],[]],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[[.,.],.]]],.],.] => [[[[],[[[]]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [[[],[[[]]],[[]]],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[[.,.],.]],.]],.] => [[[],[[[[]]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [[],[[[[[]]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [[],[[[[]]],[[]]],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [[[],[[[]]],[[[]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [[],[[[[]]],[[[]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [[],[[[]]],[[[[]]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [[],[[[]]],[[[]]],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [[[],[[[]]],[[]],[]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [[],[[[[]]],[[]],[]]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [[],[[[]]],[[[]],[]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [[],[[[]]],[[]],[[]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [[],[[[]]],[[]],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [[[[],[[[]]],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [[[],[[[]]],[],[]],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [[[],[[[[]]],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [[],[[[[[]]],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [[],[[[[]]],[],[]],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [[[],[[[]]],[[],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [[],[[[[]]],[[],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [[],[[[]]],[[[],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [[],[[[]]],[[],[]],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [[[],[[[]]],[],[[]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [[],[[[[]]],[],[[]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [[],[[[]]],[[],[[]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [[],[[[]]],[],[[[]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [[],[[[]]],[],[[]],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [[[],[[[]]],[],[],[]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [[],[[[[]]],[],[],[]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [[],[[[]]],[[],[],[]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [[],[[[]]],[],[[],[]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [[],[[[]]],[],[],[[]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [[],[[[]]],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => [[[[[[],[[]],[]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [[[[[],[[]],[]]]],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [[[[[],[[]],[]]],[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [[[[],[[]],[]]],[[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [[[[],[[]],[]]],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [[[[[],[[]],[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [[[[],[[]],[]],[]],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[[.,.],.]],.] => [[[[],[[]],[]],[[]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [[[],[[]],[]],[[[]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[[],[[]],[]],[[]],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [[[[],[[]],[]],[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[[],[[]],[]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [[[],[[]],[]],[],[[]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [[[],[[]],[]],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [[[[[],[[[]],[]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [[[[],[[[]],[]]]],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [[[[],[[[]],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [[[],[[[]],[]]],[[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [[[],[[[]],[]]],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],[.,.]],.],.]],.],.] => [[[[],[[[[]],[]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [[[],[[[[]],[]]]],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => [[[],[[[[[]],[]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [[],[[[[[[]],[]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [[],[[[[[]],[]]]],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [[[],[[[[]],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [[],[[[[[]],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [[],[[[[]],[]]],[[]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [[],[[[[]],[]]],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [[[[],[[[]],[]],[]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[[],[[[]],[]],[]],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [[[],[[[[]],[]],[]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [[],[[[[[]],[]],[]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [[],[[[[]],[]],[]],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [[[],[[[]],[]],[[]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [[],[[[[]],[]],[[]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [[],[[[]],[]],[[[]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [[],[[[]],[]],[[]],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [[[],[[[]],[]],[],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [[],[[[[]],[]],[],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [[],[[[]],[]],[[],[]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [[],[[[]],[]],[],[[]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [[],[[[]],[]],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [[[[[],[[]],[[]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [[[[],[[]],[[]]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [[[[],[[]],[[]]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [[[],[[]],[[]]],[[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [[[],[[]],[[]]],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[[.,.],.]],.]],.],.] => [[[[],[[[]],[[]]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [[[],[[[]],[[]]]],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => [[[],[[[[]],[[]]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [[],[[[[[]],[[]]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [[],[[[[]],[[]]]],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [[[],[[[]],[[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [[],[[[[]],[[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [[],[[[]],[[]]],[[]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [[],[[[]],[[]]],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[[.,.],.],.]]],.],.] => [[[[],[[]],[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [[[],[[]],[[[]]]],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[[.,.],.],.]],.]],.] => [[[],[[[]],[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => [[],[[[[]],[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [[],[[[]],[[[]]]],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [[[],[[]],[[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [[],[[[]],[[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [[],[[]],[[[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [[],[[]],[[[[]]]],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [[[],[[]],[[[]]],[]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [[],[[[]],[[[]]],[]]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [[],[[]],[[[[]]],[]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [[],[[]],[[[]]],[[]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [[],[[]],[[[]]],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [[[[],[[]],[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [[[],[[]],[[]],[]],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [[[],[[[]],[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [[],[[[[]],[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [[],[[[]],[[]],[]],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [[[],[[]],[[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [[],[[[]],[[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [[],[[]],[[[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [[],[[]],[[[]],[]],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [[[],[[]],[[]],[[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [[],[[[]],[[]],[[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [[],[[]],[[[]],[[]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [[],[[]],[[]],[[[]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[],[[]],[[]],[[]],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [[[],[[]],[[]],[],[]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [[],[[[]],[[]],[],[]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [[],[[]],[[[]],[],[]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [[],[[]],[[]],[[],[]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [[],[[]],[[]],[],[[]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [[],[[]],[[]],[],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [[[[[],[[]],[],[]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [[[[],[[]],[],[]]],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [[[[],[[]],[],[]],[]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [[[],[[]],[],[]],[[]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [[[],[[]],[],[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [[[[],[[[]],[],[]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [[[],[[[]],[],[]]],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [[[],[[[[]],[],[]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [[],[[[[[]],[],[]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [[],[[[[]],[],[]]],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [[[],[[[]],[],[]],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [[],[[[[]],[],[]],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [[],[[[]],[],[]],[[]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [[],[[[]],[],[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [[[[],[[]],[[],[]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [[[],[[]],[[],[]]],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [[[],[[[]],[[],[]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [[],[[[[]],[[],[]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [[],[[[]],[[],[]]],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [[[],[[]],[[[],[]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [[],[[[]],[[[],[]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [[],[[]],[[[[],[]]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [[],[[]],[[[],[]]],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [[[],[[]],[[],[]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [[],[[[]],[[],[]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [[],[[]],[[[],[]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [[],[[]],[[],[]],[[]]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [[],[[]],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [[[[],[[]],[],[[]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [[[],[[]],[],[[]]],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [[[],[[[]],[],[[]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [[],[[[[]],[],[[]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [[],[[[]],[],[[]]],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [[[],[[]],[[],[[]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [[],[[[]],[[],[[]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [[],[[]],[[[],[[]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [[],[[]],[[],[[]]],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [[[],[[]],[],[[[]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [[],[[[]],[],[[[]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [[],[[]],[[],[[[]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [[],[[]],[],[[[[]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [[],[[]],[],[[[]]],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [[[],[[]],[],[[]],[]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [[],[[[]],[],[[]],[]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [[],[[]],[[],[[]],[]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [[],[[]],[],[[[]],[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [[],[[]],[],[[]],[[]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [[],[[]],[],[[]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [[[[],[[]],[],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [[[],[[]],[],[],[]],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [[[],[[[]],[],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [[],[[[[]],[],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [[],[[[]],[],[],[]],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [[[],[[]],[[],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [[],[[[]],[[],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [[],[[]],[[[],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [[],[[]],[[],[],[]],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [[[],[[]],[],[[],[]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [[],[[[]],[],[[],[]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [[],[[]],[[],[[],[]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [[],[[]],[],[[[],[]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [[],[[]],[],[[],[]],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [[[],[[]],[],[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [[],[[[]],[],[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [[],[[]],[[],[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [[],[[]],[],[[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [[],[[]],[],[],[[[]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [[],[[]],[],[],[[]],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [[[],[[]],[],[],[],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [[],[[[]],[],[],[],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [[],[[]],[[],[],[],[]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [[],[[]],[],[[],[],[]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [[],[[]],[],[],[[],[]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [[],[[]],[],[],[],[[]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[],[[]],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [[[[[[[],[],[]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[[[],[],[]]]]],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [[[[[[],[],[]]]],[]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [[[[[],[],[]]]],[[]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[[],[],[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [[[[[[],[],[]]],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[[],[],[]]],[]],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [[[[[],[],[]]],[[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [[[[],[],[]]],[[[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [[[[],[],[]]],[[]],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [[[[[],[],[]]],[],[]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [[[[],[],[]]],[[],[]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [[[[],[],[]]],[],[[]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [[[[],[],[]]],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [[[[[[],[],[]],[]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [[[[[],[],[]],[]]],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [[[[[],[],[]],[]],[]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [[[[],[],[]],[]],[[]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [[[[],[],[]],[]],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [[[[[],[],[]],[[]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [[[[],[],[]],[[]]],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [[[[],[],[]],[[[]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [[[],[],[]],[[[[]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [[[],[],[]],[[[]]],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [[[[],[],[]],[[]],[]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [[[],[],[]],[[[]],[]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [[[],[],[]],[[]],[[]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [[[],[],[]],[[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [[[[[],[],[]],[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [[[[],[],[]],[],[]],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [[[[],[],[]],[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [[[],[],[]],[[[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [[[],[],[]],[[],[]],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [[[[],[],[]],[],[[]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [[[],[],[]],[[],[[]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [[[],[],[]],[],[[[]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [[[],[],[]],[],[[]],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [[[[],[],[]],[],[],[]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [[[],[],[]],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [[[],[],[]],[],[[],[]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [[[],[],[]],[],[],[[]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[],[],[]],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [[[[[[],[[],[]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [[[[[],[[],[]]]]],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [[[[[],[[],[]]]],[]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [[[[],[[],[]]]],[[]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [[[[],[[],[]]]],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [[[[[],[[],[]]],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [[[[],[[],[]]],[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [[[[],[[],[]]],[[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [[[[],[[],[]]],[],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [[[],[[],[]]],[],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [[[[[],[[[],[]]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [[[[],[[[],[]]]]],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [[[[],[[[],[]]]],[]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [[[],[[[],[]]]],[[]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [[[],[[[],[]]]],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [[[[],[[[[],[]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [[[],[[[[],[]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [[[],[[[[[],[]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [[],[[[[[[],[]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [[],[[[[[],[]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [[[],[[[[],[]]]],[]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [[],[[[[[],[]]]],[]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [[],[[[[],[]]]],[[]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [[],[[[[],[]]]],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [[[[],[[[],[]]],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [[[],[[[],[]]],[]],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [[[],[[[[],[]]],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [[],[[[[[],[]]],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [[],[[[[],[]]],[]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [[[],[[[],[]]],[[]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [[],[[[[],[]]],[[]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [[],[[[],[]]],[[[]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [[],[[[],[]]],[[]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [[[],[[[],[]]],[],[]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [[],[[[[],[]]],[],[]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[],[[[],[]]],[[],[]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [[],[[[],[]]],[],[[]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [[],[[[],[]]],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [[[[[],[[],[]],[]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [[[[],[[],[]],[]]],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [[[[],[[],[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [[[],[[],[]],[]],[[]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [[[],[[],[]],[]],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [[[[],[[[],[]],[]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[[],[[[],[]],[]]],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [[[],[[[[],[]],[]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [[],[[[[[],[]],[]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [[],[[[[],[]],[]]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [[[],[[[],[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[],[[[[],[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [[],[[[],[]],[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [[],[[[],[]],[]],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [[[[],[[],[]],[[]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [[[],[[],[]],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [[[],[[[],[]],[[]]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [[],[[[[],[]],[[]]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [[],[[[],[]],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [[[],[[],[]],[[[]]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [[],[[[],[]],[[[]]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [[],[[],[]],[[[[]]]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [[],[[],[]],[[[]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [[[],[[],[]],[[]],[]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [[],[[[],[]],[[]],[]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [[],[[],[]],[[[]],[]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [[],[[],[]],[[]],[[]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [[],[[],[]],[[]],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [[[[],[[],[]],[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [[[],[[],[]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [[[],[[[],[]],[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [[],[[[[],[]],[],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [[],[[[],[]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [[[],[[],[]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [[],[[[],[]],[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [[],[[],[]],[[[],[]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [[],[[],[]],[[],[]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [[[],[[],[]],[],[[]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [[],[[[],[]],[],[[]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [[],[[],[]],[[],[[]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [[],[[],[]],[],[[[]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [[],[[],[]],[],[[]],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [[[],[[],[]],[],[],[]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [[],[[[],[]],[],[],[]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [[],[[],[]],[[],[],[]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [[],[[],[]],[],[[],[]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [[],[[],[]],[],[],[[]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [[],[[],[]],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => [[[[[[],[],[[]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [[[[[],[],[[]]]]],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [[[[[],[],[[]]]],[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [[[[],[],[[]]]],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [[[[],[],[[]]]],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [[[[[],[],[[]]],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [[[[],[],[[]]],[]],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [[[[],[],[[]]],[[]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [[[],[],[[]]],[[[]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [[[],[],[[]]],[[]],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [[[[],[],[[]]],[],[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [[[],[],[[]]],[[],[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[[],[],[[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [[[],[],[[]]],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [[[[[],[[],[[]]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [[[[],[[],[[]]]]],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [[[[],[[],[[]]]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [[[],[[],[[]]]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [[[],[[],[[]]]],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [[[[],[[[],[[]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [[[],[[[],[[]]]]],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [[[],[[[[],[[]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [[],[[[[[],[[]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [[],[[[[],[[]]]]],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [[[],[[[],[[]]]],[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [[],[[[[],[[]]]],[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [[],[[[],[[]]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [[],[[[],[[]]]],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [[[[],[[],[[]]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [[[],[[],[[]]],[]],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [[[],[[[],[[]]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [[],[[[[],[[]]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [[],[[[],[[]]],[]],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [[[],[[],[[]]],[[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [[],[[[],[[]]],[[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [[],[[],[[]]],[[[]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [[],[[],[[]]],[[]],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [[[],[[],[[]]],[],[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [[],[[[],[[]]],[],[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [[],[[],[[]]],[[],[]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [[],[[],[[]]],[],[[]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [[],[[],[[]]],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [[[[[],[],[[[]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [[[[],[],[[[]]]]],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [[[[],[],[[[]]]],[]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [[[],[],[[[]]]],[[]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [[[],[],[[[]]]],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [[[[],[[],[[[]]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [[[],[[],[[[]]]]],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => [[[],[[[],[[[]]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [[],[[[[],[[[]]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [[],[[[],[[[]]]]],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [[[],[[],[[[]]]],[]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [[],[[[],[[[]]]],[]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [[],[[],[[[]]]],[[]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [[],[[],[[[]]]],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [[[[],[],[[[[]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [[[],[],[[[[]]]]],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [[[],[[],[[[[]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [[],[[[],[[[[]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [[],[[],[[[[]]]]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [[[],[],[[[[[]]]]]]]
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[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [[[[[[],[],[],[]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [[[[[],[],[],[]]]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [[[[[],[],[],[]]],[]]]
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[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [[[[[],[],[],[]],[]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[[[],[],[],[]],[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [[[[],[],[],[]],[[]]]]
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[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [[[],[],[],[]],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [[[[],[],[],[]],[],[]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [[[],[],[],[]],[[],[]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [[[],[],[],[]],[],[[]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[],[],[],[]],[],[],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [[[[[],[[],[],[]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [[[[],[[],[],[]]]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [[[[],[[],[],[]]],[]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [[[],[[],[],[]]],[[]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [[[],[[],[],[]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [[[[],[[[],[],[]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [[[],[[[],[],[]]]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [[[],[[[[],[],[]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [[],[[[[[],[],[]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [[],[[[[],[],[]]]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [[[],[[[],[],[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [[],[[[[],[],[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [[],[[[],[],[]]],[[]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [[],[[[],[],[]]],[],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [[[[],[[],[],[]],[]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [[[],[[],[],[]],[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [[[],[[[],[],[]],[]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [[],[[[[],[],[]],[]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [[],[[[],[],[]],[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [[[],[[],[],[]],[[]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [[],[[[],[],[]],[[]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [[],[[],[],[]],[[[]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [[],[[],[],[]],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [[[],[[],[],[]],[],[]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [[],[[[],[],[]],[],[]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [[],[[],[],[]],[[],[]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [[],[[],[],[]],[],[[]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [[],[[],[],[]],[],[],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [[[[[],[],[[],[]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [[[[],[],[[],[]]]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [[[[],[],[[],[]]],[]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [[[],[],[[],[]]],[[]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [[[],[],[[],[]]],[],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [[[[],[[],[[],[]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[[],[[],[[],[]]]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [[[],[[[],[[],[]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [[],[[[[],[[],[]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [[],[[[],[[],[]]]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [[[],[[],[[],[]]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[],[[[],[[],[]]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [[],[[],[[],[]]],[[]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [[],[[],[[],[]]],[],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [[[[],[],[[[],[]]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [[[],[],[[[],[]]]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [[[],[[],[[[],[]]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [[],[[[],[[[],[]]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [[],[[],[[[],[]]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [[[],[],[[[[],[]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [[],[[],[[[[],[]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [[],[],[[[[[],[]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [[],[],[[[[],[]]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [[[],[],[[[],[]]],[]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [[],[[],[[[],[]]],[]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [[],[],[[[[],[]]],[]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [[],[],[[[],[]]],[[]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [[],[],[[[],[]]],[],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [[[[],[],[[],[]],[]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [[[],[],[[],[]],[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [[[],[[],[[],[]],[]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [[],[[[],[[],[]],[]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [[],[[],[[],[]],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [[[],[],[[[],[]],[]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [[],[[],[[[],[]],[]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [[],[],[[[[],[]],[]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [[],[],[[[],[]],[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [[[],[],[[],[]],[[]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [[],[[],[[],[]],[[]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [[],[],[[[],[]],[[]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [[],[],[[],[]],[[[]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [[],[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [[[],[],[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [[],[[],[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [[],[],[[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [[],[],[[],[]],[[],[]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [[],[],[[],[]],[],[[]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [[],[],[[],[]],[],[],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [[[[[],[],[],[[]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [[[[],[],[],[[]]]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [[[[],[],[],[[]]],[]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [[[],[],[],[[]]],[[]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [[[],[],[],[[]]],[],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [[[[],[[],[],[[]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [[[],[[],[],[[]]]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [[[],[[[],[],[[]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [[],[[[[],[],[[]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [[],[[[],[],[[]]]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [[[],[[],[],[[]]],[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [[],[[[],[],[[]]],[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [[],[[],[],[[]]],[[]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [[],[[],[],[[]]],[],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [[[[],[],[[],[[]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [[[],[],[[],[[]]]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [[[],[[],[[],[[]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [[],[[[],[[],[[]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [[],[[],[[],[[]]]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [[[],[],[[[],[[]]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [[],[[],[[[],[[]]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [[],[],[[[[],[[]]]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [[],[],[[[],[[]]]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [[[],[],[[],[[]]],[]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [[],[[],[[],[[]]],[]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [[],[],[[[],[[]]],[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [[],[],[[],[[]]],[[]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [[],[],[[],[[]]],[],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [[[[],[],[],[[[]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [[[],[],[],[[[]]]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [[[],[[],[],[[[]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [[],[[[],[],[[[]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [[],[[],[],[[[]]]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [[[],[],[[],[[[]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [[],[[],[[],[[[]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [[],[],[[[],[[[]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [[],[],[[],[[[]]]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [[[],[],[],[[[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [[],[[],[],[[[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [[],[],[[],[[[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [[],[],[],[[[[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [[],[],[],[[[[]]]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [[[],[],[],[[[]]],[]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [[],[[],[],[[[]]],[]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [[],[],[[],[[[]]],[]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [[],[],[],[[[[]]],[]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [[],[],[],[[[]]],[[]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [[],[],[],[[[]]],[],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [[[[],[],[],[[]],[]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [[[],[],[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [[[],[[],[],[[]],[]]]]
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[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [[],[[],[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [[[],[],[[],[[]],[]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [[],[[],[[],[[]],[]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [[],[],[[[],[[]],[]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [[],[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [[[],[],[],[[[]],[]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [[],[[],[],[[[]],[]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [[],[],[[],[[[]],[]]]]
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[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [[[],[],[],[[]],[[]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [[],[[],[],[[]],[[]]]]
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[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [[[],[],[],[[]],[],[]]]
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[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [[[[[],[],[],[],[]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [[[[],[],[],[],[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [[[[],[],[],[],[]],[]]]
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[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [[[[],[[],[],[],[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [[[],[[],[],[],[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [[[],[[[],[],[],[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [[],[[[[],[],[],[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [[],[[[],[],[],[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [[[],[[],[],[],[]],[]]]
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[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [[[[],[],[[],[],[]]]]]
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[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [[[],[[],[[],[],[]]]]]
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[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [[],[[],[[],[],[]]],[]]
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[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [[],[[],[[[],[],[]]]]]
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[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [[[],[],[[],[],[]],[]]]
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[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [[[[],[],[],[[],[]]]]]
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[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [[[],[[],[],[[],[]]]]]
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[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [[],[[],[],[[],[]]],[]]
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[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [[[],[],[],[],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [[[],[[],[],[],[[]]]]]
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[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [[],[[],[],[],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [[[],[],[[],[],[[]]]]]
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[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [[[],[],[],[],[[]],[]]]
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[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [[[[],[],[],[],[],[]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[[],[],[],[],[],[]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [[[],[[],[],[],[],[]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [[],[[[],[],[],[],[]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [[],[[],[],[],[],[]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [[[],[],[[],[],[],[]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [[],[[],[[],[],[],[]]]]
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[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [[[],[],[],[[],[],[]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [[],[[],[],[[],[],[]]]]
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[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [[[[],[]],[],[],[],[],[]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [[[[[[[[],[],[]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => [[[[[[[],[],[]],[]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [[[],[],[]],[],[],[],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [[[[[[[],[],[],[]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => [[[[[[],[],[],[]]]]],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [[[],[],[],[]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [[[[[[],[],[],[],[]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [[[[],[],[],[],[]],[],[]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [[[],[],[],[],[]],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [[[[[],[],[],[],[],[]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [[[[],[],[],[],[],[]],[]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [[[],[],[],[],[],[]],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [[[[[[[[[[]]]]]]]],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [[[[[[[[[[]]]]]]],[]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => [[[[[[[[[]]]]]]],[]],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [[[[[[[[[[]]]]]],[]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [[[[[[[[[[]]]]],[]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [[[[[[[[[[]]]],[]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[]]]],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [[[[[[[[[[]]],[]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [[[[[[[[[[]],[]]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [[[[[[[[[]],[]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[[[]],[],[],[],[],[],[]],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [[[[[[[[[[],[]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[[[[[[[[],[]]]]]]]],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[],[]],[]],[]],[]],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [[[[[[[[[],[],[]]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[],[],[]],[],[],[],[],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [[[[[[[[],[],[],[]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [[[],[],[],[]],[],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [[[[[[[],[],[],[],[]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [[[],[],[],[],[]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [[[[[[],[],[],[],[],[]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [[[],[],[],[],[],[]],[],[],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [[[[[],[],[],[],[],[],[]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [[[[],[],[],[],[],[],[]],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [[[],[],[],[],[],[],[]],[],[]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[],[],[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => [[[[[[[[],[[]]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => [[[[[[],[[[[]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [[[[],[[[[[[]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [[[],[[[[[[[]]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [[[[[[[],[[]],[]]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [[[[[[],[[[]]],[]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [[[[[],[[[[]]]],[]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [[[[],[[[[[]]]]],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [[[],[[[[[[]]]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [[[],[[[[[[[[]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]] => [[],[],[],[],[[[[[]]]]],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]] => [[],[],[],[],[[[[[],[]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]] => [[],[],[],[],[[[[[[]]]]]],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]] => [[],[],[],[[[[[[]]]]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]] => [[],[],[],[[[[[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]] => [[],[],[],[],[[[[[[],[]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[[],[]]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => [[[[[[[],[]]]]]],[[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [[],[[[[[[[[]]]]]]]],[]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [[],[],[],[],[],[],[],[[]],[]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [[],[],[],[],[],[],[],[[],[]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [[],[],[],[],[],[],[],[],[[]],[]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]] => [[],[],[],[],[],[],[[[]]],[]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]] => [[],[],[],[],[],[],[[[],[]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [[],[],[],[],[],[],[],[],[[],[]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]] => [[[[[[[[],[]]]]]]],[[]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[[.,.],.]] => [[[[[[],[[]]]]]],[[]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[[.,.],.]] => [[[[[[[]],[]]]]],[[]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [[[[[[[],[[]]]]]]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => [[[],[],[[[[[[]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => [[[[],[],[[[[[]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => [[[[[],[],[[[[]]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => [[[[[[],[],[[[]]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [[[[[[[],[],[[]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[],[[]],[],[],[],[],[],[],[]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [[],[[],[],[],[],[],[],[],[]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => [[],[[],[],[],[],[],[],[],[],[]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => [[],[[],[],[],[],[],[],[[]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [[[[],[[],[],[],[],[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => [[[[[],[[],[],[],[]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => [[[[[[],[[],[],[]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => [[[[[[[],[[],[]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [[],[],[],[],[],[],[],[],[[]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => [[],[],[],[],[],[],[[]],[],[]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [[],[],[],[],[],[[]],[],[],[]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => [[],[],[],[],[[]],[],[],[],[]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => [[],[],[],[[]],[],[],[],[],[]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[],[],[[]],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]] => [[[],[],[[[[[]]]]]],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[[.,.],.],.],.],.]]] => [[[],[]],[],[[[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[[[.,.],.],.],.],.]]],.] => [[[],[[]],[[[[[]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => [[],[[]],[[[[[[[]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [[],[],[],[],[],[],[],[],[],[[]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [[[],[[]]],[],[],[],[],[]]
[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] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [[[],[],[],[[]]],[],[],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [[[],[],[],[],[[]]],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => [[[[[[[]],[[[]]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [[[[[[[[]]],[[]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.] => [[[[[[[[[]]]]]],[[]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.] => [[[[[[[[]]]]]],[[[]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]] => [[[[[],[[[[]]]]]]],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => [[[[[[[],[]],[[]]]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]] => [[],[[[[[[]],[[[]]]]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]] => [[],[[[[[[[]]],[[]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [[],[[[[[[[[]]]],[]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [[[]],[],[],[],[[[[[]]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[.,[.,.]],.],.],.],.]]] => [[[]],[],[[[[[],[]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [[[],[[[[[[],[]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => [[[]],[[[[[[]]]]]],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [[[],[[[[[[]]]]]]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [[[],[]],[[[[[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]] => [[[],[[[[[]]]]]],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => [[],[[[[[[[]]]]]]],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]] => [[[],[[[[]]]]],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]] => [[],[[[[[[]]]]]],[],[[]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]] => [[[],[[[]]]],[],[],[[]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]] => [[],[[[[[]]]]],[],[[[]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[[[.,.],.],.]]]] => [[[],[[]]],[],[],[[[]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]] => [[],[[[[]]]],[],[[[[]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]] => [[[],[]],[],[],[[[[]]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]] => [[],[[[]]],[],[[[[[]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]] => [[],[[]],[],[[[[[[]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [[],[],[],[[[[[[[]]]]]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]] => [[[],[]],[[]],[],[],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]] => [[[],[],[[]],[],[],[]],[]]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]] => [[[],[],[]],[],[[]],[],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]] => [[[],[],[],[[]],[]],[],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [[[],[],[],[]],[],[],[[]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [[[],[],[],[],[],[]],[[]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [[],[],[[],[],[],[],[],[],[]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]] => [[[],[],[],[],[]],[],[[]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [[],[],[],[[],[],[],[],[],[]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [[],[],[],[],[[],[],[],[],[]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]] => [[[],[],[]],[],[],[],[[]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [[],[],[],[],[],[[],[],[],[]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [[],[],[],[],[],[],[[],[],[]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[[[.,.],.],[.,.]],.],[[[.,.],.],.]] => [[[[[[]]],[]]],[[[]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [[[[[[[],[[]]],[]]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [[[[[],[[]],[]],[]],[]],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] => [[[[],[[[]],[]],[]],[]],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => [[[],[[[[]],[]],[]],[]],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [[],[[[[[]],[]],[]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [[],[],[[[[[[[[]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[]],[[]],[[]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => [[[]],[[]],[[],[[]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => [[[]],[[],[[]]],[[]],[[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => [[[]],[[],[[]],[[]]],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => [[[]],[[],[[],[[]]]],[[]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => [[[]],[[],[[]],[[]],[[]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => [[[]],[[],[[]],[[],[[]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => [[[]],[[],[[],[[]]],[[]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => [[[]],[[],[[],[[]],[[]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[[]],[[],[[],[[],[[]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => [[[],[[]]],[[]],[[]],[[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]] => [[[],[[]]],[[],[[]]],[[]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]] => [[[],[[]]],[[],[[]],[[]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => [[[],[[]]],[[],[[],[[]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => [[[],[[]],[[]]],[[]],[[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => [[[],[[]],[[]]],[[],[[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]] => [[[],[[],[[]]]],[[]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => [[[],[[],[[]]]],[[],[[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [[[],[[]],[[]],[[]]],[[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]] => [[[],[[]],[[],[[]]]],[[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]] => [[[],[[],[[]]],[[]]],[[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]] => [[[],[[],[[]],[[]]]],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => [[[],[[],[[],[[]]]]],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [[[],[[],[[],[[],[[]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[[]],[[]],[[]],[[]],[[]],[[]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]] => [[[]],[[]],[[]],[[],[[]]],[[]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]] => [[[]],[[]],[[],[[]]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]] => [[[]],[[]],[[],[[]],[[]]],[[]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]] => [[[]],[[]],[[],[[],[[]]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] => [[[]],[[],[[]]],[[]],[[]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] => [[[]],[[],[[]]],[[],[[]]],[[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] => [[[]],[[],[[]],[[]]],[[]],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] => [[[]],[[],[[],[[]]]],[[]],[[]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] => [[[]],[[],[[]],[[]],[[]]],[[]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] => [[[]],[[],[[]],[[],[[]]]],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] => [[[]],[[],[[],[[]]],[[]]],[[]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] => [[[]],[[],[[],[[]],[[]]]],[[]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] => [[[]],[[],[[],[[],[[]]]]],[[]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => [[[]],[[],[[]],[[]],[[]],[[]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => [[[]],[[],[[]],[[]],[[],[[]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => [[[]],[[],[[]],[[],[[]]],[[]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => [[[]],[[],[[]],[[],[[]],[[]]]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => [[[]],[[],[[]],[[],[[],[[]]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => [[[]],[[],[[],[[]]],[[]],[[]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => [[[]],[[],[[],[[]]],[[],[[]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => [[[]],[[],[[],[[]],[[]]],[[]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => [[[]],[[],[[],[[],[[]]]],[[]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => [[[]],[[],[[],[[]],[[]],[[]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => [[[]],[[],[[],[[]],[[],[[]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => [[[]],[[],[[],[[],[[]]],[[]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => [[[]],[[],[[],[[],[[]],[[]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => [[[]],[[],[[],[[],[[],[[]]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[],[[]]],[[]],[[]],[[]],[[]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => [[[],[[]]],[[]],[[],[[]]],[[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => [[[],[[]]],[[],[[]]],[[]],[[]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] => [[[],[[]]],[[],[[]],[[]]],[[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] => [[[],[[]]],[[],[[],[[]]]],[[]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => [[[],[[]]],[[],[[]],[[]],[[]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => [[[],[[]]],[[],[[]],[[],[[]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => [[[],[[]]],[[],[[],[[]]],[[]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => [[[],[[]]],[[],[[],[[]],[[]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[[],[[]]],[[],[[],[[],[[]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] => [[[],[[]],[[]]],[[]],[[]],[[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] => [[[],[[]],[[]]],[[],[[]]],[[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] => [[[],[[]],[[]]],[[],[[]],[[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] => [[[],[[]],[[]]],[[],[[],[[]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] => [[[],[[],[[]]]],[[]],[[]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] => [[[],[[],[[]]]],[[],[[]]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] => [[[],[[],[[]]]],[[],[[]],[[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] => [[[],[[],[[]]]],[[],[[],[[]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] => [[[],[[]],[[]],[[]]],[[]],[[]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] => [[[],[[]],[[]],[[]]],[[],[[]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] => [[[],[[]],[[],[[]]]],[[]],[[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => [[[],[[]],[[],[[]]]],[[],[[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] => [[[],[[],[[]]],[[]]],[[]],[[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] => [[[],[[],[[]]],[[]]],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] => [[[],[[],[[]],[[]]]],[[]],[[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] => [[[],[[],[[]],[[]]]],[[],[[]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] => [[[],[[],[[],[[]]]]],[[]],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] => [[[],[[],[[],[[]]]]],[[],[[]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => [[[],[[]],[[]],[[]],[[]]],[[]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => [[[],[[]],[[]],[[],[[]]]],[[]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => [[[],[[]],[[],[[]]],[[]]],[[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => [[[],[[]],[[],[[]],[[]]]],[[]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => [[[],[[]],[[],[[],[[]]]]],[[]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] => [[[],[[],[[]]],[[]],[[]]],[[]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] => [[[],[[],[[]]],[[],[[]]]],[[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] => [[[],[[],[[]],[[]]],[[]]],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] => [[[],[[],[[],[[]]]],[[]]],[[]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] => [[[],[[],[[]],[[]],[[]]]],[[]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] => [[[],[[],[[]],[[],[[]]]]],[[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] => [[[],[[],[[],[[]]],[[]]]],[[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] => [[[],[[],[[],[[]],[[]]]]],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] => [[[],[[],[[],[[],[[]]]]]],[[]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [[],[],[],[],[[[[[[]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]] => [[],[],[],[],[],[[[[],[]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [[[[[[],[],[],[[]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [[[[[[[[]],[[]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [[],[],[],[],[],[],[],[[[]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [[],[],[],[],[],[],[],[],[[[]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [[[[],[[[[[]]]]]]],[]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [[],[],[],[],[],[[[[[]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [[],[],[],[],[],[],[[[[]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.] => [[[[[],[]],[]],[[]],[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [[[[]],[[[[[[]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [[],[[],[],[],[],[],[],[]],[]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[[[]],[]],[],[],[],[[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[[],[[[[],[]],[]],[]]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[],[[[[[],[]],[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [[[],[[[[],[]],[]],[]],[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.] => [[[],[[],[],[],[],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]] => [[[[[]],[]],[]],[[[]],[]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[[],[]],[[]],[[]],[[]],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]] => [[[],[[]],[]],[[]],[[]],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] => [[[],[[[]],[]],[]],[[]],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]] => [[[]],[[[[],[]],[]],[]],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]] => [[[[[]],[]],[]],[[],[]],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[[],[[[],[[],[]]],[]]],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[],[[[[],[]],[[],[]]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[],[[[],[[[],[]],[]]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[],[[[[],[[],[]]],[]],[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[[],[]],[]],[]],[]],[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [[[[],[[[],[[],[]]],[]]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[[[],[]],[]],[]],[[],[]]],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[[],[[],[]]],[]],[[],[]]],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[[[[],[]],[[],[]]],[[],[]]],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[[[],[[[],[]],[]]],[[],[]]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[[],[[[[],[]],[[],[]]],[]]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [[[],[[[],[[[],[]],[]]],[]]],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[[[[],[]],[]],[[[],[]],[]]],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[[[],[[],[]]],[[[],[]],[]]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [[[],[[[[],[[],[]]],[]],[]]],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[[[],[]],[[[[],[]],[]],[]]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[[],[[[[[],[]],[]],[]],[]]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [[[],[[[],[[],[]]],[]]],[[],[]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [[],[[[[],[[],[]]],[[],[]]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[],[[[[[],[]],[]],[[],[]]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [[],[[[],[[[[],[]],[]],[]]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[],[[[[],[]],[[[],[]],[]]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[],[[[[[],[]],[[],[]]],[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [[],[[[[],[[[],[]],[]]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [[],[[[[[],[[],[]]],[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[],[[[[[[],[]],[]],[]],[]],[]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]] => [[[]],[[]],[[]],[[[]],[]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.] => [[[[]],[],[[]],[[[]],[]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]] => [[[]],[[[]],[],[[[]],[]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.] => [[[[]],[[],[],[[[]],[]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]] => [[[]],[[]],[[[]],[[],[]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.] => [[[[]],[],[[[]],[[],[]]]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]] => [[[]],[[[]],[[],[[],[]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.] => [[[[]],[[],[[],[[],[]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]] => [[[]],[[]],[[]],[[]],[[[]],[]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]],.] => [[[[]],[],[[]],[[]],[[[]],[]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]] => [[[]],[[[]],[],[[]],[[[]],[]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[.,.],[[[.,.],[.,.]],.]]]],.]],.] => [[[[]],[[],[],[[]],[[[]],[]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]] => [[[]],[[]],[[[]],[],[[[]],[]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.] => [[[[]],[],[[[]],[],[[[]],[]]]]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]] => [[[]],[[[]],[[],[],[[[]],[]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[.,[[[.,.],[.,.]],.]]],.]],.]],.] => [[[[]],[[],[[],[],[[[]],[]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]] => [[[]],[[]],[[]],[[[]],[[],[]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]],.] => [[[[]],[],[[]],[[[]],[[],[]]]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]] => [[[]],[[[]],[],[[[]],[[],[]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[[.,.],[[.,[.,.]],.]],.]]],.]],.] => [[[[]],[[],[],[[[]],[[],[]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]] => [[[]],[[]],[[[]],[[],[[],[]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]],.] => [[[[]],[],[[[]],[[],[[],[]]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [[[]],[[[]],[[],[[],[[],[]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.] => [[[[]],[[],[[],[[],[[],[]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [[[],[],[],[],[],[],[]],[[]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [[[],[],[],[]],[[[[[]]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [[[[[],[]],[[]],[]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [[[[[],[]],[]],[[]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [[[[[],[]],[]],[]],[[]],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => [[],[[],[[[[]],[]],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]] => [[[[[]],[]],[]],[[]],[]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[[]],[]],[[]],[[],[]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]] => [[[[],[]],[]],[[[]],[]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => [[[],[]],[[[[]],[]],[]],[]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.] => [[[[],[[]]],[[],[[],[[],[]]]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.] => [[[],[[[]],[]],[[]],[]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]] => [[],[[[],[]]],[[]],[[],[]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => [[],[[[],[[],[]]]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => [[],[[[],[[]],[]]],[[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => [[],[[[],[[],[[]],[]]]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]] => [[],[[[],[[],[]]]],[[]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => [[],[[[],[[]],[]]],[[],[[]],[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => [[],[[[],[[],[[]],[]]]],[[]],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,[.,.]],.]]] => [[],[[[],[[]],[[],[]]]],[[],[]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]] => [[[]],[[[],[]]],[[],[]],[]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [[],[[]],[[]],[[]],[[]],[]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [[],[[]],[[]],[[]],[[]],[[]],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],[.,.]]] => [[[[]],[[[]]]],[[]],[]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]] => [[[]],[[]],[[[],[]],[]],[]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [[],[[]],[[]],[[]],[[],[]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]] => [[[[],[[],[],[]]],[]],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]] => [[[[],[],[]],[]],[[]],[]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => [[],[[],[[],[[],[[]],[]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => [[],[[],[[],[[[]],[]],[]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]] => [[],[[[]],[[],[[],[[]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => [[],[[[]],[[],[[],[[],[[]]]]]]]
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
- if $x$ is the left child of $y$, $x$ becomes the first child of $y$.
searching the database
Sorry, this map was not found in the database.