Identifier
Mp00026:
Dyck paths
—to ordered tree⟶
Ordered trees
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary 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 2150 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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[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[],[[[[]]]],[[]]] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[],[[[[]]],[]],[]] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[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] => [[],[[[[],[]]]],[]] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[[[[[]]]]],[]] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => [[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[[]]] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[[],[]]] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[]],[],[[],[]],[]] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[]],[],[[],[],[]]] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[]],[],[[],[[]]]] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[]],[],[[[]],[]]] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[]],[],[[[],[]]]] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[[[[]]]]] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[[]],[],[[]]] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[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] => [[[]],[[],[]],[],[]] => [[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[]],[[],[]],[[]]] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[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] => [[[],[[[]],[]],[]]] => [.,[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[[],[[[]],[],[]]]] => [.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[[],[[[]],[[]]]]] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[],[[[],[]]]],[]] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[[],[[[],[]]],[]]] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[[],[[[],[]],[]]]] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[[],[[[],[],[]]]]] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[[],[[[],[[]]]]]] => [.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[[],[[[[]]],[]]]] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[[],[[[[]],[]]]]] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[[],[[[[],[]]]]]] => [.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[]]],[],[],[[]]] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[]]],[],[[],[]]] => [[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[[]]],[[],[]],[]] => [[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[[]]],[[],[],[]]] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[[]]],[[],[[]]]] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[[]]],[[[]],[]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[[]]],[[[],[]]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[]]],[[[[]]]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[]],[]],[],[],[]] => [[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[[]],[]],[],[[]]] => [[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[]],[]],[[]],[]] => [[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[]],[]],[[],[]]] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[[]],[]],[[[]]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[[]],[],[]],[],[]] => [[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[[]],[],[]],[[]]] => [[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[[]],[],[],[]],[]] => [[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[]]] => [.,[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[[]],[],[],[[]]]] => [.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[[]],[],[[]]],[]] => [[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[[]],[],[[]],[]]] => [.,[[[[.,[.,.]],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[[]],[],[[],[]]]] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[[]],[],[[[]]]]] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[]],[[]]],[],[]] => [[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[[]],[[]]],[[]]] => [[.,[[.,[.,.]],[.,.]]],[.,.]]
[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] => [[[[]],[[[]]]],[]] => [[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[]],[[[]]],[]]] => [.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[[]],[[[]],[]]]] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[[]],[[[],[]]]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[]],[[[[]]]]]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[],[]]],[],[],[]] => [[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[[],[]]],[],[[]]] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[],[]]],[[]],[]] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[],[]]],[[],[]]] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[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] => [[[[],[]],[]],[],[]] => [[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[[],[]],[]],[[]]] => [[.,[[.,[[.,.],.]],.]],[.,.]]
[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] => [[[[],[]],[[]]],[]] => [[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[[],[]],[[]],[]]] => [.,[[[.,[[.,.],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[[],[]],[[],[]]]] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[[],[]],[[[]]]]] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[],[],[]]],[],[]] => [[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[[],[],[]]],[[]]] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[[],[],[]],[]],[]] => [[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[[],[],[]],[],[]]] => [.,[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[[[],[],[]],[[]]]] => [.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[],[]]],[]] => [[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[],[]],[]]] => [.,[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[],[]]]] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[[],[],[],[[]]]]] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[[],[],[[]]]],[]] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[[],[],[[]]],[]]] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[[],[],[[]],[]]]] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[[],[],[[],[]]]]] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[[],[],[[[]]]]]] => [.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[],[[]]]],[],[]] => [[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[[],[[]]]],[[]]] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[[],[[]]],[]],[]] => [[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[[],[[]]],[],[]]] => [.,[[[.,[[.,.],[.,.]]],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[[],[[]]],[[]]]] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[[],[[]],[]]],[]] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[[],[[]],[]],[]]] => [.,[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[[],[[]],[],[]]]] => [.,[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[[[],[[]],[[]]]]] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[[],[[],[]]],[]]] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[[],[[],[]],[]]]] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[[],[[],[],[]]]]] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[[],[[],[[]]]]]] => [.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[[[]]]]],[]] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[[],[[[]]]],[]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[[],[[[]]],[]]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[[],[[[]],[]]]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[[],[[[],[]]]]]] => [.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[[],[[[[]]]]]]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[]] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[[]]]],[],[[]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[[]]]],[[]],[]] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[[]]]],[[],[]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[[]]]],[[[]]]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[[]]],[]],[],[]] => [[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[[]]],[]],[[]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[[]]],[],[]],[]] => [[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[]]] => [.,[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[[]]],[],[[]]]] => [.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[[]]],[[]]],[]] => [[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[[]]],[[]],[]]] => [.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[[]]],[[],[]]]] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[[]]],[[[]]]]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[[]],[]]],[],[]] => [[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[[]],[]]],[[]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[[]],[]],[]],[]] => [[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[[]],[]],[],[]]] => [.,[[[.,[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[[]],[]],[[]]]] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[[]],[],[]]],[]] => [[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[[]],[],[]],[]]] => [.,[[.,[[[.,[.,.]],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[[]],[],[],[]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]]
[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] => [[[[[]],[[]]],[]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[[]],[[]],[]]]] => [.,[.,[[[.,[.,.]],[.,.]],.]]]
[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] => [[[[[],[]]],[]],[]] => [[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[[],[]]],[],[]]] => [.,[[[.,[.,[[.,.],.]]],.],.]]
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[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[],[],[[],[[[],[]]]]] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[],[[],[[[[]]]]]] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
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[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[],[],[[[]]],[[[]]]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
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[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[],[],[[[]],[],[]],[]] => [[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[],[],[[[]],[],[],[]]] => [[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[],[],[[[]],[],[[]]]] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[],[],[[[]],[[]]],[]] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
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[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[],[],[[[]],[[[]]]]] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
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[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[],[],[[[],[[]],[]]]] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[],[[[],[[],[]]]]] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[],[[[],[[[]]]]]] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[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] => [[],[],[[[[]],[]]],[]] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
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[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[],[[[[]],[[]]]]] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
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[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[],[[[[],[]]],[]]] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[],[[[[],[]],[]]]] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[],[[[[],[],[]]]]] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[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] => [[],[],[[[[[]]]]],[]] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[],[[[[[]]]],[]]] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[],[[[[[]]],[]]]] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[],[[[[[]],[]]]]] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[],[[[[[],[]]]]]] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[],[[[[[[]]]]]]] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
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[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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[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[],[[[]]]] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[[]],[],[]] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[],[[]],[],[[],[]],[]] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[],[[]],[],[[],[],[]]] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[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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[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[],[[]],[],[[[],[]]]] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[],[[]],[],[[[[]]]]] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
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[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[],[[]],[[],[]],[[]]] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
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[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[],[[]],[[],[],[[]]]] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[],[[]],[[],[[]]],[]] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
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[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[],[[]],[[],[[],[]]]] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[],[[]],[[],[[[]]]]] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
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[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[],[[]],[[[]],[]],[]] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[],[[]],[[[]],[],[]]] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[],[[]],[[[]],[[]]]] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[],[[]],[[[],[]]],[]] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[],[[]],[[[],[]],[]]] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[],[[]],[[[],[],[]]]] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[],[[]],[[[],[[]]]]] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[],[[]],[[[[]]],[]]] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[],[[]],[[[[]],[]]]] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[],[[]],[[[[],[]]]]] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[],[[]],[[[[[]]]]]] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[],[[],[]],[],[],[],[]] => [[[[[[.,.],[[.,.],.]],.],.],.],.]
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[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[],[[],[]],[],[[[]]]] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[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] => [[],[[],[],[]],[[]],[]] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[],[[],[],[]],[[],[]]] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[],[[],[],[]],[[[]]]] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[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] => [[],[[],[],[[[],[]]]]] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[],[[[[]]]]]] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[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] => [[],[[],[[]],[]],[],[]] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[],[[],[[]],[]],[[]]] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[],[[],[[]],[],[]],[]] => [[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[],[[],[[]],[],[],[]]] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[],[[],[[]],[],[[]]]] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[],[[],[[]],[[]]],[]] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[],[[],[[]],[[]],[]]] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[],[[],[[]],[[],[]]]] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[],[[],[[]],[[[]]]]] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[],[[],[[],[]]],[],[]] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[],[[],[[],[]]],[[]]] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[],[[],[[],[]],[]],[]] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[],[[],[[],[]],[],[]]] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[],[[],[[],[]],[[]]]] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[],[[],[[],[],[]]],[]] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[],[[],[[],[],[]],[]]] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[],[[],[[],[],[],[]]]] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[],[[],[[],[],[[]]]]] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[],[[],[[],[[]]]],[]] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[],[[],[[],[[]]],[]]] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[],[[],[[],[[]],[]]]] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[],[[],[[],[]]]]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[],[[],[[],[[[]]]]]] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[],[[],[[[]]]],[],[]] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[],[[],[[[]]]],[[]]] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[],[[],[[[]]],[]],[]] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[],[[],[[[]]],[],[]]] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[],[[],[[[]]],[[]]]] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[],[[],[[[]],[]]],[]] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[],[[],[[[]],[]],[]]] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[],[[],[[[]],[],[]]]] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[],[[],[[[]],[[]]]]] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[],[[],[[[],[]]]],[]] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[],[[],[[[],[]]],[]]] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[],[[],[[[],[]],[]]]] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[],[[],[[[],[],[]]]]] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[],[[],[[[],[[]]]]]] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[],[[],[[[[]]]]],[]] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[],[[],[[[[]]]],[]]] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[],[[],[[[[]]],[]]]] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[],[[],[[[[]],[]]]]] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[],[[],[[[[],[]]]]]] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[],[[],[[[[[]]]]]]] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[],[[[]]],[],[],[[]]] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[],[[[]]],[],[[],[]]] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[],[[[]]],[],[[[]]]] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[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] => [[],[[[]]],[[],[]],[]] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[],[[[]]],[[],[],[]]] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[],[[[]]],[[],[[]]]] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[],[[[]]],[[[]],[]]] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[],[[[]]],[[[],[]]]] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[],[[[]]],[[[[]]]]] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[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] => [[],[[[]],[],[[]],[]]] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[],[[[]],[],[[],[]]]] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[],[[[]],[],[[[]]]]] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[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] => [[],[[[]],[[[],[]]]]] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[],[[[]],[[[[]]]]]] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[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] => [[],[[[],[]]],[[]],[]] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[],[[[],[]]],[[],[]]] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[],[[[],[]]],[[[]]]] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[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] => [[],[[[],[],[]]],[[]]] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]]
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[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[],[[[[]],[],[[]]]]] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[],[[[[]],[[]]]],[]] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
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[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[],[[[[]],[[],[]]]]] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
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[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]],[],[[]]] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[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] => [[[],[]],[],[[],[]],[]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[],[]],[],[[],[],[]]] => [[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[],[]],[],[[],[[]]]] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[],[]],[],[[[]]],[]] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[],[]],[],[[[]],[]]] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[],[]],[],[[[],[]]]] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[],[]],[],[[[[]]]]] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[],[]],[[]],[],[],[]] => [[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[],[]],[[]],[],[[]]] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[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] => [[[],[]],[[]],[[],[]]] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[],[]],[[]],[[[]]]] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[],[]],[[],[]],[],[]] => [[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[],[]],[[]]] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[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] => [[[],[]],[[[[],[]]]]] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[],[]],[[[[[]]]]]] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[],[],[]],[],[],[],[]] => [[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[],[],[]],[],[],[[]]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]]
[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] => [[[[],[],[],[]],[]],[]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.]
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[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [[[[],[],[[]],[[]]]]] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
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[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[],[[]]],[[[]]]]] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
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[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[],[[]],[]]],[[]]] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
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[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[],[[]],[],[[]]]]] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[],[[]],[[]]]],[]] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[],[[]],[[]]],[]]] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[[]],[]]]] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
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[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[],[[]],[[[]]]]]] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
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[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] => [[[[[],[],[[]],[]]]]] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
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[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[[]],[]]]]],[]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [[[[[[[]],[]]]],[]]] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[[[[[[]],[]]],[]]]] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[[[[[[]],[]],[]]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[[[[[[]],[],[]]]]]] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [[[[[[[]],[[]]]]]]] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[[],[]]]]]],[]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [[[[[[[],[]]]]],[]]] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [[[[[[[],[]]]],[]]]] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [[[[[[[],[]]],[]]]]] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[[],[]],[]]]]]] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[[],[],[]]]]]]] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[[],[[]]]]]]]] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[[[[[[[]]]]]],[]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[[[[[[]]]]],[]]]] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[[[[[]]]],[]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[[[[[[[]]],[]]]]]] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[[[[[[[]],[]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[[[[[[],[]]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[[]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[] => [] => .
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[],[[],[[],[[],[]]]]]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[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] => [[[[[[],[]],[]],[]],[]],[[],[]]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
searching the database
Sorry, this map was not found in the database.