Identifier
Mp00026:
Dyck paths
—to ordered tree⟶
Ordered trees
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00050: Ordered trees —to binary tree: right brother = right 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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[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => [.,[.,[[[.,.],.],[[.,.],.]]]]
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[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => [.,[[[.,[[[.,.],.],.]],.],.]]
[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] => [[[[[],[]]]],[[]]] => [[[[.,[.,.]],.],.],[[.,.],.]]
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[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[],[[],[[],[]]],[[]]] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
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[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] => [[],[[],[[],[],[[]]]]] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
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[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[],[[],[[],[[[]]]]]] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]]
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[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[],[[],[[[]]],[]],[]] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
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[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[],[[],[[[]]],[[]]]] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]]
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[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[],[[],[[[],[[]]]]]] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]]
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[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[],[[[]]],[[[],[]]]] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]]
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[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[],[[[],[]],[],[]],[]] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
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[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] => [[],[[[],[]],[[],[]]]] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
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[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[],[[[],[],[]],[]],[]] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[],[[[],[],[]],[],[]]] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[],[[[],[],[]],[[]]]] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[],[[[],[],[],[]]],[]] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[],[[[],[],[],[]],[]]] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[],[]]]] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[],[[[],[],[],[[]]]]] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[],[[[],[],[[]]]],[]] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[],[[[],[],[[]]],[]]] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[],[[[],[],[[]],[]]]] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[],[[],[]]]]] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[],[[[]]]]]] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[],[[[],[[]]]],[],[]] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[],[[[],[[]]]],[[]]] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[],[[[],[[]]],[]],[]] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[],[[[],[[]]],[],[]]] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[],[[[],[[]]],[[]]]] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[],[[[],[[]],[]]],[]] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[],[[[],[[]],[]],[]]] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[],[[[],[[]],[],[]]]] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
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[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[],[[[],[[],[]]]],[]] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[],[[[],[[],[]]],[]]] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[],[[[],[[],[]],[]]]] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[],[[[],[[],[],[]]]]] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[],[[[],[[],[[]]]]]] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[],[[[],[[[]]]]],[]] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[],[[[],[[[]]]],[]]] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[],[[[],[[[]]],[]]]] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[],[[[],[[[]],[]]]]] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[],[[[],[[[],[]]]]]] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[],[[[],[[[[]]]]]]] => [.,[[[.,[[[[.,.],.],.],.]],.],.]]
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[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[],[[[[]]],[]],[],[]] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[],[[[[]]],[]],[[]]] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[],[[[[]]],[],[]],[]] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[],[[[[]]],[],[],[]]] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[],[[[[]]],[],[[]]]] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[],[[[[]]],[[]]],[]] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[],[[[[]]],[[]],[]]] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[],[[[[]]],[[],[]]]] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[],[[[[]]],[[[]]]]] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[],[[[[]],[]]],[],[]] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[],[[[[]],[]]],[[]]] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[],[[[[]],[]],[]],[]] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[],[[[[]],[]],[],[]]] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[],[[[[]],[]],[[]]]] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[],[[[[]],[],[]]],[]] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[],[[[[]],[],[]],[]]] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[],[[[[]],[],[],[]]]] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[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] => [[],[[[[]],[[]]]],[]] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[],[[[[]],[[]]],[]]] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[],[[[[]],[[]],[]]]] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[],[[[[]],[[],[]]]]] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[],[[[[]],[[[]]]]]] => [.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[],[[[[],[]]]],[],[]] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[],[[[[],[]]]],[[]]] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[],[[[[],[]]],[]],[]] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[],[[[[],[]]],[],[]]] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[],[[[[],[]]],[[]]]] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[],[[[[],[]],[]]],[]] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[],[[[[],[]],[]],[]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[],[[[[],[]],[],[]]]] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[],[[[[],[]],[[]]]]] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[],[[[[],[],[]]]],[]] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[],[[[[],[],[]]],[]]] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[],[[[[],[],[]],[]]]] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[],[]]]]] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[],[[[[],[],[[]]]]]] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[],[[[[],[[]]]]],[]] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[],[[[[],[[]]]],[]]] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[],[[[[],[[]]],[]]]] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[],[[[[],[[]],[]]]]] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[[[],[[],[]]]]]] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[],[[[[[]]]]],[[]]] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[],[[[[[]]]],[]],[]] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[],[[[[[]]]],[],[]]] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[],[[[[[]]]],[[]]]] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[],[[[[[]]],[]]],[]] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[],[[[[[]]],[]],[]]] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[],[[[[[]]],[],[]]]] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[],[[[[[]]],[[]]]]] => [.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[],[[[[[]],[]]]],[]] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[],[[[[[]],[]]],[]]] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[],[[[[[]],[]],[]]]] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[],[[[[[]],[],[]]]]] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[],[[[[[]],[[]]]]]] => [.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[],[[[[[],[]]]]],[]] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[],[[[[[],[]]]],[]]] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[],[[[[[],[]]],[]]]] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[],[[[[[],[]],[]]]]] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[],[[[[[[]]]]],[]]] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[],[[[[[[]]]],[]]]] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => [.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => [.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[],[[[[[[[]]]]]]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
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[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[],[[[]]]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[],[[]],[[]]] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[]],[],[],[[],[]],[]] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[]],[],[],[[],[],[]]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[]],[],[],[[],[[]]]] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[],[[[]]],[]] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
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[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] => [[[[],[],[],[]],[]],[]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[[],[],[],[]],[],[]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[[[],[],[],[]],[[]]]] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[],[],[]]],[]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[],[],[]],[]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[],[],[]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[[],[],[],[],[[]]]]] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[[[],[],[],[[]]]],[]] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [[[[],[],[],[[]]],[]]] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [[[[],[],[],[[]],[]]]] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [[[[],[],[],[[],[]]]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[[],[],[],[[[]]]]]] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[],[],[[]]]],[],[]] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[[[],[],[[]]]],[[]]] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[[[],[],[[]]],[]],[]] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [[[[],[],[[]]],[],[]]] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [[[[],[],[[]]],[[]]]] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[[[],[],[[]],[]]],[]] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [[[[],[],[[]],[]],[]]] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [[[[],[],[[]],[],[]]]] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [[[[],[],[[]],[[]]]]] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[],[[],[]]]],[]] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [[[[],[],[[],[]]],[]]] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [[[[],[],[[],[]],[]]]] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[[[],[],[[],[],[]]]]] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [[[[],[],[[],[[]]]]]] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[],[[[]]]]],[]] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [[[[],[],[[[]]]],[]]] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [[[[],[],[[[]]],[]]]] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [[[[],[],[[[]],[]]]]] => [[[.,[.,[[[.,.],[.,.]],.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [[[[],[],[[[],[]]]]]] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [[[[],[],[[[[]]]]]]] => [[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[],[[]]]],[],[],[]] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[],[[]]]],[],[[]]] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[],[[]]]],[[]],[]] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[],[[]]]],[[],[]]] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[],[[]]]],[[[]]]] => [[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[],[[]]],[]],[],[]] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[],[[]]],[]],[[]]] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[],[[]]],[],[]],[]] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[],[[]]],[],[],[]]] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[],[[]]],[],[[]]]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[],[[]]],[[]]],[]] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[],[[]]],[[]],[]]] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[],[[]]],[[],[]]]] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[],[[]]],[[[]]]]] => [[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[],[[]],[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[],[[]],[]]],[[]]] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[],[[]],[]],[]],[]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[],[[]],[]],[],[]]] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[],[[]],[]],[[]]]] => [[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[],[[]],[],[]]],[]] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[],[[]],[],[]],[]]] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[],[[]],[],[],[]]]] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[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] => [[[[],[[]],[[]],[]]]] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[],[[]],[[],[]]]]] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[],[[]],[[[]]]]]] => [[[.,[[.,.],[[[.,.],.],.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[],[[],[]]]],[],[]] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[],[[],[]]]],[[]]] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[],[[],[]]],[]],[]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[],[[],[]]],[],[]]] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[],[[],[]]],[[]]]] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[],[[],[]],[]]],[]] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[],[[],[]],[]],[]]] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[],[[],[]],[],[]]]] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[],[[],[]],[[]]]]] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[],[[],[],[]]]],[]] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[],[[],[],[]]],[]]] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[],[[],[],[]],[]]]] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[],[[],[],[],[]]]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[[[],[[],[],[[]]]]]] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[],[[],[[]]]]],[]] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[],[[],[[]]]],[]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[],[[],[[]]],[]]]] => [[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[],[[],[[]],[]]]]] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[],[[],[[],[]]]]]] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [[[[],[[],[[[]]]]]]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[],[[[]]]]],[],[]] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[],[[[]]]]],[[]]] => [[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[],[[[]]]],[]],[]] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[],[[[]]]],[],[]]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[],[[[]]]],[[]]]] => [[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[],[[[]]],[]]],[]] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [[[[],[[[]]],[]],[]]] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [[[[],[[[]]],[],[]]]] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [[[[],[[[]]],[[]]]]] => [[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[],[[[]],[]]]],[]] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[],[[[]],[]]],[]]] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[],[[[]],[]],[]]]] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[],[[[]],[],[]]]]] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [[[[],[[[]],[[]]]]]] => [[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[],[[[],[]]]]],[]] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[],[[[],[]]]],[]]] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[],[[[],[]]],[]]]] => [[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[],[[[],[]],[]]]]] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[],[[[],[],[]]]]]] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[],[[[],[[]]]]]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[],[[[[]]]]]],[]] => [[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[],[[[[]]]]],[]]] => [[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [[[[],[[[[]]]],[]]]] => [[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[],[[[[]]],[]]]]] => [[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[],[[[[]],[]]]]]] => [[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[],[[[[],[]]]]]]] => [[[.,[[[[.,[.,.]],.],.],.]],.],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[],[[[[[]]]]]]]] => [[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[],[]] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[[]]]],[],[],[[]]] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[]]]],[],[[]],[]] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[[[]]]],[],[[],[]]] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[[]]]],[],[[[]]]] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[[]]]],[[]],[],[]] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[[]]]],[[]],[[]]] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[[[]]]],[[],[]],[]] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[[[[]]]],[[],[],[]]] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [[[[[]]]],[[],[[]]]] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[[]]]],[[[]]],[]] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [[[[[]]]],[[[]],[]]] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
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[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] => [[[[[]]],[]],[],[[]]] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
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[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] => [[[[[]]],[],[]],[],[]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
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[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[[[[]]],[],[],[]],[]] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
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[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [[[[[]]],[],[[[]]]]] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
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[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [[[[[]]],[[],[[]]]]] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
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[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [[[[[]]],[[[]],[]]]] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
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[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] => [[[[[]],[]],[]],[],[]] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
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[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] => [[[[[]],[]],[[[]]]]] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
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[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] => [[[[[]],[],[]],[]],[]] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
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[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [[[[[]],[],[]],[[]]]] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
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[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] => [[[[[]],[],[],[[]]]]] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
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[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] => [[[[[]],[[]]]],[[]]] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
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[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [[[[[]],[[]]],[[]]]] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
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[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[[]],[]],[]]] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[[]],[],[]]]] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[[[]],[[]],[[]]]]] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[[[[]],[[],[]]]],[]] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[[[]],[[],[]]],[]]] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [[[[[]],[[],[]],[]]]] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[[[[]],[[],[],[]]]]] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [[[[[]],[[],[[]]]]]] => [[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [[[[[]],[[[]]]]],[]] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [[[[[]],[[[]]]],[]]] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [[[[[]],[[[]]],[]]]] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [[[[[]],[[[]],[]]]]] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [[[[[]],[[[],[]]]]]] => [[[[.,.],[[[.,[.,.]],.],.]],.],.]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [[[[[]],[[[[]]]]]]] => [[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[[],[]]]],[],[],[]] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[[],[]]]],[],[[]]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[[[],[]]]],[[]],[]] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[[[],[]]]],[[],[]]] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[[],[]]]],[[[]]]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[[[],[]]],[]],[],[]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[[[[],[]]],[]],[[]]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[[[[],[]]],[],[]],[]] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[[],[]]],[],[],[]]] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [[[[[],[]]],[],[[]]]] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[[[[],[]]],[[]]],[]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [[[[[],[]]],[[]],[]]] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[[[[],[]]],[[],[]]]] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [[[[[],[]]],[[[]]]]] => [[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[[[],[]],[]]],[],[]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[[[[],[]],[]]],[[]]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[],[]],[]],[]],[]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [[[[[],[]],[]],[],[]]] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[[],[]],[]],[[]]]] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[[[[],[]],[],[]]],[]] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [[[[[],[]],[],[]],[]]] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[[],[]],[],[],[]]]] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [[[[[],[]],[],[[]]]]] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [[[[[],[]],[[]]]],[]] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [[[[[],[]],[[]]],[]]] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [[[[[],[]],[[]],[]]]] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[[[[],[]],[[],[]]]]] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [[[[[],[]],[[[]]]]]] => [[[[.,[.,.]],[[[.,.],.],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[[[],[],[]]]],[],[]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[[[[],[],[]]]],[[]]] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[[[[],[],[]]],[]],[]] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[[],[],[]]],[],[]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[[[[],[],[]]],[[]]]] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[],[]],[]]],[]] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [[[[[],[],[]],[]],[]]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[[],[],[]],[],[]]]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[[],[],[]],[[]]]]] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[],[]]]],[]] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[[],[],[],[]]],[]]] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[],[],[],[]],[]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[],[],[],[],[]]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[[],[],[],[[]]]]]] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[[[[],[],[[]]]]],[]] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [[[[[],[],[[]]]],[]]] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[[[[],[],[[]]],[]]]] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [[[[[],[],[[]],[]]]]] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [[[[[],[],[[],[]]]]]] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [[[[[],[],[[[]]]]]]] => [[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[[[],[[]]]]],[],[]] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[[[[],[[]]]]],[[]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[[[[],[[]]]],[]],[]] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [[[[[],[[]]]],[],[]]] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [[[[[],[[]]]],[[]]]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[[[[],[[]]],[]]],[]] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [[[[[],[[]]],[]],[]]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [[[[[],[[]]],[],[]]]] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [[[[[],[[]]],[[]]]]] => [[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[[[[],[[]],[]]]],[]] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [[[[[],[[]],[]]],[]]] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [[[[[],[[]],[]],[]]]] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [[[[[],[[]],[],[]]]]] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [[[[[],[[]],[[]]]]]] => [[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[[[],[[],[]]]]],[]] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[[[],[[],[]]]],[]]] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [[[[[],[[],[]]],[]]]] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [[[[[],[[],[]],[]]]]] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [[[[[],[[],[],[]]]]]] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[[[[],[[],[[]]]]]]] => [[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[[],[[[]]]]]],[]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [[[[[],[[[]]]]],[]]] => [[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [[[[[],[[[]]]],[]]]] => [[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [[[[[],[[[]]],[]]]]] => [[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [[[[[],[[[]],[]]]]]] => [[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [[[[[],[[[],[]]]]]]] => [[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[[[[],[[[[]]]]]]]] => [[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[]]]]],[],[],[]] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[[[]]]]],[],[[]]] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[[[]]]]],[[]],[]] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[[[[[]]]]],[[],[]]] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[]]]]],[[[]]]] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[[[[]]]],[]],[],[]] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[[[[[]]]],[]],[[]]] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[[[[[]]]],[],[]],[]] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [[[[[[]]]],[],[],[]]] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [[[[[[]]]],[],[[]]]] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [[[[[[]]]],[[]]],[]] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [[[[[[]]]],[[]],[]]] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [[[[[[]]]],[[],[]]]] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [[[[[[]]]],[[[]]]]] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[[[[]]],[]]],[],[]] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [[[[[[]]],[]]],[[]]] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[[[[]]],[]],[]],[]] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [[[[[[]]],[]],[],[]]] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [[[[[[]]],[]],[[]]]] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[[[[[]]],[],[]]],[]] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [[[[[[]]],[],[]],[]]] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [[[[[[]]],[],[],[]]]] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [[[[[[]]],[],[[]]]]] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[[[[[]]],[[]]]],[]] => [[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [[[[[[]]],[[]]],[]]] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [[[[[[]]],[[]],[]]]] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [[[[[[]]],[[],[]]]]] => [[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [[[[[[]]],[[[]]]]]] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[[[[]],[]]]],[],[]] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[[[[[]],[]]]],[[]]] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[[[[]],[]]],[]],[]] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [[[[[[]],[]]],[],[]]] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [[[[[[]],[]]],[[]]]] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[[[[]],[]],[]]],[]] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[]],[]],[]],[]]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [[[[[[]],[]],[],[]]]] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [[[[[[]],[]],[[]]]]] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[[[[[]],[],[]]]],[]] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [[[[[[]],[],[]]],[]]] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [[[[[[]],[],[]],[]]]] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[[[[[]],[],[],[]]]]] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[[[[[]],[],[[]]]]]] => [[[[[.,.],[.,[[.,.],.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[[[[[]],[[]]]]],[]] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [[[[[[]],[[]]]],[]]] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [[[[[[]],[[]]],[]]]] => [[[[[.,.],[[.,.],.]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [[[[[[]],[[]],[]]]]] => [[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [[[[[[]],[[],[]]]]]] => [[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [[[[[[]],[[[]]]]]]] => [[[[[.,.],[[[.,.],.],.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [[[[[[],[]]]]],[],[]] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[[[[[],[]]]]],[[]]] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[[[[[],[]]]],[]],[]] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[[[[[],[]]]],[],[]]] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [[[[[[],[]]]],[[]]]] => [[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[[[[[],[]]],[]]],[]] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[[[[[],[]]],[]],[]]] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [[[[[[],[]]],[],[]]]] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [[[[[[],[]]],[[]]]]] => [[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [[[[[[],[]],[]]]],[]] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[[[[],[]],[]]],[]]] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [[[[[[],[]],[]],[]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [[[[[[],[]],[],[]]]]] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [[[[[[],[]],[[]]]]]] => [[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[[[[[],[],[]]]],[]]] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [[[[[[],[],[]]],[]]]] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [[[[[[],[],[]],[]]]]] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[[],[],[],[]]]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[[],[],[[]]]]]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[[],[[]]]]]],[]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [[[[[[],[[]]]]],[]]] => [[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [[[[[[],[[]]]],[]]]] => [[[[[.,[[.,.],.]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[[[[[],[[]]],[]]]]] => [[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[[[[[],[[]],[]]]]]] => [[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[[[[],[[],[]]]]]]] => [[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[[[[[],[[[]]]]]]]] => [[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[[[[]]]]]],[],[]] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[[]]]]]],[[]]] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[[[[[[]]]]],[]],[]] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [[[[[[[]]]]],[],[]]] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [[[[[[[]]]]],[[]]]] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[[[[[[]]]],[]]],[]] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [[[[[[[]]]],[]],[]]] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [[[[[[[]]]],[],[]]]] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [[[[[[[]]]],[[]]]]] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[[]]],[]]]],[]] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [[[[[[[]]],[]]],[]]] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [[[[[[[]]],[]],[]]]] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [[[[[[[]]],[],[]]]]] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [[[[[[[]]],[[]]]]]] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[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: right brother = right child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.
searching the database
Sorry, this map was not found in the database.