Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ 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 3610 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] => [[[.,.],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],.]
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[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
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[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [[.,[[.,[.,.]],[[.,.],.]]],.]
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[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => [[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => [[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => [[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => [[[.,.],[[[.,[.,.]],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[[[[.,.],.],.],.]],.] => [[[.,.],[[[[.,.],.],.],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => [[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,.],.],[[[.,.],.],.]],.] => [[[[.,.],[[[.,.],.],.]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[.,.],[[[.,.],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[[[.,[[[.,.],.],.]],.],.],.] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => [[[[[.,[[.,.],.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[.,.],.],.],[[.,.],.]],.] => [[[[[.,.],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[[[[.,.],.],[[.,.],.]],.],.] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[[[[.,.],[[.,.],.]],.],.],.] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],.] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[[[[.,.],.],.],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[[[.,.],.],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[[[.,.],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
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[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [[.,[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [[.,[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[.,[[[.,.],[[[.,.],.],.]],.]],.] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[.,[[[[.,.],.],[[.,.],.]],.]],.] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [[[.,[.,[[[.,.],[.,.]],.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [[[.,[[.,.],[.,[[.,.],.]]]],.],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [[[.,[[.,.],[[[.,.],.],.]]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [[[.,[[[[.,[.,.]],.],.],.]],.],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [[[.,.],[[[.,[[.,.],.]],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [[[.,.],[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[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] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [[[[.,[.,.]],[[[.,.],.],.]],.],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [[[[.,.],[[[.,[.,.]],.],.]],.],.]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[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] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[.,[[[.,.],.],.]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [.,[[[[[[[.,.],.],[.,.]],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[.,[[[.,.],.],.]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[.,[[[.,.],.],.]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],[[.,.],.]],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],[[.,.],.]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [.,[[[[[[[.,.],.],.],[.,.]],.],.],.]] => [.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [.,[[[[[[.,[.,.]],[.,.]],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],[[.,.],.]],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[.,[[[[.,.],.],.],.]],.],.],.]] => [.,[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]] => [[[[[[[.,[.,.]],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[.,[[.,.],[.,.]]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [.,[[[[[[[.,.],.],.],.],[.,.]],.],.]] => [.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => [.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]] => [.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[[[[[.,[[.,.],[.,.]]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[.,[[[[[.,.],.],.],.],.]],.],.]] => [.,[[[.,.],.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]] => [[[[[[[[.,[.,.]],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],[.,.]] => [[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[.,[[[[[.,.],.],.],.],.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [[[[[[.,.],.],[[.,.],.]],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [.,[[[[[[.,.],.],[[.,.],.]],.],.],.]] => [.,[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]] => [.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]]
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[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
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[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [[.,[[[[.,.],.],[.,[.,[.,.]]]],.]],.] => [[.,.],[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[.,[[[[.,[[[.,.],.],.]],.],.],.]],.] => [[.,.],[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[.,[[[[[.,[.,[.,.]]],.],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,[[[[[.,[[.,.],.]],.],.],.],.]],.] => [[.,.],[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[.,[[[[[[.,.],.],[.,.]],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],[.,.]],.],.]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,[[[[[[.,.],[.,.]],.],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,[[[[[.,.],.],.],.],.]]],.] => [[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.] => [[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],.] => [[[.,.],[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.] => [[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.] => [[[.,.],[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.] => [[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[.,.],[[[[[.,[.,.]],.],.],.],.]],.] => [[[.,.],[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[.,[.,.]],[[[[[.,.],.],.],.],.]],.] => [[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,[.,[.,.]]]],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.],.] => [[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[.,[.,[[[.,.],.],.]]]]],.],.] => [[[.,.],.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.],.] => [[[.,.],.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[.,[.,[[[.,.],.],.]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [[[.,[.,[[[.,.],.],.]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => [[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]],.] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [[[.,.],.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [[[.,[[[.,.],.],[[[.,.],.],.]]],.],.] => [[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,[.,[.,.]]]],.],.]],.],.] => [[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[[.,[[[[[.,.],.],.],.],.]],[.,.]],.] => [[[.,.],[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],[[.,.],[[.,.],[.,.]]]],.] => [[[[.,.],[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[[[.,.],.],[[[[.,[.,.]],.],.],.]],.] => [[[[.,.],[[[[.,.],.],.],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],[[[[[.,.],.],.],.],.]],.] => [[[[.,.],[[[[[.,.],.],.],.],.]],.],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.] => [[[[.,.],[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[.,.],[.,.]],[[[[.,.],.],.],.]],.] => [[[[.,.],[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,[.,[.,.]]]],.]],.],.] => [[[[.,.],.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,.],[[[[[.,.],.],.],.],.]],.],.] => [[[[.,.],.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]],.] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.],.] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]],.] => [[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,[.,[.,.]]],.],[[[.,.],.],.]],.] => [[[[.,.],[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [[[[.,[.,[.,.]]],[[[.,.],.],.]],.],.] => [[[[.,.],.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0] => [[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.] => [[[[.,.],.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => [[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [[[[.,[[.,[.,[.,.]]],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[[.,[[.,[[.,[.,.]],.]],.]],.],.],.] => [[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [[[[.,[[[.,.],.],[[.,.],.]]],.],.],.] => [[[[.,.],.],.],[[[.,[[.,.],.]],.],.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[[[.,[[[.,.],[.,.]],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[[.,[[[[.,.],.],.],.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[.,[[[[[.,.],.],.],.],.]],.],.],.] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0] => [[[[[.,.],.],.],[[[.,[.,.]],.],.]],.] => [[[[[.,.],[[[.,.],.],[.,.]]],.],.],.]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],[[[[.,.],.],.],.]],.] => [[[[[.,.],[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0] => [[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.] => [[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0] => [[[[[.,.],[.,.]],.],[[[.,.],.],.]],.] => [[[[[.,.],[[[.,.],.],.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.] => [[[[[.,.],.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [[[[[.,.],[[.,.],[[.,.],.]]],.],.],.] => [[[[[.,.],.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [[[[[.,.],[[[.,.],.],[.,.]]],.],.],.] => [[[[[.,.],.],.],[[[.,[.,.]],.],.]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0] => [[[[[.,[.,.]],.],.],[.,[.,[.,.]]]],.] => [[[[[.,.],[.,[.,[.,.]]]],.],.],[.,.]]
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[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
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[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]
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[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],.],[[[[.,.],.],.],.]] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[[[.,.],.],.]] => [[[[[.,[[[.,.],.],.]],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]],.] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]],.] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]] => [.,[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,.]]],[[[[.,[.,.]],.],.],.]] => [[.,[[[[.,.],.],.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [[.,.],[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]] => [[.,[[[[.,.],.],.],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.] => [[.,.],[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,[.,[.,.]]]],.],.],.]] => [[.,[[[[.,.],.],.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => [[.,.],[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => [[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[.,[[[[.,.],.],.],.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [[[.,[[[.,.],.],[[[.,.],.],.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[.,[[.,.],.]],.],.],[[[.,.],.],.]] => [[[[.,[[[.,.],.],.]],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]] => [.,[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],[[.,.],.]] => [[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,.],[[[[[[.,.],.],.],[.,.]],.],.]] => [[.,[[[[[[.,.],.],[.,.]],.],.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [[[[[.,.],.],[.,.]],.],[[[.,.],.],.]] => [[[[[.,[[[.,.],.],.]],.],[.,.]],.],.]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],.],[[[[[.,.],[.,.]],.],.],.]] => [[[.,[[[[[.,.],.],.],[.,.]],.]],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]] => [.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]] => [.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]],.] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]],.] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]],.] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]],.] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]] => [[.,[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],[.,.]],.]]],[.,.]] => [[.,[.,.]],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]] => [.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.] => [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.] => [[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.] => [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]],.] => [[.,.],[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]],.] => [[.,.],[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]],.] => [[.,.],[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]],.] => [[.,.],[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]],.] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]],.] => [[.,.],[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]],.] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]],.] => [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],.],[[[.,.],.],.]],.],.],.],.] => [[[[[[[.,.],.],.],.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.] => [[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.] => [[[[[[.,.],.],[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.] => [[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]
[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] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => [[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]],.] => [[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.] => [[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]],.] => [[[[[[[.,.],[.,.]],.],.],.],.],[[.,.],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]],.] => [[.,.],[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]],.] => [[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]] => [[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,[.,[.,.]]]],.]] => [[[[.,[[.,.],[.,[.,[.,.]]]]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,[.,[.,.]]],.]] => [[[[.,[[.,.],[.,[.,.]]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],.],[[.,[.,.]],.]] => [[[[.,[[.,.],[.,.]]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.] => [[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.] => [[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,.],[[[[[.,.],.],.],.],.]],.]] => [.,[[[.,.],[[[[[.,.],.],.],.],.]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[.,[[.,.],.]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.] => [[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],[.,.]] => [[.,[.,.]],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]] => [[.,[[.,[[.,[.,.]],[[.,.],.]]],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.] => [[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[[[.,.],.],.],[[[[[.,.],.],.],.],.]],.] => [[[[[.,.],[[[[[.,.],.],.],.],.]],.],.],.]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.] => [[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],[.,.]] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [[[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.],.] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,[.,.]]]]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]] => [[[[[.,[.,[.,.]]],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]] => [.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]] => [[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]] => [[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],.]]]] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.],.],.] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [[[[[[.,[.,[.,[.,.]]]],.],[.,.]],.],.],.] => [[[[[[.,.],.],.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[[.,.],.]],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],[[.,.],.]],.]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],.],[[[[[.,.],.],.],[.,.]],.]] => [[[.,[[[[[.,.],[.,.]],.],.],.]],.],.]
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[.,[[[[[.,.],.],.],.],.]]],.]] => [.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]] => [[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]] => [[[[[[.,[.,[.,.]]],.],.],[.,.]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[.,[.,.]],.],.],.],[[[[.,.],.],.],.]] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[[.,.],[.,.]],.],.],[[[.,.],.],.]] => [[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,[.,[.,.]]]]]] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,[.,.]]]]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [[[[[.,.],.],.],[[[.,.],.],.]],[.,.]] => [[[[[.,[.,.]],[[[.,.],.],.]],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [.,[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[[.,.],.],[[[[[.,.],.],[.,.]],.],.]] => [[[.,[[[[[.,.],.],[.,.]],.],.]],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[[.,.],.]]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[[.,.],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],[.,.]] => [[[.,[.,.]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,.]] => [[[.,[.,.]],[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[[.,.],.]],[[.,[[.,.],.]],.]] => [[[.,[[.,.],[[.,.],.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,[[.,.],.]],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],[[.,.],.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],.]],[[.,.],[[.,.],[.,.]]]] => [[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => [.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],[.,.]] => [[.,[.,.]],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],[.,.]],.]]],[.,.]] => [[.,[.,.]],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],[.,.]] => [[.,[.,.]],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],[.,.]] => [[.,[.,.]],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[.,[.,[[.,[[[.,.],.],.]],.]]]] => [[.,[.,[.,[[.,.],[[[.,.],.],.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],[.,.]]]] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,[.,.]]] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [[[[[[.,.],.],.],.],[[.,.],.]],[.,.]] => [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]] => [.,[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]] => [.,[.,[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[.,[[[.,.],.],.]],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[[[[[.,.],.],.],.],.]],[.,.]] => [[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]] => [.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[.,.],[[[.,.],[[.,.],[.,.]]],.]]] => [.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]] => [.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]] => [[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]] => [[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]] => [.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]] => [[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]] => [.,[[[.,.],[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]] => [[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]] => [.,[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]] => [.,[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[.,.]]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]]] => [.,[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,.],[[.,[[.,.],.]],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]] => [.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[.,[[.,[.,.]],.]]] => [[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]] => [.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]] => [.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]] => [.,[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]] => [.,[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]] => [.,[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]] => [.,[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.] => [[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],.] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[[[[.,.],.],.],.],[.,.]]],.]] => [.,[[.,.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],[[[[.,.],.],.],.]] => [[[.,[[[[.,.],.],.],.]],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[[.,.],.]],[[[[[.,.],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]] => [[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[.,[[[.,.],[[.,.],[[.,.],.]]],.]]] => [.,[.,[[[.,.],[[.,[[.,.],.]],.]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,[.,[.,.]]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]] => [.,[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]]] => [.,[.,[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]] => [.,[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]] => [.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]] => [[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]] => [[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]] => [[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]] => [[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]] => [[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]] => [[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.] => [[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],.] => [[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],.] => [[[[.,.],[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.] => [[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]] => [[.,[[[[.,.],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]] => [[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.] => [[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]] => [[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]] => [[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]] => [[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.] => [[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.] => [[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]] => [[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.] => [[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]] => [[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],.]]]] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]] => [[.,[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[[.,.],.]]] => [[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]] => [[.,[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]] => [[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]] => [[.,[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]] => [[.,[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]] => [[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],.]] => [[[[.,[[.,.],.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],.]] => [[[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[[.,.],.]] => [[[[.,[[.,.],.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],.]] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],.]]] => [[.,[[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]] => [[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]] => [[.,[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[[.,.],.]] => [[[.,[[.,.],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]] => [[.,[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]] => [[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],.]]] => [[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]] => [[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[[[.,[[.,.],.]],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]]] => [[.,[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],.]] => [[[.,[[.,.],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],.]] => [[[[.,[[.,.],.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],.]] => [[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]] => [[.,[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]] => [[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[[.,.],.]] => [[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]] => [[.,[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]] => [[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]] => [[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]] => [[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[[.,.],[.,.]],[.,.]],.]] => [[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]] => [[.,[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],.]] => [[[.,[[[[.,.],[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.]] => [[.,[[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.] => [[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],.] => [[[[.,.],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]],.] => [[[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]] => [[.,[[.,[[[.,.],[[[.,[.,.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]] => [[[.,[[[.,.],[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],.] => [[[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]] => [[.,[[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],.] => [[[.,.],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],.]] => [[.,[[[[.,.],[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],.] => [[[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.]] => [[.,[[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.] => [[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]] => [[.,[[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],.] => [[[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]] => [[.,[[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]],.] => [[[.,.],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]],.] => [[[[.,.],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]],.] => [[[[.,.],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]],.] => [[[[[.,.],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],.] => [[[[[.,.],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],.] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]],.] => [[[[.,.],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],.] => [[[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]] => [[.,[[.,[[[[.,.],[.,.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]] => [[[.,[[[[.,.],[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]],.] => [[[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]] => [[.,[[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],.] => [[[.,.],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],.] => [[[[.,.],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]] => [[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]] => [[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],.] => [[[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.] => [[[.,.],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]] => [[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]] => [[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[[[.,.],[.,.]],.]]] => [[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]] => [[.,[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,[[[.,.],[.,.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]] => [[.,[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],[[[.,.],[.,.]],.]] => [[[[.,[[[.,.],[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[[.,.],[.,.]],.]] => [[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]] => [[.,[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]] => [[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],.]] => [[[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],.]]] => [[.,[[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],[[[.,.],[.,.]],.]] => [[[.,[[[.,.],[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]] => [[.,[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]] => [[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.] => [[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]] => [[.,[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],.] => [[[.,.],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.] => [[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],.] => [[[[.,.],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],.] => [[[[[.,.],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.]] => [[.,[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],.] => [[[.,.],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],.] => [[[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]] => [[.,[[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.] => [[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]] => [[.,[[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]] => [[[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[[.,.],[.,.]]],.]] => [[[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]] => [[.,[[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[[.,.],[[.,.],[.,.]]],.]] => [[[.,[[[.,.],[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],.] => [[[.,.],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],.] => [[[[.,.],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],.] => [[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]] => [[.,[[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]] => [[[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]] => [[.,[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.] => [[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],[.,.]]] => [[.,[[[.,[.,.]],.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]] => [[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.],.] => [[[[.,.],.],[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]] => [[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,.]],[[[[[.,.],.],.],.],[.,.]]] => [[.,[[[[[.,[.,.]],.],.],.],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],.],.],[[.,.],[.,.]]] => [[[[[.,[[.,[.,.]],.]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],[.,.]]] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [[[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,.]],[[[[.,.],.],.],[.,.]]] => [[[.,[[[[.,[.,.]],.],.],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]] => [[[[.,[[[.,[.,.]],.],.]],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],[.,.]]] => [[[[[[.,[[.,[.,.]],.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [.,[[[[.,[[.,[.,.]],.]],.],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]]] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]] => [.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[.,[[[.,[[.,.],[.,.]]],.],.]]]] => [.,[[.,[.,[[[.,.],.],[[.,[.,.]],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => [.,[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => [.,[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => [.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]],.]] => [.,[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]] => [.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]] => [.,[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[.,[[.,.],[.,[[[.,[[.,.],[.,.]]],.],.]]]],.]] => [.,[[.,.],[[.,[.,[[[.,.],.],[[.,[.,.]],.]]]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => [.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]] => [.,[[.,.],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]] => [.,[[.,.],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]]] => [.,[[.,[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]] => [.,[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]] => [.,[[.,.],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]] => [.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]] => [.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => [[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,.],[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],[.,.]]] => [[[.,[[.,[.,.]],[[.,.],.]]],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[[[[.,.],.],.],.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]],.] => [[[[[.,.],[[[[.,.],.],.],.]],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]] => [[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],.] => [[[.,.],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => [.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]] => [.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => [[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]] => [[[.,[[[.,.],[[.,.],.]],.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]] => [.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],.],[.,.]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [.,[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[.,.]],[[[.,.],[[.,[.,.]],.]],[.,.]]] => [[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [.,[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,.]]] => [.,[[[[.,[.,.]],[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [.,[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]] => [.,[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [[[[[.,[.,.]],[[.,.],.]],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]],.] => [[[[[.,.],[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,[.,.]],[.,.]]] => [[[[[.,[[.,[.,.]],[.,.]]],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]],.] => [[[[.,.],[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,.]],[[[.,.],[[.,[.,.]],.]],[.,.]]] => [[[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[[[.,.],[[.,[.,.]],.]],[.,.]]] => [[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]],.] => [[[.,.],[[[[.,.],.],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.] => [[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.] => [[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.] => [[[.,.],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.] => [[[[.,.],[.,[[.,.],.]]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],.]],.]]],.] => [[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],[.,.]],.]]],.] => [[[.,.],[.,[[[.,.],[.,.]],[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,[[.,.],.]],.]]],.] => [[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.] => [[[.,.],[.,[[[.,.],[.,.]],.]]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]] => [.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]] => [[.,[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]] => [.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [.,[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],[.,.]] => [[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]],.] => [[[[.,.],[[[.,[[[.,.],.],.]],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],[.,[.,.]]] => [[[[[[.,[.,[.,.]]],.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],[.,[.,.]]]] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.],.] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.],.] => [[[[[[[.,.],.],.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]] => [[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]] => [[.,[[.,[.,.]],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],.]]] => [[[.,[[.,[[[.,.],.],[.,.]]],.]],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.],.] => [[[[[.,.],.],.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.],.] => [[[[[.,.],.],.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,[.,[.,.]]]],.]] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]] => [.,[[.,.],[[[.,.],[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,[.,.]],.],.]]] => [[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]] => [.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]],.] => [[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[[.,[.,[.,.]]],[[.,.],[[.,.],.]]],.],.] => [[[[.,.],.],[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0] => [[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],.],.] => [[[[[[.,.],.],[.,.]],[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0] => [[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],[.,.]],.] => [[[[.,.],[.,.]],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]] => [[.,[[.,.],.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,[.,.]]],[.,.]] => [[[[[.,[.,.]],[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]] => [[[[[.,[.,[.,.]]],[.,.]],[.,.]],.],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[[[[[.,.],[.,.]],[.,.]],.],[.,.]],[.,.]] => [[[[[[.,[.,.]],[.,.]],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,.],.]] => [[[[[.,[[.,.],.]],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[[[[[.,.],[.,.]],[.,.]],[.,[.,.]]],[.,.]],[.,.]] => [[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]]] => [.,[.,[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],.] => [[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.] => [[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[[.,.],[.,.]]] => [[[[[.,[[.,[.,.]],.]],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]] => [[[[.,[[.,[.,.]],.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],[.,.]],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]] => [.,[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]] => [[.,[[.,[[[[.,.],[[.,.],.]],.],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],[[.,.],.]]] => [[[[.,[[.,[[.,.],.]],.]],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[[.,.],.],[[.,.],.]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],[.,.]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [.,[.,[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]] => [.,[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [.,[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]] => [.,[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[[[.,.],[.,.]],.],[[.,.],[[.,.],[.,.]]]]]] => [.,[.,[[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,[.,.]],.]]] => [[.,[[.,[[.,.],[.,.]]],.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,.],[[[.,.],.],.]],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]] => [.,[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]] => [.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]] => [.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]] => [.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,[.,.]],.]]]] => [[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]] => [[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,.]]],.] => [[[[.,.],[[.,[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,.],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]] => [.,[[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]] => [.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]] => [.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]] => [.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,.]],.]]] => [.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]] => [.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]]] => [.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]] => [.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,[.,.]],.]]] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]] => [.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => [.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[[.,[.,.]],.]]] => [.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]] => [.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]] => [[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]] => [[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]] => [[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]] => [[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]] => [[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]] => [[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => [[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]] => [[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[[.,.],[[.,[.,.]],.]]]] => [[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[[[.,[.,.]],[.,.]],.]]] => [[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]],.] => [[.,.],[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]],.] => [[.,.],[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]],.] => [[.,.],[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]],.] => [[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],[.,.]]],.] => [[[.,.],[[[.,[.,.]],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],[.,.]]],.] => [[[[.,.],[[.,[.,.]],[[.,.],[.,.]]]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],[.,.]]],.] => [[[[.,.],[[[.,[.,.]],[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],[.,.]]],.] => [[[.,.],[[.,[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],[.,.]]],.] => [[[[.,.],[[.,[.,.]],[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],[.,.]]],.] => [[[[.,.],[[.,[.,.]],[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],[.,.]]],.] => [[[[[.,.],[[.,[.,.]],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0] => [[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0] => [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0] => [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0] => [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0] => [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,[.,.]]],.] => [[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,.]]],.] => [[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]] => [.,[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
searching the database
Sorry, this map was not found in the database.