Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00016: Binary trees —left-right 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 3091 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0] => [[.,[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0] => [[.,[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0] => [[[[.,[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[.,.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[.,.],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[.,.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[.,[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [[[[[.,.],.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],.],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => [[[[.,.],[[.,[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [[[.,[[.,[[.,.],.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [[[.,[[.,[.,[.,.]]],.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [[[.,[.,[[.,[.,.]],.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [[[.,[[.,.],[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [[[.,[.,[.,[[.,.],.]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [[.,[[[.,[.,[.,.]]],.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [[.,[[.,[.,[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [[.,[.,[[[.,.],[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[.,.]]
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[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[.,.]]
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[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],.]],[.,.]]
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[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [.,[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [.,[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,.],.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[.,.],[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[.,.],.]]]]
[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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[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
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[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.]
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[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.]
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[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
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[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
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[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [[[.,.],[.,[[[[.,.],.],.],.]]],.]
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[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.]
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[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
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[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
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[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
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[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
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[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
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[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
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[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
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[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
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[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
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[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]]
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[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],.],[.,.]]
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[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[.,[[[.,.],[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [.,[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[.,[[[[.,.],.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[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] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
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[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
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[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
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[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] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
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[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[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] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
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[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[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] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[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] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]
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[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]
[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] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
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[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] => [[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]
[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] => [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]] => [[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]
[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] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]
[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] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [.,[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => [.,[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]]
[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] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[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] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,.],[[[[[[.,.],.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]] => [[[[[[.,.],[[[.,.],.],.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[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] => [[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[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] => [[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.] => [.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]],.] => [.,[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]],.] => [.,[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]],.] => [.,[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]]
[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] => [[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]],.] => [.,[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]],.] => [.,[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]]
[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] => [[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[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] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]
[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] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]
[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] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]
[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] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]
[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] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[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] => [[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[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] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[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] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]] => [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[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] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[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] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]] => [[[.,[[[[[.,.],.],.],[.,.]],.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]]
[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] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[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] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.]
[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] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => [[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]
[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] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]] => [[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]]
[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] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]] => [[[[.,.],[[.,[.,[.,[.,.]]]],.]],.],.]
[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] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],[.,.]] => [[.,.],[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]]
[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] => [[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [[[[[[.,.],[[.,.],.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]] => [[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]] => [[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]]
[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] => [[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [.,[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]] => [[[[[.,.],.],[[[.,.],.],[.,.]]],.],.]
[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] => [[[[[[.,[.,[.,[.,.]]]],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[.,[[[.,[.,[.,[.,.]]]],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[[[[.,.],.],.],.]]],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]] => [[[[[.,[[[.,.],[.,.]],.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.] => [.,[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[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] => [.,[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[[.,.],[.,.]],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[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] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[[.,[.,.]],.]]]],.],.],.],.] => [.,[.,[.,[.,[[[[.,[[.,.],.]],.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]]
[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] => [[.,.],[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[[.,.],.]],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]] => [[[[.,.],[[[[.,.],.],.],[.,.]]],.],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[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] => [[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],[.,.]] => [[.,.],[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,[.,[.,.]]],.],.]]
[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] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],.]],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]] => [[[[.,.],[[[[[.,.],.],.],.],.]],.],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]] => [[[[.,.],[[[[[.,.],.],.],.],.]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [[[[[[.,.],.],.],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]] => [[[[[[.,.],[[.,.],[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]] => [[[[[.,.],[.,[[.,.],[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]] => [[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[.,.],.],[[[[.,.],.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]]]
[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] => [[[.,.],[[[[[.,.],.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [[[[[[[[.,[.,.]],.],.],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [[[[[[[[.,[.,.]],.],.],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[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] => [.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]] => [[[.,[[.,.],[[.,[.,.]],.]]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]] => [[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,.],[[.,[[.,.],.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]] => [[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]] => [[.,[[[[[[.,.],.],.],.],[.,.]],.]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]] => [[[.,[[[[[.,.],.],.],.],.]],[.,.]],.]
[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] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]] => [[[[.,.],.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[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] => [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],.] => [.,[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]] => [[.,.],[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[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] => [[.,[[.,.],.]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]] => [[[[[.,[[[.,[.,.]],.],.]],.],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]],.] => [.,[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]]
[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] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[[.,[.,.]],.]]]
[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] => [.,[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],[[.,.],[.,.]]],.],.],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]] => [[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]] => [[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [[[.,.],[[[[[.,.],.],.],.],.]],[[.,.],.]]
[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] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,[[.,.],.]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[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] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.],.] => [.,[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => [[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => [[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => [[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]] => [[[.,.],[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]] => [[.,[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]],.]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => [.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]] => [[.,[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]] => [[.,[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]] => [[[.,.],[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]]],.]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]] => [[.,[[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]],.]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]] => [[.,[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]],.]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]],.]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,.],[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]]
[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] => [.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]] => [[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.] => [.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0] => [[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => [[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0] => [[.,[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],.]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0] => [[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0] => [[.,[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]],.]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0] => [[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0] => [[.,[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]]],.]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0] => [[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[[.,[[.,[.,.]],.]],.],[[.,[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0] => [[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => [[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0] => [[.,[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]],.]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0] => [[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]],.]]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0] => [[.,[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.]],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [[.,[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [[.,[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]],.] => [.,[[.,[.,[.,[[[.,.],.],.]]]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[.,[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]],.] => [.,[[.,[[[.,.],[[[.,[.,.]],.],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[[[.,[[.,.],[[.,[.,.]],.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[[.,[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]],[.,.]],.] => [.,[[.,.],[[.,[[[[.,[[.,.],.]],[.,.]],.],.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[[.,.],[.,.]]],.],.]
[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] => [[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[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] => [[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[.,.],[[[[.,.],[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],[.,.]]]],[.,.]]
[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] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [[[[.,[.,[.,[[[.,[.,.]],.],.]]]],.],.],.] => [.,[.,[.,[[[[.,[.,[[.,.],.]]],.],.],.]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[.,[.,[[[.,[.,[.,.]]],.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,[[[.,.],.],.]]],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.],.] => [.,[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],[.,.]]
[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] => [[[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[[[[.,.],.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [[[[[.,[[.,.],[.,.]]],.],.],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],.],[[.,.],.]]
[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] => [[[[.,[.,[.,.]]],[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0] => [[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],.],.] => [.,[.,[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [[[.,.],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.],.] => [.,[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,[[.,.],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]]]
[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] => [[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]]
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [.,[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[[.,[[.,.],.]],.]]
[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] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[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] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]] => [[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]] => [[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],.]
[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] => [.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]
[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] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]] => [[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]] => [[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,.],[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]] => [[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]] => [[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]] => [[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[.,.]],.]
[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] => [.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],[.,.]],.]]]] => [[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,.]],.]]] => [[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,[[.,.],.]],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],.]]],[.,[[.,[[.,.],.]],.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,[[.,.],[[.,.],.]]],.]]],.]
[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] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]
[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] => [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[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] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[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-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
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