Identifier
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
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 3119 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] => [[[[.,[.,.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],.]],.]
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[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] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [[[.,[[.,.],[.,[.,.]]]],.],.]
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[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],.],.]]
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[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],.]],.]
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[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],.]],.]
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[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],.]
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[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],.],.]
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[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],.]],.]
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[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] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],.],.]]
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[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] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],.]],.]],.]
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[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] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [[[.,[.,[.,[[.,.],.]]]],.],.]
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[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] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [[[.,[[.,[.,[.,.]]],.]],.],.]
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[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],.],.]],.]
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[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],.],.]]
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[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] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],.],.]
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[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] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[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] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[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] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[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] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[[.,.],.]],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[[.,.],.],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[[.,.],.],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,.],[.,.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[[.,.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[[.,.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => [[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[[.,.],.]]]],.],.] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => [[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => [[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],.],[.,.]]],.],.] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => [[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => [[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => [[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => [[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => [[.,[[.,.],[.,[[.,[.,.]],.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],[.,.]]],.],.] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.] => [.,[.,[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],[.,.]],.]]],.],.] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => [[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => [[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],.],[.,.]],.],.]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => [[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => [[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => [[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => [[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => [[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => [.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,[.,.]],.]],.],.]],.] => [.,[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => [[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [[[.,[[.,.],[.,[[.,.],.]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => [[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => [[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => [[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => [[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => [[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => [[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => [[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => [[[.,[.,[[[.,.],[.,.]],.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => [[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => [[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => [[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => [[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => [[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => [[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => [[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => [[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => [[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => [[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => [[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => [[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [[[.,[[.,.],[[[.,.],.],.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => [[[[.,[.,.]],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => [[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => [[[.,.],[[[.,[[.,.],.]],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => [[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => [[[[[.,.],[.,[[.,.],.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => [.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => [[.,[[[[.,.],[[.,.],.]],.],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => [[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => [[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => [[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => [[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => [[[.,.],[[[[.,[.,.]],.],.],.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => [[[[.,.],[[[.,[.,.]],.],.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],.],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => [[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [[.,[[[[[.,.],[.,.]],.],.],.]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => [[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => [.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => [.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => [[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [[.,[[[.,[[[.,.],.],.]],.],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => [[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => [[[[[.,.],[[[.,.],.],.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [[.,[[[[.,[[.,.],.]],.],.],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => [[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [[.,[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => [[[.,[[[[.,[.,.]],.],.],.]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => [[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.] => [.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.] => [.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => [.,[[[[[.,[[[.,.],.],.]],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [[[[[.,[[[.,.],.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => [[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]],.] => [.,[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.] => [.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.] => [.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.] => [.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]
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[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.] => [.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]
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[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [[[[[.,[[.,.],[.,.]]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]] => [[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.] => [.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => [.,[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.] => [.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]],.] => [.,[[[[[.,.],[[[.,.],.],.]],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [[[[.,[[[[[.,.],.],.],.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.] => [.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.] => [.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]
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[] => . => .
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
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[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
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[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[[.,.],.]]] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
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[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[.,[[[.,.],.],.]]] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]] => [[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
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[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[[[.,.],.],.],.]]] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]] => [[[[.,.],[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]] => [[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[[[.,.],.],.],.]]]] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => [[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[[[.,.],.],.]]]]] => [[[[[.,[.,[.,.]]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
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[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],[.,.]],.],[.,.]] => [[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],[.,[.,.]]],.],.] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],[.,[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[.,[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.] => [.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
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[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]]
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[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => [.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.] => [.,[.,[[.,.],[[[[.,.],.],.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
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[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],[[.,.],.]]]
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[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]
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[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
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[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
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[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
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[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => [[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]] => [[[.,.],.],[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[[.,.],.],[[.,.],.]]]]
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[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,[.,.]]] => [[[.,.],.],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[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] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]],.] => [.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]
[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] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
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[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] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[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] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
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[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
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[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
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[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] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
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[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
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[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] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
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[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]
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[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[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] => [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[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] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[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] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[[[.,.],.],.],.],[[[.,.],.],.]],.] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],[[.,.],.]],.],.] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[[.,.],.]],[.,.]] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => [.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[[.,[.,.]],.]]],.] => [.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.] => [.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]]
[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] => [.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]] => [[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[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] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]
[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] => [[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[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] => [[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.] => [.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.] => [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]] => [[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[[.,[.,.]],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],[.,.]] => [[.,.],[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[[[.,.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]] => [[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]] => [[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => [.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],[.,.]],.],.]] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => [[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[[[.,.],.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]] => [[.,.],[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[[[.,.],.],.]],[.,[.,[.,[.,.]]]]] => [[[[[.,.],.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],[.,.]],[.,[.,.]]]
[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] => [[.,[[[[[[.,.],.],.],.],[.,.]],.]],.] => [.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],[[.,.],.]]],.] => [.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],[[.,.],.]],.] => [.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,.],.],[[.,.],.]],.],.],.]],.] => [.,[[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[[[.,.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.],.] => [.,[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.] => [.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],[[.,.],.]] => [[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]] => [[[[[.,[.,.]],.],.],.],[[.,.],[.,.]]]
[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] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]] => [[.,[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.] => [.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[[[.,.],.],.],.]],.]]],.] => [.,[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[[[.,.],.],.],.],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[.,[.,.]],.],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[[.,.],[.,.]]],.],.],.],.] => [.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,[.,.]]]] => [[[[.,.],.],.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[[[.,.],.],.],[.,.]]]],.],.] => [.,[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],.],[[.,.],.]],.],.],.] => [.,[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],.] => [.,[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[[.,.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => [[[.,.],[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]] => [[[.,[[[.,.],.],.]],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],.] => [.,[[.,.],[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,[[.,.],.]],.]]],.],.] => [.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[[[.,.],.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[[[.,.],.],.]],.],.],.],[.,.]] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[[[.,.],.],.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.] => [.,[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.] => [.,[[[.,.],[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[.,.],[.,[[.,[[[[.,.],.],.],.]],.]]] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[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] => [[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[[[.,.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => [[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,[[.,.],[.,.]]],[.,.]],.]] => [[.,[[.,.],[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[[[.,.],.],.],.],.]],.],.] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],.] => [.,[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]],.] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.] => [.,[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.] => [.,[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[[[[.,[.,.]],.],.],.]]],.],.] => [.,[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]] => [[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]] => [[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,[[.,.],.]]],.] => [.,[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[[[.,.],[.,.]],.]]],[.,.]],.] => [.,[[.,.],[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]] => [[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]] => [[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,.],[[.,.],.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]],.] => [.,[[[[[.,.],.],.],.],[[.,[.,.]],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]],.] => [.,[[.,.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.] => [.,[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [.,[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]],.] => [.,[[[[.,.],.],.],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]],.] => [.,[[[.,.],.],[[[.,[[.,.],.]],.],.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.] => [.,[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.] => [.,[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],.]],.] => [.,[[.,[[[[.,[.,.]],[.,.]],.],.]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],.] => [.,[[.,[[.,[[[.,[.,.]],.],.]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]
[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] => [[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]] => [[[.,.],[.,[[[.,.],[.,.]],.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]] => [[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]],.] => [.,[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]] => [[.,[[[[.,[[.,.],[.,.]]],[.,.]],.],[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[.,.],[[[.,.],[.,.]],.]]]],.]],.] => [.,[[.,[[[[.,[[.,.],[.,.]]],[.,.]],.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]] => [[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.] => [.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]] => [[.,[[.,[[[.,[[.,.],[.,.]]],.],.]],[.,.]]],[.,.]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[.,[[[.,.],[.,.]],.]]],.]],.]],.] => [.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],.]],.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,.],.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]] => [[[[.,[[.,[[.,.],.]],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]],.] => [.,[[[[.,[[.,[[.,.],.]],[.,.]]],[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]] => [[.,[[[.,[[.,[[.,.],.]],[.,.]]],.],[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[[.,.],[[.,[.,.]],.]],.]]],.]],.] => [.,[[.,[[[.,[[.,[[.,.],.]],[.,.]]],.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]] => [[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]],.] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],.],[.,.]]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]] => [[.,[.,[.,.]]],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]] => [[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[[[[[.,.],.],.],.],.],.]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]] => [[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[[.,.],.]] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[.,.],[.,.]],.],.],[[[.,.],.],.]] => [[.,[.,[.,.]]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[[[.,.],[.,.]],.]],[.,.]]],.] => [.,[[[.,.],[[.,[[.,.],[.,.]]],.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] => [[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],[[.,.],[.,.]]],.] => [.,[[[.,.],[.,.]],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]] => [[[.,.],.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => [[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]] => [[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] => [[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],[.,.]]] => [[[.,.],[[.,.],.]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],[.,.]] => [[.,.],[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]],.] => [.,[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.],.] => [.,[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]],.] => [.,[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.],.] => [.,[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]],.] => [.,[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],.] => [.,[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],.]] => [[.,[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.] => [.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => [[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]] => [[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],[.,.]],.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]] => [[[[.,.],[[.,.],.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]] => [[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[[.,.],[.,.]],.]],[.,.]],.] => [.,[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],[[.,[.,.]],.]]],[.,.]],.] => [.,[[.,.],[[[.,[[.,.],.]],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],[[.,.],.]],.],.],[.,.]] => [[.,.],[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.] => [.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[[[.,.],.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],[[.,.],.]],.],.],.],.] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]]]
[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] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.] => [.,[[.,[[[[[.,.],.],.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]],.] => [.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[[[.,.],.],.],.]] => [[.,[.,[.,[.,.]]]],[[[.,[.,.]],.],.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]] => [[[[.,.],[[.,.],[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]] => [[.,[[[.,[[.,.],.]],[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]],.]] => [[.,[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,[.,[.,.]]],.]],.],.]],.] => [.,[[.,[.,[[.,[[[.,.],.],.]],.]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,[.,[.,.]]],.]],.]],.],.] => [.,[.,[[.,[[.,[[[.,.],.],.]],.]],.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.] => [.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]] => [[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]],.] => [.,[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[.,.]] => [[.,.],[[.,[[[.,[[.,[.,.]],.]],.],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],.]],.]],.] => [.,[[.,[[.,[.,[[.,[[.,[[.,.],.]],.]],.]]],.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],[.,.]] => [[.,.],[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],[[.,.],[.,.]]],[.,.]]] => [[[.,.],[[[.,.],[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]] => [[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]
[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] => [[[.,[[.,[.,[[.,.],.]]],.]],[.,.]],.] => [.,[[.,.],[[.,[[[.,[.,.]],.],.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]] => [[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,.]] => [[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],[.,.]] => [[.,.],[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]] => [[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],.] => [.,[[.,.],[[[.,[[.,.],.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.] => [.,[[.,.],[[.,.],[[[.,[[.,.],.]],.],[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[[.,.],.]],[[.,.],.]]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[[.,.],[[.,.],.]]],.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.] => [.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => [[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[[.,.],[.,.]],.]],[.,.]],.],.] => [.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]] => [[[.,.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]],.] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]] => [[[.,.],[.,.]],[[[.,[.,.]],.],[.,.]]]
[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] => [[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],[[.,.],.]]]],.],.]] => [[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,[[.,.],.]],.]]],.],.]] => [[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],[[.,.],.]]],.]],.],.]] => [[.,[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]] => [[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[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] => [[[[.,.],[.,.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[.,.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[[.,.],[.,[[.,.],.]]],[.,.]],[.,.]],[[.,.],.]] => [[.,[.,.]],[[.,.],[[.,.],[[[.,[.,.]],.],[.,.]]]]]
[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] => [[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] => [[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] => [[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[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] => [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,[[.,.],.]],.]] => [[.,[[.,[.,.]],.]],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]],[[.,.],.]] => [[.,[.,.]],[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] => [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] => [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] => [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] => [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]],.]] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]],.]] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]],.]] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]],.]] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]],.]] => [[.,[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]],.]] => [[.,[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]],.]] => [[.,[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.],.]] => [[.,[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.],.]] => [[.,[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.],.]] => [[.,[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.],.]] => [[.,[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.],.]] => [[.,[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.],.]] => [[.,[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.],.]] => [[.,[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.],.]] => [[.,[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.],.]] => [[.,[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]],.]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.],.]] => [[.,[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.],.]] => [[.,[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.],.]] => [[.,[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.],.]] => [[.,[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]],.]
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path D of semilength n with n>1 may be uniquely decomposed into L1R0 for Dyck paths L,R of respective semilengths n1,n2 with n1+n2=n−1.
This map sends D to the binary tree T consisting of a root node with a left child according to L and a right child according to R and then recursively proceeds.
The base case of the unique Dyck path of semilength 1 is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path D of semilength n with n>1 may be uniquely decomposed into L1R0 for Dyck paths L,R of respective semilengths n1,n2 with n1+n2=n−1.
This map sends D to the binary tree T consisting of a root node with a left child according to L and a right child according to R and then recursively proceeds.
The base case of the unique Dyck path of semilength 1 is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
searching the database
Sorry, this map was not found in the database.