edit this map or download as text // json
Identifier
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ 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] => [[.,.],[.,[[[.,.],.],.]]]
>>> Load all 6231 entries. <<<
[1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]]
[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] => [[[[[.,.],.],.],[[.,.],.]],.]
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[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
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[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
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[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
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[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
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[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
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[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
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[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
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[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
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[1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,.],[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
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[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
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[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] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
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[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[[[.,.],.],.],[.,[.,.]]]],.],.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[.,.]],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],[.,.]],[.,[.,[.,.]]]],.],.],.]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[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] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[[[[.,[.,.]],[.,.]],[.,[.,.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],[.,[.,.]]],.],.],.],.],.]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[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] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]],.]
[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] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,[.,.]]]
[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] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]],.]
[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] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[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] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[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] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],[[.,.],.]],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],[[[.,.],.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[[[.,.],.],.]],.]]
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[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]
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[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
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[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
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[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
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[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]
[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] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],[.,[.,[.,.]]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],[.,[[[.,.],.],.]]],.],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],[.,[[.,.],.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],.],[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],[[[.,.],.],.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[.,.],[[[.,.],.],.]],.],.],.]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,.],.],[[.,.],.]],.],.],.]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[.,.],.],.],[.,.]],.],.],.]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,[[[.,.],.],.]],.],.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[.,[[.,.],.]],.],.],.]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]],.]
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[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]
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[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]
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[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,[[.,.],.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[[[[.,.],.],.],.]]],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[[[.,.],.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[[[[[.,.],.],.],.],.]]],.]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,[.,.]],.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[[.,.],.],.],[.,.]],[[.,.],.]],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[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] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,[[[.,[.,.]],[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[[.,.],[.,.]]],.],.],.],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[[[.,.],.],[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[.,[.,[.,.]]],.],.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],.],[.,[.,[.,.]]]],.],.]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[[[[.,.],.],.],[.,[.,.]]]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[[.,[[[[.,.],.],.],.]],.],[[.,.],.]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[.,[[[.,.],.],.]],.],[[[.,.],.],.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,.]],[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[.,[[.,.],.]],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]
[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] => [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[[.,.],.]]]],.],.],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[.,[.,[.,.]]],.],.],.],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,.],[.,.]],.],.],.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,[[[.,.],.],.]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,.],.],.],[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],[.,[.,.]]],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.],.]
[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] => [[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[[.,.],[.,.]],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]]
[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] => [[[[.,.],[.,.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[[.,[.,.]],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],[[.,[.,.]],.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],.],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[.,[.,[.,.]]],.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],[[.,.],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],[[.,[.,.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[[[.,[.,.]],.],.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[[[.,[.,.]],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[[[[.,.],.],.],.]],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],[[[.,.],.],.]]],.]]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[[[.,.],.],.],[[.,.],.]]]],.]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],.],[.,[[.,.],.]]]],.]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],[.,[[[.,.],.],.]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],.]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[[[.,[.,.]],.],.],.],.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[[.,[.,.]],.],.],.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[.,[[.,.],.]]]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[.,[[.,.],.]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[.,[[.,.],.]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[.,[[.,.],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[[[.,.],[.,.]],.],[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,[.,.]],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[[.,[.,.]],.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[[[.,.],[.,.]],.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,[.,.]]],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[[.,[.,[.,.]]],.],[.,.]],.]],.]
[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] => [[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[[.,[.,.]],.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[[.,[.,.]],.]]],.],[.,.]],.]
[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] => [[[.,.],[.,[[[.,.],[[.,[.,.]],.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[[.,[.,.]],.]],.]]
[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] => [[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]]
[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] => [[[[[[[.,.],[.,.]],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],[[[.,.],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[[.,.],.],[.,.]],.],.]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[[[[.,.],.],.],.],.]],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[[.,[[[[[.,.],.],.],.],.]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[[[.,.],.],.]]]],.],.],.],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[[.,[.,.]],.],.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,[[.,.],[.,.]]],[[.,.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.],.]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,[[.,.],.]],[.,.]]],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[.,.]],[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],[.,[[.,.],.]]]],.],[[.,.],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,[[.,.],.]]],[[.,.],.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,[.,[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[.,[[.,.],.]]],.]]
[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] => [[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[[.,[[.,.],.]],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,.],.]],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[[[[.,.],.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[.,[[.,.],.]],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[[[.,.],[.,.]],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[.,.],[[.,.],.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[.,.],[[.,.],.]],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[[.,[.,.]],.],.]],.]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,[[.,[.,.]],.]]],[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,[.,.]],[[.,.],.]],.]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[.,.]],[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[[.,.],[[.,.],.]],.]],.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],[.,.]]],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],[.,.]],[[.,.],.]]]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],[[.,.],.]],[.,.]]]],.]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]],.]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[[[.,.],.],[.,.]]],.]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,[.,.]]],[[.,.],.]],.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[[[.,[.,.]],.],.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]],.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,[.,.]],[[.,.],.]],.]]],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,[[.,.],.]],[.,.]],.]]],.]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[[[[.,[.,.]],.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[[.,[.,.]],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[.,[[[.,.],[.,.]],.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[[.,.],.]],.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[[[.,.],[.,.]],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[[[.,.],[.,.]],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[[.,.],[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[[.,[.,.]],.],[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,.],.],[.,.]]],.],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],.],.]],[.,.]],.],.]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],[[[.,.],.],.]]]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,[[[.,.],.],.]],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[.,[.,.]],.],[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[[[.,.],.],.]]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[[[.,.],.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[[[.,.],.],.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],[[[.,.],.],.]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[[[.,[.,.]],.],.]],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[.,.],.],[.,[.,.]]],.],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[[[.,.],.],[.,.]]]],.],.]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[[.,.],.],[.,.]],.],[.,.]]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],[[[.,.],.],.]]],[.,.]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,[[[.,.],.],.]],.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[[.,.],.],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[[[.,.],.],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[[.,.],.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,[[[.,.],.],.]],.]],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[[.,.],.],[.,.]],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[[.,[.,.]],.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[[[.,.],.],[.,.]]],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[[[.,.],.],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,[[[.,.],.],.]],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],[[[.,.],.],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[[.,.],.],.]],.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,[[[[.,.],.],.],.]],.],.],.]]]
[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] => [[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,[[[.,.],.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[.,[.,.]],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[[.,.],[[[.,[.,.]],.],.]]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[[[.,.],.],[.,.]]],.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[.,[.,[[.,.],.]]]],.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[[[[.,.],.],.],.]],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[[[.,.],.],.],.]],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],[[.,[.,.]],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[[[.,.],[.,[.,.]]],.]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,.],[[[.,.],.],.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[[[.,[.,.]],.],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[.,[[.,[.,.]],.]],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[.,[[.,.],.]]],.]],.]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[[[.,[.,.]],.],.]],[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,[.,.]],[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[.,[.,.]]],.]],.]],.]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[[.,[.,[.,.]]],[.,.]],.],.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,[.,[.,.]]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,[[.,.],.]],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],[.,[.,[.,.]]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,.],[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],[.,.]],[.,[.,.]]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[[.,.],[.,.]],.]],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[[.,[.,.]],.],.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,[.,[[.,.],.]]],.]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[.,[[.,.],.]]]],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[.,[[[.,.],.],.]],[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[[[.,.],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[[[[.,.],.],.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,[.,.]]],.]],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],[.,.]]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[[[.,[.,.]],.],[[.,.],.]],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[[.,[[.,.],.]],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[.,[[.,[.,.]],.]],.],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[[.,[.,.]],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[[.,[[.,.],.]],.],[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[[[.,.],.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[[.,[[.,.],.]],.],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[[.,.],.],[[.,.],.]]],[.,.]],.],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[[.,.],.],[[.,.],.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [[.,.],[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[[.,.],[.,[.,.]]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[.,.],.],[[.,.],.]],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],[[.,.],.]]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]],.],.]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[[[.,[.,.]],.],.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,[.,[[.,.],.]]],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,[.,[[.,.],.]]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[[.,.],[.,.]],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[[.,[.,.]],.]]]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,[[.,[.,.]],.]]]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,[[.,[.,.]],.]]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[[[.,[.,.]],.],[.,[.,.]]],.],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,[.,.]]],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,[.,[[.,.],.]]],.],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[[[.,.],[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[[.,.],[.,.]],.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],[[.,.],.]],[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.],.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[[[[.,.],.],.],.],[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,[[[[.,.],.],.],[.,.]]]],.],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[[[[.,.],.],.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[[[.,.],.],.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]],.],.]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[[.,.],.],[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,.],.],[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[[.,.],.],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[[.,.],.]],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[[.,.],[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[[.,.],[[.,.],.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,[[.,.],.]],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,[[.,.],.]],.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[[.,[.,[.,.]]],.]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]],.]
[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] => [[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[[[.,.],.],.],.],.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[[.,.],.],.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[[[[.,.],.],.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[[[.,.],.],.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[[.,.],[[.,.],.]],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[[[.,.],[.,.]],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[[[[.,.],.],.],.],.]]]]
[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] => [[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,.],.]]
[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] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[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] => [[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]],.]
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[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],[[[[[.,.],.],.],.],.]],.],.]
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[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[.,.]],[.,[.,[.,.]]]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[[[[.,.],.],.],.],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],[[.,.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]]
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[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[[.,.],.],[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[.,.],[[.,.],[[.,.],.]]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[.,[[.,.],[[.,.],.]]]]],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[.,[[.,.],[[.,.],.]]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[.,[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],.]],.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],[.,.]],.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[[[.,.],[.,.]],.],[.,[[.,.],.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [[[[.,.],[.,.]],.],[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,[.,.]],.],[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[[.,[.,.]],.],[.,[[.,.],.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],[[[.,.],[.,.]],.]],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],[[.,.],[.,[[.,.],.]]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,[[.,.],[.,[[.,.],.]]]],.],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],[.,[.,[[.,.],.]]]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,[.,[[.,.],.]]]],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[[.,[.,[.,[[.,.],.]]]],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,[[.,.],.]]],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[[.,.],[.,[[.,.],.]]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[[.,.],[.,[[.,.],.]]],.]]],.]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[[.,.],[.,[[.,.],.]]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[[.,[.,[[.,.],.]]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[[.,[.,[[.,.],.]]],.]]],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[[.,[.,[[.,.],.]]],.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[[.,[.,[[.,.],.]]],.]],.]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[[.,[.,[[.,.],.]]],.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,[.,[[.,.],.]]],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,.]],.],[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[[[.,.],[.,.]],.],[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[[[.,.],[.,.]],.],[.,.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],.],[.,.]]]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[[[.,[.,.]],.],[.,.]]]],.],[.,.]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[[[.,[.,.]],.],[.,.]]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [[.,.],[[.,.],[[[.,.],[[[.,[.,.]],.],[.,.]]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[.,.],[[[.,[.,.]],.],[.,.]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[[[.,[.,.]],.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[[[.,[.,.]],.],[.,.]]],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[[.,[.,.]],.],[.,.]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[[[.,.],[.,.]],.],[.,[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,[.,.]]],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[[.,[.,[.,.]]],.],[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],[[[.,.],[.,.]],.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,[[[.,.],[.,.]],.]],.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],[.,.]],.],[[.,[.,.]],.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[[.,.],[[.,[.,.]],.]],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[[.,[[.,[.,.]],.]],.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[[.,.],[[.,.],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],[[[.,.],[[.,.],[.,.]]],.]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[[[[.,.],[.,[[.,.],[.,.]]]],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[[.,.],[[.,[[.,.],[.,.]]],.]],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],[[.,.],[.,.]]],.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[[[[.,.],[.,[.,.]]],.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,[.,.]]]],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],[[[.,.],[.,[.,.]]],.]],.],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[[[[.,.],[.,[.,[.,.]]]],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[[[[.,.],[[.,[.,[.,.]]],.]],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[[[.,.],[[.,.],[.,.]]],.],[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[[[.,.],[.,.]],.],[.,[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[[[.,[.,.]],.],[.,[.,.]]],.],[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[[[.,.],[.,[.,.]]],.],[.,.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[[[.,[.,[.,.]]],.],[.,.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [[.,.],[[.,.],[[[[[.,.],[.,[.,.]]],.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[.,[[[[[.,.],[.,[.,.]]],.],[.,.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[[[.,[.,[.,.]]],.],[.,.]],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[[[.,[.,[.,.]]],.],[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [[.,.],[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,[[.,.],[[[.,.],[.,.]],.]]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[.,[[[.,.],[.,.]],.]]]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[.,[[[.,.],[.,.]],.]]]],.],[.,.]],.]
[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] => [[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[.,[[[.,.],[.,.]],.]]],.]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[.,[[[.,.],[.,.]],.]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[.,[[[[.,.],[.,.]],.],[[.,[.,.]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[[[.,.],[[.,.],[.,.]]],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],[[.,.],[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[[.,.],[[[.,.],[.,.]],.]],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[[[.,.],[[.,[.,.]],.]],.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],[[.,.],[[.,[.,.]],.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[[[.,[[.,.],[[.,[.,.]],.]]],.],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],[.,[[.,[.,.]],.]]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[[[[.,.],[.,[[.,[.,.]],.]]],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[[[.,[.,[[.,[.,.]],.]]],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [[[.,.],[.,[[.,.],[[[.,.],[[.,[.,.]],.]],.]]]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],[.,[[[.,.],[[.,[.,.]],.]],.]]]
[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] => [[[.,.],[[.,[.,[[[.,.],[[.,[.,.]],.]],.]]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],[[.,[[.,[.,.]],.]],.]]],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[[.,.],[.,[[.,[[.,[.,.]],.]],.]]],.],[.,.]],.]
[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] => [[[.,.],[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,[[.,[.,.]],[[.,.],.]]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,.],[[[.,.],.],[.,.]]],[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],[.,.]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,.],.]],[[.,.],[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,[[.,.],.]],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[[.,.],[.,.]]],[[.,.],.]]]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[[.,[[.,.],[.,.]]],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]],[[.,.],.]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]],.]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,[[.,[[.,.],[.,.]]],.]],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]]],.]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]],.],.]
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[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[[.,.],.]],.],[[.,[.,.]],[[.,.],[[.,.],.]]]]
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[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,[.,.]],[[.,.],.]]]]],.]
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[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],[[.,[.,.]],[[.,.],.]]]],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => [[[.,.],.],[[.,.],[[.,[[.,[.,.]],[[.,.],.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.]],.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,[[.,.],[[.,[.,.]],.]]],[[.,.],.]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]],.]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[[.,.],.],[[.,.],[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]],.],.]
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,[[.,.],.]]]],[[.,[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],[[.,.],[.,[[.,.],.]]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]]],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[[.,.],[.,[[.,.],.]]]],.]],[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,[[.,.],[.,[[.,.],.]]]],.]],.]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[.,[[.,.],.]]],[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[.,[[.,.],.]]],[[.,.],.]]],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],[[.,[.,[[.,.],.]]],.]]],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],[[.,[.,[[.,.],.]]],.]]],.]],.],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],[[.,.],.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,.],.]]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[[.,.],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],.],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],.]]],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],[[.,.],.]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,[.,[[.,.],[[.,.],.]]]],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[.,[[.,.],.]],.],[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[.,[[.,.],.]],.],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[.,.],[[.,.],.]],[[.,.],[.,[[.,[[.,.],.]],.]]]]
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[1,0,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]]
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[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],[.,[[.,[[.,.],.]],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]]],.]
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[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[.,[[.,.],[.,[[.,.],.]]]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[[.,.],.]],[.,[[.,.],.]]]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]]],.],.]
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[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[.,[[.,[[.,.],.]],.]],[[.,[.,[[.,.],.]]],.]],.]
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[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]]],.]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[[.,.],[[.,.],[.,.]]]],.]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],[[.,.],[.,.]]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,[[.,.],.]],[[.,.],[.,.]]]],.]],.],.]
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[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],[[.,[[.,.],[.,.]]],.]]],.],.]
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[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],[[.,[[.,.],.]],[.,.]]]],[[.,.],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,[[.,.],[[.,[[.,.],.]],[.,.]]]],.]],.],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,[[.,[[.,.],.]],[.,.]]],.]]],.],.]
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[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[[.,[[.,[[.,.],.]],.]],[.,.]]],.],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[[.,[[.,.],[[.,.],.]]],[.,.]]],[[.,.],.]],.]
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[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[.,.],.]],[[.,.],[[.,[.,.]],[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[[.,.],.]],[[.,.],[[.,[.,.]],.]]]],.],.]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],[[.,[[.,.],.]],[[.,[.,.]],.]]]],.],.]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],[[.,[[.,[.,.]],.]],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[[[[.,[.,.]],[.,.]],.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]],.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[[[[.,[.,.]],.],[.,.]],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],[.,[[.,[[.,.],.]],.]]],.]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[[.,[.,[.,.]]],[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],[.,[[.,.],[[.,.],.]]]],.]]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[.,[[.,.],[[[[.,.],.],[.,.]],[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[.,.],[[.,[.,.]],[.,[[.,.],[[.,[.,.]],.]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[[.,.],.],[[.,[.,.]],.]]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[[[.,.],.],[.,.]],[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[.,.],[[[[.,.],[[.,.],.]],[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [.,[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,.],[[[.,.],[[.,.],.]],[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[[[.,[.,.]],.],.],[.,.]]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[.,.],[[[.,[.,.]],.],.]],[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,[.,[[.,[.,.]],.]]],[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[[[.,[.,.]],[[.,.],.]],.],.]],.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[[.,.],[.,[.,[.,.]]]],[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[.,[[[[.,[[.,.],.]],[.,.]],.],.]],.]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,.],[[[.,[[.,.],[.,.]]],.],.]],.]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]]]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[[[[.,[.,.]],[.,.]],.],.]],.]]]]
[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[[.,[.,.]],[.,[.,[.,.]]]]],[.,.]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[[[[.,[.,.]],.],[.,.]],.]],.]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],[.,[[.,[[.,.],.]],.]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[[.,[[.,.],.]],[.,[.,.]]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[[[[.,.],[.,.]],.],[.,.]]],.]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[[.,.],[[[.,[.,[.,[.,.]]]],[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,0] => [.,[[.,.],[.,[[.,[[[[.,.],.],[.,.]],[.,.]]],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[[[.,.],[.,.]],[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,[.,.]],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[[[.,.],[[.,.],.]],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,[.,.]],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],[[[.,.],.],[.,.]]],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],[[.,.],.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,[.,[.,.]]],[[.,.],.]],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],[[[.,[.,.]],.],.]],.]]]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,[.,[[.,[.,.]],.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[[[.,[.,.]],[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,[.,.]]],[.,.]]]]
[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] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],[.,[.,.]]]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],[.,[.,.]]]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[[.,.],[[.,.],.]],.]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[[.,.],[[.,.],.]],.]],.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],[.,.]]],.],[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.],[.,.]]]
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[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[[[.,[.,.]],[[.,.],.]],.]]],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]],.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,[[[.,[[.,.],.]],[.,.]],.]]],.],[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[[[[.,[.,.]],[.,.]],.],.]]]],.]]
[1,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]],.]],.]]
[1,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[[[[.,[.,.]],.],[.,.]],.]]]],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,[[.,[[.,.],.]],.]]],.]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[[.,[.,[.,.]]],[[.,.],.]]]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[.,.],[[.,.],.]],[.,[.,.]]]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,[[.,.],[[.,.],.]]]],.]],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]]],.]]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[[[[.,.],[.,.]],.],[.,.]]]]],.]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]],.]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],[[[[.,.],.],[.,.]],[.,.]]]]],.]]
[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[[.,.],[[.,[.,.]],.]]]]],.]]
[1,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[[[.,.],.],[[.,[.,.]],.]]],.]],.]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[[[.,.],.],[.,.]],[[.,.],.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],[[.,.],.]],[.,[.,[.,.]]]],.]],.]]
[1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[[[[.,.],.],[[.,.],.]],[.,.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],[[.,.],.]],[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,[.,.]]],[[[.,.],.],[.,.]]],.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[.,[.,.]]],[[.,.],.]],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[[[[.,[.,.]],.],.],[.,.]]],.]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],[[[.,[.,.]],.],.]],[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,[[.,[.,.]],.]]],[[.,.],.]],.]],.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[[.,[.,.]],[[.,.],.]],.],.]],.]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,[.,[.,.]]]],[[.,.],.]],.]],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[.,[[[[.,[[.,.],.]],[.,.]],.],.]],.]],.]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[[[.,[[.,.],[.,.]]],.],.]],.]],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[[[[.,[.,.]],[.,.]],.],.]],.]]],.]]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,[.,.]],[.,[.,[.,.]]]]],[.,.]]],.]]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[[[[.,[.,.]],.],[.,.]],.]],.]]],.]]
[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]]],.]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],[.,.]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],.]]],.]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,[[.,.],.]],[.,[.,.]]]],[.,.]]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]]],.]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[[[[.,.],[.,.]],.],[.,.]]],.]]],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[[.,[.,[.,[.,.]]]],[.,.]],.]]],.]]
[1,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[[[[.,.],.],[.,.]],[.,.]]],.]]],.]]
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[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.]
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[1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[.,[[[[[.,.],.],[.,.]],.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,[[.,.],[[[.,.],.],.]]],.]]]
[1,1,0,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0] => [[.,[.,.]],[[.,.],[[.,[[.,[[[.,.],.],.]],.]],.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],[.,.]],[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],[[[.,[.,.]],.],.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],[[[.,.],.],[.,.]]],.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,[[[.,.],.],.]],[.,.]],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],[.,.]],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],.],[.,.]],[[.,[[[.,.],.],.]],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],[[[[[.,[.,.]],.],[.,.]],.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[[.,[.,.]],[[[.,.],.],.]]],.]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[[.,[[[.,[.,.]],.],.]],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,.]],[[[.,.],.],[.,.]]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[[[.,.],.],[.,[.,.]]],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[[.,.],[[[.,.],.],[.,.]]]],.],.]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[[[.,.],.],.]],[.,.]]],.],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[[[[.,[.,.]],.],[.,.]],.],[.,.]]],.],.]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[[.,[.,.]],[[[.,.],.],.]]],[.,.]],.],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[[.,[[[.,[.,.]],.],.]],.]],[.,.]],.],.]]
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[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],.]]]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[[[[[.,.],.],[.,.]],.],.]]]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,[[.,.],[[[.,.],.],.]]],.]]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,[[.,[[[.,.],.],.]],.]],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],.],[.,.]],[[[.,.],.],.]]]],.]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],[[[.,.],.],[.,.]]],.],.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[[[.,[.,.]],.],.]],[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[[.,.],[[[.,.],.],.]]]],.]],.]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],[[.,[[[.,.],.],.]],.]]],.]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[.,[[[[[.,[.,.]],.],[.,.]],.],.]]],.]],.]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[.,.]],[[[.,.],.],.]]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]],.]
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[1,0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[[.,[[[.,.],.],.]],.]],.]]
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[1,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[.,.],.],[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,.],.],[[[[.,[.,.]],[[[.,.],.],[.,.]]],.],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[[.,[[[.,[.,.]],.],.]],[.,.]],.],.]]
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[1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],[[.,[[[.,.],.],.]],.]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[[[[.,[.,.]],.],[.,.]],.],.]]],.]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[[.,[.,.]],[[[.,.],.],.]]],.]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[[[.,.],.],[.,.]]],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[[[[[[.,.],.],[.,[.,.]]],.],[.,.]],.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[[[[.,.],.],[.,[.,.]]],[[[.,.],.],.]]],.]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[[[.,.],.],[[[.,[.,[.,.]]],.],.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[[.,[[[.,.],.],.]],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[[[.,.],.],.]],[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[[.,[[[.,[.,.]],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[[.,.],[[[.,.],.],[.,.]]]],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,.],[[[.,.],.],[.,[.,.]]]],.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[[.,[[[.,.],.],.]],[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[[.,[[[.,.],.],.]],[.,[.,.]]],.],.]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[[[[.,.],.],[.,.]],.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[[[[[.,.],.],[.,.]],.],[.,[.,.]]],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[[.,.],[[[.,.],.],.]]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,[[.,.],[[[.,.],.],.]]],[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[[.,[[[.,.],.],.]],.]],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,[[.,[[[.,.],.],.]],.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]],.],.]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[[.,[[[.,.],.],.]],[.,.]]]],.],.]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[[[[[.,.],.],[.,.]],.],[.,.]]]],.],.]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,[[.,.],[[[.,.],.],.]]],[.,.]]],.],.]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,[[.,[[[.,.],.],.]],.]],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[[[.,.],.],[.,.]],[[[.,.],.],[.,.]]]],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[.,.],.],[[[.,[.,.]],.],.]],[.,.]]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[.,.],[[[.,.],.],[.,.]]],.],[.,.]]],.],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],[.,.]],.],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[[.,.],.],.]],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,.],[.,[[[[[.,.],.],[.,.]],.],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],[[[.,.],.],.]]],[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0] => [[.,.],[[.,.],[[.,[[.,[[[.,.],.],.]],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[[[[.,.],.],[.,.]],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],[[[.,[.,.]],.],.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],[[[.,.],.],[.,.]]],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,[[[.,.],.],.]],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[[[[.,.],.],[.,.]],[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [.,[[[[.,.],.],[.,.]],[[.,[[[.,.],.],.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[[[.,.],.],[[[[[.,[.,.]],.],[.,.]],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,[.,.]],[[[.,.],.],.]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,[[[.,[.,.]],.],.]],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[[[[.,.],.],[.,[.,.]]],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[[[.,.],.],.]],[[[.,[.,.]],.],.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[[.,.],[[[.,.],.],[.,.]]]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[.,[[[[[.,.],.],[.,.]],.],[.,.]]],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,[[.,.],[[[.,.],.],.]]],[.,.]],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[[.,[[.,[[[.,.],.],.]],.]],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[[.,[[[.,.],.],.]],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[[[[.,.],.],[.,.]],.],.]]]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,[[.,.],[[[.,.],.],.]]],.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,[[.,[[[.,.],.],.]],.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],.],[.,.]],[[[.,.],.],.]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],.],[[[.,[.,.]],.],.]],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],[[[.,.],.],[.,.]]],.],.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,[[[.,.],.],.]],[.,.]],.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],[[.,.],[[[.,.],.],.]]]],.]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],[[.,[[[.,.],.],.]],.]]],.]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,[[[[[.,.],.],[.,.]],.],.]]],.]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,.],[[[.,.],.],.]]],.]],.]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0] => [.,[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.],.]]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],.]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,[[[.,[.,.]],.],.]]],.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],[[.,[.,.]],[[.,.],.]]],.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],[.,[[[.,.],.],.]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0] => [.,[.,[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],[.,.]],.],[.,.]],.],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[[[.,[.,.]],.],[[.,.],.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],[[[.,.],[[.,.],.]],.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[[.,[.,.]],[.,.]],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,[[.,[.,[[.,.],.]]],.]],.]],.]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,[[.,[[.,.],[.,.]]],.]],.],.]]]
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[[[[.,.],[.,[.,.]]],.],.]]],.]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,[.,[[.,.],.]]],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],[.,.]]],[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[.,.]],.],[.,[[.,[.,.]],.]]],.]],.]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0] => [.,[.,[[[[[.,[.,.]],.],[[.,[.,.]],[.,.]]],.],.]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[[.,.],[.,[.,[[.,.],.]]]],.]],.]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[[.,.],[.,[[.,.],[.,.]]]],.],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[[[.,[.,.]],.],.]],[[.,[.,.]],.]]],.]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],[[.,.],.]],[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],[.,[[[[.,.],.],[.,[.,.]]],.]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[[.,[[[.,[.,.]],.],.]],.]],[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,[[[.,[.,.]],[[.,.],.]],.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[[[.,[[.,.],.]],.],[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],.],[.,.]],.],[.,.]],.]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[[[[.,.],[.,.]],.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,[.,[[[.,.],.],.]]],[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],.],[[.,[[.,.],.]],[.,.]]],.]]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],[.,[[[.,.],.],[.,.]]]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],.],.],[.,.]],[.,.]],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,[.,.]],[[[[.,.],.],[.,.]],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0] => [.,[[.,[.,.]],[.,[[[[.,.],.],[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[.,[[[.,[.,.]],.],[[.,.],[[[.,.],[.,.]],.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[[[.,[.,[.,.]]],[.,.]],.]],.],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,[[.,[.,[.,.]]],.]],[[.,.],.]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],[.,.]],[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[[.,[.,[[.,.],.]]],.]],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,.],[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[[.,.],[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[.,[[[.,[.,[.,.]]],.],.]],[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],[[.,.],.]],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[[.,[[.,[.,[.,.]]],.]],.]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[[[.,[.,[.,.]]],[.,.]],.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[[.,.],.]],[.,[.,.]]],[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,.],.]],[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,.],.]],[.,[.,.]]],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0] => [.,[[.,.],[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,.],[[.,.],[.,[.,.]]]],[.,[[.,.],.]]],.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[[[.,.],[.,[.,[.,.]]]],.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,.],[[.,.],[.,[.,.]]]],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],[[.,[.,[.,.]]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],[.,.]],.],[.,[.,[.,.]]]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[[[.,.],[.,.]],.],[.,[.,.]]]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],.],[.,.]],[.,[.,[.,.]]]],.]],.]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[.,[[[[.,.],.],[.,.]],[.,[.,.]]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,[.,.]]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[[[.,.],[.,.]],.]],.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],[[[.,[.,.]],.],.]]],[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[[.,.],.]],[[.,.],.]],[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],[[[.,.],.],[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[[.,[.,[[.,.],.]]],.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[[.,.],.],[[.,[.,.]],.]]],[.,[.,.]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[[.,.],[.,[[.,.],.]]]],[.,[.,.]]],.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[[[.,.],.],.]],[.,.]],[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],[[.,.],.]],[[.,.],[.,[.,.]]]]],.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[[[.,.],[.,.]],[.,[.,.]]]]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]
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[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],[.,.]],[.,.]],.],.],[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],[.,[[[.,[.,.]],.],.]]],.]],[.,.]]]
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[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],[.,[[[.,.],.],.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => [.,[.,[[.,[[[[.,[[.,.],.]],.],[.,.]],.]],[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],[.,.]],.],[.,.]],.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[[[.,[.,.]],.],[[.,.],.]]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[[[.,.],[[.,.],.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0] => [.,[.,[[[.,.],[.,.]],[[.,.],[[[.,.],.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,[[.,[.,[[.,.],.]]],.]],.]],[.,.]]]
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[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]],[.,.]]]
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[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],[.,.]],.],[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,[.,[[[.,.],.],.]]],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0] => [.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],[[.,[[.,.],.]],[.,.]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,.],[.,[[[.,.],.],[.,.]]]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[[.,.],.],[[.,.],[.,.]]],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],[[[.,[.,.]],.],.]],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],[.,.]],.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,[[.,.],.]],[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],[[[.,[.,.]],.],.]]]]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],[.,[[.,[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[.,[.,.]],[[[[.,.],[.,[[.,.],[[.,.],.]]]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[[[.,.],.],[.,.]]],.]],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,.],[[.,[[[.,.],.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [[.,[.,.]],[.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,[[[.,.],.],.]],.],[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],[[[.,.],.],[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[[.,[[.,[.,[.,.]]],.]],.]]],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],[.,.]]],.],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[[[.,[.,[.,.]]],.],[.,.]]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[.,[[.,[.,.]],.]],.],[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],[[[.,.],[.,[.,.]]],.]],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[.,[.,.]],.],[[.,.],[.,.]]],.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],[[[.,[.,.]],.],[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,[[.,[[.,[.,.]],.]],.]]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[[[.,[.,.]],.],[[.,.],.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[.,[[[.,[.,.]],.],[.,.]]],[.,[.,.]]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],[[[.,[.,.]],.],.]],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],[.,.]],.],[[[.,.],.],.]]]],.]
[1,1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0] => [[.,[.,[.,[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,[[.,[.,.]],.]],[[[.,.],.],.]]],.]],.]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],[.,[[.,[[.,.],.]],.]]],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],[.,[[.,.],[[.,.],.]]]],.],.]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[[.,[[.,[[[.,[.,.]],.],[.,.]]],.]],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,[[[.,.],.],.]],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[.,[.,.]],[[[.,.],.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[[[.,[.,.]],.],.]],.],[.,.]],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],.],[[[.,.],.],[.,.]]],.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[[.,.],[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[.,[[.,[[.,.],.]],.]]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,.],.],[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[[[.,.],.],[.,.]],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[[[.,[.,.]],[.,[.,.]]],.]],.],.]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[[.,[.,.]],[.,.]]],.],[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[[[[[.,[.,.]],.],[[.,.],.]],.],.]],.]
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0] => [[.,.],[.,[[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[[[.,.],[.,[.,[.,.]]]],.]],.],.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[[.,[[.,.],[.,[.,.]]]],.],[[.,.],.]]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [[.,[.,[[.,.],.]]],[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[[[.,[[.,[.,.]],.]],.],.]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],[[[.,[.,.]],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[[[.,[[.,.],.]],.],[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,[[.,.],.]],.],[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[[[.,.],.],[[.,.],[.,.]]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,.],.],[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]],.]]],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,[[[.,[[.,.],.]],.],.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[[[.,[[.,.],.]],.],.]],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[.,[[[.,.],.],[[.,.],.]]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[[[.,.],.],[[.,.],.]]],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]],.],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[[[[[.,.],.],[[.,.],.]],.],[.,.]]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]],.],.]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,[[[.,[[[.,.],[.,[.,.]]],.]],.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[[.,[[.,.],.]],.],[[.,[.,.]],[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],[[[.,.],[.,[.,.]]],[.,.]]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[[.,.],[[[.,[.,.]],.],.]]]],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[[[[.,.],.],[[.,.],.]],.],.]],[.,.]],.],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,.],[.,[[.,.],[[.,.],.]]]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[.,[[.,[[[.,.],.],[.,.]]],.]]],[.,.]],.],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],[[[.,[.,.]],.],.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[.,.],[.,[[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],[[[.,.],.],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[.,.],[[[.,.],.],[[.,.],[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[.,[[.,[[.,.],.]],.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0] => [[.,.],[[[[.,.],[.,[[.,.],[[.,.],.]]]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,[[.,[[[.,.],.],[.,.]]],.]],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,.],[[.,[[[.,.],.],.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[[.,.],[[[.,.],.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,[[[.,.],.],.]],.],[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],[[[.,.],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [.,[.,[[[.,.],[.,[.,.]]],[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[[[.,[[.,.],[.,.]]],.],[[.,.],.]],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [.,[[.,[[.,.],[.,.]]],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[[[.,[.,[.,.]]],.],[.,.]]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[[[.,[[.,.],.]],.],[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[[[.,[[.,.],.]],.],[.,.]],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[[[.,.],.],[[[.,.],[.,[.,.]]],.]],.],[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[[[.,.],.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0] => [.,[.,[[[.,.],[[[.,[.,.]],.],[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[.,[[.,[[.,.],.]],.]]],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[[[.,.],.],[[.,.],.]],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [.,[[.,.],[[.,[[.,.],[[.,.],[.,[.,.]]]]],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[.,[[[.,[[[.,.],.],[.,.]]],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],[[[.,[.,.]],.],.]],.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],[.,.]],.],[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[[.,[[.,[[.,.],.]],.]],.],.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[.,[[.,[[.,.],.]],[[[.,.],.],.]]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],[[.,.],[[[.,[.,.]],.],.]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],.],[.,[[.,[[.,.],.]],.]]],.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],[.,[[.,.],[[.,.],.]]]],.],.]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,[[[.,.],.],[.,.]]],.]],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,[[[.,.],.],.]],[[.,.],.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[.,[[.,.],[[[.,.],.],[[.,.],[[.,.],.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,[[[.,.],.],.]],.],[.,.]],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0] => [[.,[.,[[[[.,.],.],[[[.,.],.],[.,.]]],.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[[[[.,[.,[.,.]]],.],[.,.]],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[.,[[.,.],[.,.]]],[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,[[[.,.],.],[.,.]]],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[[[[.,[.,[.,.]]],.],[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]],[.,.]],.],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],[[[.,[.,.]],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[[[.,[.,[.,.]]],.],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]],[.,.]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[[[.,.],.],[.,.]]],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,[[.,.],[.,.]]],[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,[[.,[.,.]],.]],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[[[.,[.,.]],.],[.,[[.,.],.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[[[.,[[.,[.,[.,[.,.]]]],.]],[.,[[.,.],.]]],.],.]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[[[.,[.,[.,[.,.]]]],.],.]],[.,[[.,.],.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[[.,.],.]],[[.,.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,[.,[[[.,.],[.,[.,.]]],.]]],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[[.,.],[[[.,.],[.,[.,.]]],.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[[[.,[.,[[.,[.,[.,.]]],.]]],.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,[[.,.],[[.,[.,[.,.]]],.]]],[.,[[.,.],.]]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],.],[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[.,[[[.,[.,[.,.]]],.],.]]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[[[[[.,.],[.,.]],.],[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[[[[.,[.,.]],.],.],[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[[[.,.],[[.,[.,[.,.]]],.]],[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[[[.,.],[.,.]],.],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[[[.,[.,[.,.]]],.],.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[[.,.],[[.,.],.]],[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[[.,[.,.]],.],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[[.,.],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[[.,[[[.,.],.],.]],[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[[.,[.,.]],.],[.,[.,[[.,[.,.]],.]]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[[.,[[.,[.,.]],.]],[.,[.,[[.,[.,.]],.]]]],.],.]
[1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],[[.,.],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,[[[.,[.,.]],.],.]],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],[[.,.],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[.,[.,[[.,.],.]]],.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[.,[.,[[.,.],.]]],.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[.,[[[[.,.],[.,.]],.],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],[[.,.],.]],[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,[[[.,[.,.]],.],[.,.]]]],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],[.,[[.,[[.,.],.]],[.,.]]]],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,.]],.],[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => [[[.,[.,.]],.],[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[[.,[.,.]],.],[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[.,.],.]],[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[[[.,[.,.]],.],[.,[.,.]]],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[[.,[.,.]],.]],[.,[.,.]]],.],.]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[[.,[.,.]],.],[[.,.],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,[[[.,[.,.]],.],.]],[.,[.,.]]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[[.,[.,[[.,.],.]]],.],[.,[.,.]]],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,[[.,.],[[.,.],.]]],[.,[.,.]]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,[.,.]]],.],[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,[[.,.],.]]],.],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[[[.,.],[.,.]],.],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[[[.,[.,.]],.],.]],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[[.,.],[[.,.],.]],[.,.]]],[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],.]]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[[[.,[.,[.,.]]],.],[.,.]],.],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[.,[[.,.],[.,.]]],[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[[.,[[[.,.],.],[.,.]]],[.,.]],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[[.,[[.,[[.,.],[.,.]]],[.,.]]],[.,.]],.],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[[.,[.,.]],.],[[[.,[.,.]],.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[[.,[.,[.,.]]],.],[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[[[.,[[.,.],[.,.]]],[.,.]],.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[[.,.],[.,.]]],[[[.,.],.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[[[.,[.,.]],.],[.,[[.,.],.]]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[[.,[.,[.,.]]],.]],[.,[[.,.],.]]],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[[.,[.,.]],.],[[.,.],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[.,[.,.]]],.],.]],[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,[.,.]]],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],[[[.,.],[.,.]],.]]],[.,[.,.]]],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,[[.,[.,.]],.]]],.],[.,[[.,.],.]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],[[.,[.,.]],.]]],[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[.,.]]],.],[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],[[[.,[.,.]],.],.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[[.,[.,[.,.]]],.],[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,[.,[[[.,[.,.]],.],.]]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[[[[.,.],[.,.]],.],[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[[[.,[.,.]],.],.],[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],.],[.,.]]],[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[[[[.,.],[.,.]],.],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],[[[.,[.,.]],.],.]],[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],.]],[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],[.,.]]],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[[.,.],.],.]],[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[.,.]],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[[.,.],.],[[.,.],[[.,.],[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[[.,.],.],[[.,.],[.,[[[.,.],[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [[[[.,.],.],.],[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[[[.,.],.],[[.,.],[[.,.],.]]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[[[.,.],.],[[.,.],.]],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[.,.],[[.,.],.]],[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [[[.,.],[[.,.],.]],[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,.],[[.,[[.,.],.]],.]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [[[.,.],.],[[[.,.],[[.,.],[[.,.],[.,[.,.]]]]],.]]
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [[[[.,.],.],.],[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,.],.],[[[.,[[.,.],.]],[[.,.],[.,[.,.]]]],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],.],[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[[.,.],.],.],[.,.]],[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],.]]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[[.,[[.,.],.]],.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0] => [[[[[.,.],.],.],[.,[[.,[.,.]],.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],[[.,.],.]],.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[[.,.],.],.],[[.,[.,[.,.]]],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[.,[[.,.],.]],.],[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [[[.,[[.,.],.]],.],[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[[.,[[.,.],.]],.],[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],.]],[[.,.],.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[[.,.],.]],.],[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[.,[[.,.],.]],.],.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[[.,.],.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,[[.,.],.]],.],.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[[.,[[.,.],.]],.],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],[[.,.],.]]],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[[.,.],[[.,.],.]]],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,[[.,.],.]],.]],.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,[[.,[[.,.],.]],.]],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,.],[[.,.],[[.,.],.]]]],.],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,.],[[.,[[.,.],.]],.]]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[[.,.],.]],[[.,.],.]]],.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[[.,.],[[.,.],.]]],.]],.],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[[[.,.],.],[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[.,.]]]]],.]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[[[.,.],.],[[[.,.],[.,.]],.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[[.,.],.],[.,[[[.,.],[.,.]],.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[[.,.],[[.,.],[[.,.],.]]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[[[.,[[.,.],.]],[[.,.],.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,[[.,.],[[.,.],.]]],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[[.,.],[[.,[.,.]],[.,.]]]],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],[.,.]],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,[[[.,.],[.,[.,.]]],.]]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,.]],[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[[.,[[.,.],.]],.],[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[[[.,.],[.,[.,[.,.]]]],.]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],[.,[[.,[.,.]],.]]],[.,.]],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[[.,[[.,.],.]],.],[[.,[.,[.,.]]],.]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[[[[.,.],.],[[.,[.,[.,.]]],.]],[.,.]],[.,.]],.]
[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] => [[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[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] => [[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[[.,.],.]],[.,[[.,.],.]]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],[[.,.],.]]
[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] => [.,[[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.],.]]
click to show experimental identities (only identities of compositions of up to three maps are shown)
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 $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Properties
bijective, graded
Sage code
def mapping(elt):
    return elt.to_binary_tree("L1R0")
Weight
26
Created
Jan 29, 2020 at 13:25 by FindStatCrew
Updated
Jan 29, 2020 at 13:25 by Martin Rubey