- FindStat

Identifier
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
=>
            
              Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
            

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[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
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[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]
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[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
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[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
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[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
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[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,[[.,.],.]],.]]
          
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.