- FindStat

Identifier
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Images
=>
            
              Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
            

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[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
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[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
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[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
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[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]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
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[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]
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[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
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[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]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
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[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]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
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[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]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]
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[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]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]
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[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
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[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]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
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[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
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[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],.]=>[[[.,.],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[.,[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]=>[[[[[.,[[[.,[.,.]],.],.]],.],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[[.,.],[[.,.],.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[[[.,.],.],.]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]]=>[.,[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]]=>[.,[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]]
[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]=>[[[[[.,[.,.]],.],.],.],[[[[.,.],.],.],.]]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],[.,.]]=>[[[[.,[.,.]],[[[.,[.,.]],.],.]],.],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]=>[[[.,.],[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]],.]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[[[.,.],.],.]]
[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]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[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]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[[.,[.,.]],.],.],.],.]],.]=>[[[.,.],[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,[.,.]]],.],.]],.]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]=>[.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]=>[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]],.]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]=>[[[.,.],[.,[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[.,.]]]=>[[.,[[[[.,[.,.]],.],[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]=>[[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]=>[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],.]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]],.]=>[[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]=>[[[.,.],[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>[[.,[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],[[.,[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]=>[[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]]=>[[.,[[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,.]],.]],.]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]=>[[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],[.,.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]]=>[.,[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[[[.,.],.],.],.],.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,[.,.]],.]]]],.],.]=>[[[.,.],.],[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[[.,[.,.]],.]],.]]],.]=>[[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.],.]=>[[[.,.],.],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],.]=>[[[.,.],[[.,[[.,[[.,.],[.,.]]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],[[.,.],.]]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]]=>[.,[[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]],.]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]],.]]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]]]=>[.,[[.,[.,[.,[[[[.,.],.],.],.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[.,.]],.]]],.]]]=>[.,[[.,[[.,.],[[.,[[.,.],[.,.]]],.]]],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]=>[.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[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]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]=>[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[[.,.],[.,.]]],.]]]=>[.,[[[.,[[.,.],[[.,[.,.]],.]]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]]]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]],.]
[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]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]=>[[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],[[.,.],.]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]],.]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,[[.,.],.]],.]]],.]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]=>[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]]=>[[.,[[.,[[.,[[.,[[[.,[.,.]],.],.]],.]],.]],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]]=>[.,[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]]
[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]=>[[[[[[[.,.],[.,.]],[[.,.],.]],.],.],.],.]=>[[[[[[[.,.],.],.],.],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[[[.,.],.],.]],.]
[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]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]=>[[[[[[.,[[[.,[.,.]],.],.]],.],.],.],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[.,[.,[.,[.,[[[[.,.],.],.],.]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]],.]=>[[[.,.],[[.,[[[.,.],[.,.]],[.,.]]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[[[.,.],.],.]]]]=>[.,[.,[[[.,[[[.,.],.],.]],[.,.]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,.],[.,.]]],.],[.,.]]]]=>[.,[[.,[[[.,[.,.]],.],[[.,[.,.]],.]]],.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[.,.]]]=>[.,[[.,[.,.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]]=>[.,[[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]],.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]]]=>[.,[.,[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,[.,.]]],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[.,[[.,[.,[[.,[[.,.],.]],.]]],.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[[.,[[[.,[[.,.],.]],.],.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]=>[[.,[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],.],.]=>[[[.,.],.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[[.,.],[[.,.],[.,.]]]]]]=>[[.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],.]],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,[.,.]]]],.],.]]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],[.,.]]
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[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,.],[[.,.],.]]],.]]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]=>[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,[[.,.],.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,[[.,.],.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>[.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>[.,[[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]],.]]=>[.,[[[.,.],[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.],.]]=>[.,[[[.,.],.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
          
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.