- FindStat

Identifier
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
=>
            
              Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
            

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[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
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[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
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[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
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[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
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[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
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[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[[[.,.],.],.],.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
          
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-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.