- FindStat

Identifier
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
=>
            
              Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2Cc0010;cc-rep-3
            

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[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
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[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
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[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
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[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
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[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
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[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
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[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
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[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
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[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
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[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]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
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[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]
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[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
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[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]
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[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]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
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[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]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
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[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]
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[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
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[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]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]
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[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]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
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[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]
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[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]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
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[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]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
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[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]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]
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[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]
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[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]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
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[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
          
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 rotate
Description
Return the result of left rotation applied to a binary tree.
Left rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the right child of the root of $T$ is a node. Let $A$ be the left child of the root of $T$, and let $B$ and $C$ be the left and right children of the right child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of $T$ is the binary tree in which the right child of the root is $C$, whereas the left child of the root is a node whose left and right children are $A$ and $B$.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.