- FindStat

Identifier
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ 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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[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
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[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,.],.],.],.]]]
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[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],.]
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[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
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[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
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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]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
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[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]
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[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
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[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]
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[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]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
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[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[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]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
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[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]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[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]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[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]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
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[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
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[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]
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[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]
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[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
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[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]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]
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[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]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
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[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]
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[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]
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[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]
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[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]
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[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
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[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]
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[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
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[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
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[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]
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[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
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[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
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[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
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[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
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[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
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[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: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
left 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.