- FindStat

Identifier
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Images
=>
            
              Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
            

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[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[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]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]
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[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
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[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]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
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[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]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
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[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]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
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[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]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
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[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
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[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
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[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]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
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[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]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
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[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
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[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]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
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[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
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[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
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[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
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[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
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[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]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]
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[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
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[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[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]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[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]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[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]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[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]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[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]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[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]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
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[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]],.]
          
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 border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.