- 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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[]=>.=>.
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[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]],.]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]],.]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]],.]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[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]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],[.,.]]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]=>[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]],.]=>[[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]],.]=>[[.,.],[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]],.]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]],.]=>[[.,.],[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]],.]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]],.]=>[[.,.],[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]],.]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[[.,.],[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]],.]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]],.]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[.,.],[[.,.],.]],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
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[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[.,.],.],[[[.,.],.],.]],.],.],.],.]=>[[[[[[[.,.],.],.],.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]=>[[[[[[.,.],.],[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]=>[[[[[[.,.],[[[[.,.],.],.],.]],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>[.,[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>[.,[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[.,[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[.,[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>[.,[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[.,[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]
[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]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
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[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
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[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]=>[[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],.]],[[.,.],[.,.]]],.]]=>[.,[[[.,.],[[.,[.,.]],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]=>[[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]]=>[.,[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],.]]=>[.,[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],[.,.]]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],[.,.]]]],.]]]=>[.,[[.,[[.,.],[[.,[[.,[.,.]],.]],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]=>[.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[.,[[.,[.,.]],.]]]=>[[[[[.,[.,[[.,.],[.,.]]]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]=>[.,[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]]=>[.,[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]]=>[.,[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[.,[[.,.],.]],.]]],.]]=>[.,[[[.,.],[.,[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]],.]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[[[.,.],.],.],.],[.,.]]],.]]=>[.,[[.,.],[[[[[.,[.,.]],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[[.,.],.]]],.]]]=>[.,[.,[[[.,.],[[.,[[.,.],.]],.]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]]=>[.,[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]]]=>[.,[.,[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]]=>[.,[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]=>[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]=>[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]]=>[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]=>[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]=>[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.]=>[[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]=>[[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.]=>[[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]=>[[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]=>[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]=>[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]=>[[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]=>[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]=>[[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]]=>[[.,[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]]=>[[.,[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[[[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]]=>[[.,[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]]=>[[.,[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],.]]]=>[[[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]=>[[[[.,[[.,.],.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],.]]=>[[[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],.]]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],.]]]=>[[.,[[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]]=>[[.,[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]]=>[[.,[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]=>[[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]=>[[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]]=>[[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]]]=>[[.,[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],.]]=>[[[[.,[[.,.],.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],.]]=>[[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]]=>[[.,[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]=>[[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]]=>[[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]=>[[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]=>[[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],.]]]=>[[.,[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],.]]=>[[[.,[[[[.,.],[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.]]=>[[.,[[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]=>[[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],.]=>[[[[.,.],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]],.]=>[[[[[.,.],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]]=>[[.,[[.,[[[.,.],[[[.,[.,.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]=>[[[.,[[[.,.],[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]=>[[[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]]=>[[.,[[[.,.],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],.]=>[[[.,.],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],.]=>[[[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.]]=>[[.,[[[[[.,.],[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]=>[[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]]=>[[.,[[[[[.,.],[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]],.]=>[[[.,.],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]],.]=>[[[[.,.],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]],.]=>[[[[[.,.],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],.]=>[[[[[.,.],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],.]=>[[[[[.,.],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]]=>[[.,[[.,[[[[.,.],[.,.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]=>[[[.,[[[[.,.],[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]=>[[[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]]=>[[.,[[[.,.],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],.]=>[[[.,.],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]]=>[[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]=>[[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]=>[[[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[[.,[[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.]=>[[[.,.],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]=>[[.,[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]=>[[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]=>[[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]]=>[[.,[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,[[.,[[[.,.],[.,.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]]=>[[.,[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],[[[.,.],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]]=>[[.,[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]=>[[[.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],.]]]=>[[.,[[[.,[[[.,.],[.,.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]]=>[[.,[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]=>[[[.,[[[[.,.],[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]=>[[.,[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],.]=>[[[.,.],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],.]=>[[[[[.,.],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.]]=>[[.,[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]=>[[[.,.],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[[[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]]=>[[.,[[[[[.,.],[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]=>[[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]]=>[[.,[[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]=>[[[.,[[.,[[[.,.],[[.,[.,.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]=>[[[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]]=>[[.,[[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[[.,.],[[.,.],[.,.]]],.]]=>[[[.,[[[.,.],[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]]=>[[.,[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],.]=>[[[.,.],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],.]=>[[[[.,.],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],.]=>[[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]]=>[[.,[[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]=>[[[.,[[[.,.],[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]=>[[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]]=>[[.,[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]=>[[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]=>[[.,[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.],.]=>[[[[.,.],.],[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]=>[[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,.]],[[[[[.,.],.],.],.],[.,.]]]=>[[.,[[[[[.,[.,.]],.],.],.],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],[.,.]]]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]],.],.]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[.,[[[[.,[.,.]],.],.],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]]=>[[[[.,[[[.,[.,.]],.],.]],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],[.,.]]]=>[[[[[[.,[[.,[.,.]],.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,[.,.]],.],[.,.]],[.,.]],[.,.]]]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[.,[[[.,[[.,.],[.,.]]],.],.]]]]=>[.,[[.,[.,[[[.,.],.],[[.,[.,.]],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]]=>[.,[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]]=>[.,[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]]],.]]=>[.,[[.,.],[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,[[.,[[.,.],.]],.]]]]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]]=>[.,[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,.],[.,[[[.,[[.,.],[.,.]]],.],.]]]],.]]=>[.,[[.,.],[[.,[.,[[[.,.],.],[[.,[.,.]],.]]]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]]=>[.,[[.,.],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]]]=>[.,[[.,[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]]=>[.,[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]]=>[.,[[.,.],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]]=>[.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[.,[[.,[.,.]],[[.,.],.]]],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]],.]=>[[[[[.,.],[[[[.,.],.],.],.]],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],[.,.]],[[.,.],.]]],.]]=>[.,[[.,.],[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[.,[[[.,.],[[.,.],.]],.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],.]]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],[.,.]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,.]],[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[[[.,[.,.]],.],[[.,[.,.]],.]],[.,.]]]=>[.,[[[[.,[.,.]],[[.,.],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[[.,.],.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]],.]=>[[[[[.,.],[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[[[.,[[.,[.,.]],[.,.]]],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]],.]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]],.]=>[[[.,.],[[[[.,.],.],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]=>[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]=>[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[.,[[.,[[.,.],.]],.]]],.]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,[[.,.],.]]],.]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],.]],.]]],.]=>[[[[.,.],[.,[[.,.],[[[.,.],[.,.]],.]]]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[[.,[[.,.],.]],[.,.]],.]]],.]=>[[[.,.],[.,[[[.,.],[.,.]],[[.,.],.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,[[.,[[.,.],.]],.]]],.]=>[[[[.,.],[.,[[.,.],[[.,.],.]]]],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,[[[.,.],[.,.]],.]]],.]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]=>[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]=>[[.,[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[.,[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[[.,.],[.,.]],.]],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]],.]=>[[[[.,.],[[[.,[[[.,.],.],.]],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,[.,.]]]=>[[[[[[.,[.,[.,.]]],.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.],.]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,[[.,[[[.,.],.],[.,.]]],.]],.],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,[.,.]]]],.]]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]]=>[.,[[.,.],[[[.,.],[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,[.,.]],.],.]]]=>[[[[.,[.,[[[.,.],.],[.,.]]]],.],.],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]=>[.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],[[.,.],[[.,.],.]]],.],.]=>[[[[.,.],.],[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[.,.],[.,[[.,[[[.,.],[.,.]],.]],.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[[.,.],[[[.,.],[.,.]],.]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],[.,.]]=>[[[[[.,[.,.]],[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],[.,.]],[.,.]],.],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],.],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],[[.,.],.]]=>[[[[[.,[[.,.],.]],[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[[[.,.],[.,.]],[.,.]],[.,[.,.]]],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,[[[.,.],[.,.]],.]]],.]]]=>[.,[.,[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]=>[[[.,.],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]=>[[[[[[[[.,.],.],.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],[.,.]]]=>[[[[[.,[[.,[.,.]],.]],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],[.,.]],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]]=>[.,[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]=>[[.,[[.,[[[[.,.],[[.,.],.]],.],.]],.]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],[[.,.],.]],.],[[.,.],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],.]],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[[[.,[[.,.],.]],.],.]],.],[.,.]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]]=>[.,[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]]=>[.,[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[[[.,.],[.,.]],.],[[.,.],[[.,.],[.,.]]]]]]=>[.,[.,[[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,.],[[.,.],.]]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]=>[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,.],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]]=>[.,[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]]=>[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]]=>[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]=>[.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]]]=>[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[[.,[.,.]],.]]]=>[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]]=>[.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]=>[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]=>[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]=>[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]=>[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]=>[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]],.]=>[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[.,.],[[[.,[.,.]],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],[[.,.],[.,.]]]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[[.,.],[[[.,[.,.]],[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],[.,.]]],.]=>[[[.,.],[[.,[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[.,.],[[.,[.,.]],[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[[.,.],[[.,[.,.]],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
          
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 $T_1, T_2, T_3$.