Identifier
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1
[]=>.
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[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]
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[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[.,[[.,.],.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,[[.,.],.]],[.,.]]],.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,.],.],[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[[.,[.,.]],.]]],.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[[[.,.],.],[.,.]]],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,[[[.,.],.],.]],[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[.,.],[[.,.],[[[.,.],.],[.,.]]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[.,[[[.,.],.],.]],[.,.]]],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[[[.,.],.],.]],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[[.,.],.],[.,.]],.],[.,.]]],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[[[.,.],.],.]]],[.,.]],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,[[[.,.],.],.]],.]],[.,.]],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[[[.,[.,.]],.],.]],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,[[.,.],.]],[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],[[.,.],.]]],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[[.,[[.,.],.]],.]],[.,.]]],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,[.,.]],.],[.,.]],.]]
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[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,.],[.,.]]],.]
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[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[[.,.],[.,[.,.]]]],.]]
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[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,[[.,.],.]],.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],[[.,.],.]]],.]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,[[.,.],.]],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[[.,.],[[.,.],.]]]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],[[.,[[.,.],.]],.]]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[[.,.],[[.,.],.]]],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[[.,[[.,.],.]],.]],.]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[[.,.],[.,.]]],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],[.,.]]],[.,.]],.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],[.,.]],[.,.]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]],.]]
[1,1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]],.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],[.,.]]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],[[.,.],.]],.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[[.,.],[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[.,[.,[.,.]]],.]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[[.,.],.]],.]],[.,.]],[.,.]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[[.,.],.]],.],[[.,.],.]],.]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[[.,.],[.,.]],.]],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,[.,[.,.]]],.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],[[.,.],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[[.,[.,.]],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[[.,.],.]],[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,[[.,.],.]],.]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[.,.],[[.,[.,.]],.]],.],[.,.]],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[[.,.],[[.,.],.]],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[[[.,.],[.,.]],.]]],.],[.,.]],.]
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[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[[.,[[.,.],.]],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]],.]
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[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]
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[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]
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[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]
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[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]],.],[.,.]]
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[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
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[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]
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[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[.,.]]
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[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[.,.]]
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[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[[.,[.,[.,.]]],[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],[[[.,.],[.,.]],.]],.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,.],[[[.,.],[[[.,.],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[.,.],[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[[.,.],[[.,.],[.,.]]],.]],.]],.]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],[[.,[.,[.,.]]],.]],.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],[[.,.],.]],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[[[[.,.],[.,.]],[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[[[.,.],[[[.,.],[.,.]],.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],[[[.,.],[[.,.],.]],.]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,.],[.,.]],[[.,.],[[[[.,.],[.,.]],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[[.,[[.,[.,.]],.]],.]],.],[.,.]],.]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,[[.,.],.]],.]],[[.,[.,.]],.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[[.,.],[[.,[.,.]],.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[[.,.],[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[[.,[[.,[.,.]],.]],.],[.,.]],.]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[[.,[[.,.],.]],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,[[.,[.,.]],.]],.]],.]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]
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[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]
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[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,[[.,.],.]],[[[.,.],[.,.]],.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],[.,[[[.,.],[.,.]],.]]],.]
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[1,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.]]
[1,1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]]
[1,1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]]
[1,1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]],.]],.]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]],.]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[.,[.,[[.,[[.,[[.,[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]],.]],.]],.]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,[.,[[.,[[.,[.,[.,[[.,[[.,[.,[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]]],.]],.]]]],.]],.]]]],.]]]]]],.]
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Properties
bijective, graded
Sage code
def mapping(elt): return elt.to_binary_tree("L1R0")
Created
Jan 29, 2020 at 13:25 by FindStatCrew
Updated
Jan 29, 2020 at 13:25 by Martin Rubey
searching the database
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