Identifier
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1
[]=>.
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[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[[[.,.],.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[.,[[[[.,.],.],.],.]],.],.],.],.],.]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[.,[[[[[[[.,.],.],.],.],.],.],.]],.],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
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[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]],.]
[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]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]
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[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]]]
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[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
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[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]
[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]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],.]]
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[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],[.,[.,.]]],[.,.]]]
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[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]]
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[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]]
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[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[.,.],[[[[.,[.,[[.,.],.]]],[.,.]],.],.]]
[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]=>[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],[[.,.],.]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],[[.,.],.]]
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[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[[.,.],[.,.]]],.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[.,[[.,[[[.,.],[[.,.],.]],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[[[.,.],.],[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]]
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[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[.,[[.,[[[.,.],.],[.,.]]],.]]]
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[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,[[.,.],[.,.]]]]
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[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],[[.,.],.]]
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[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]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]],.]
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[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[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]=>[[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],.]
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[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]=>[[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]
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[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[[.,[.,.]],[[.,.],.]],[.,.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[.,[.,.]],[[.,.],.]],[.,.]],[.,.]],[.,[.,.]]]
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[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[[.,[[[[.,[[[.,.],[.,.]],.]],[.,.]],[.,.]],.]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],[[[.,.],[.,.]],.]],[[.,[.,.]],.]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[[.,.],[.,.]],.]],[.,.]],[.,[.,.]]]
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[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[[[.,.],[.,.]],[.,.]],.]],[.,.]],.]],.]
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[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[[[.,[.,.]],.],[.,.]],.]],[.,.]],[.,[.,.]]]
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[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[.,[[[[.,.],.],[[.,.],[.,.]]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[.,[.,[[.,[[[.,[[.,.],[[.,.],.]]],.],.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[.,[.,[[[.,[[.,[[.,.],.]],[[.,.],.]]],.],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[.,.],[.,.]]],[[[[.,.],.],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[.,[.,.]],[[[.,[[.,.],[[.,.],.]]],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],[[.,[[.,.],.]],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[[[.,[.,.]],[.,.]],[[.,[[.,.],.]],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],[[[.,.],.],[.,.]]]]
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[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],[[[.,.],.],[.,.]]]]
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[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[.,[[[.,[[.,.],[[.,.],.]]],.],[.,.]]]]
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[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,[[.,[[.,.],.]],.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],[[[.,.],.],[.,.]]]]
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[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],[.,.]]]]
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[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,.],[.,.]]]]
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[1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[[.,[[.,[.,.]],.]],.],[[.,.],[.,.]]]]
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[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[[.,.],[[.,[.,.]],.]]]
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[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]
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[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]=>[[.,[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[[.,[.,.]],.]]]]
[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]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
click to show experimental identities
(only identities of compositions of up to three maps are shown)
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.
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.
Properties
bijective, graded
Sage code
def mapping(D): return D.to_binary_tree("1L0R")
Weight
26
Created
Jan 19, 2020 at 07:29 by FindStatCrew
Updated
Jan 19, 2020 at 07:29 by Martin Rubey
searching the database
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