Identifier
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1
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[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],.],.],[.,.]],[[.,.],[.,.]]]]
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[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[.,[[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[.,[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],.],[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[[[[.,.],.],[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[[.,.],[.,.]]]]
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[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],[.,[.,.]]]]
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[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[[.,.],.]]]]
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[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]],.]
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[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]
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[1,0,1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]
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[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,[.,.]],[.,.]]]]
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[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],[.,[.,.]]]]
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[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,[[.,[[.,.],.]],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[.,[[[.,.],.],[.,.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],[[.,.],.]]],.]
[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]=>[[[.,.],.],[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]
[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]=>[[[.,[[.,[.,.]],.]],.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[.,[.,.]],.],[[.,[[.,.],.]],.]],[.,.]]
[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]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.]
[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]=>[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]
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[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]
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[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],[[.,.],.]]]],.]
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[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]
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[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]=>[[.,[[.,[.,.]],.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],[.,[.,.]]]
[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]=>[[[.,[.,.]],.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],[.,[.,.]]]
[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]=>[[[[[.,[.,.]],[[.,.],.]],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],[.,.]]
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[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,0]=>[[[[.,.],.],[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.],.]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,.]],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],[[[.,.],.],.]]],.]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[.,[[[.,.],[.,.]],[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[[.,.],.],[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[.,.],[.,.]],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[[.,.],.]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[[.,[.,.]],[.,.]],.],.],.],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[.,[[[.,.],[.,[[.,.],.]]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[[[[[.,.],[[.,.],.]],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[.,[[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[.,.],.],.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[[[[.,.],[[.,.],[.,.]]],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[[[.,.],.],.]],.],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[[[.,.],.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[[.,.],.],.]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,[[.,.],.]]],.]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[[[[[[.,.],[.,.]],.],.],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[[[[[.,[.,.]],[.,.]],.],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[.,[[.,.],.]]],.],.]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],[[.,[.,.]],.]],.],.]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[[.,[.,.]],.]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[.,.],[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.],.]
[1,1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[.,[[[.,.],.],[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
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[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
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[1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]
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[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],[[.,.],.]],[[.,[.,.]],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],[[.,.],[[.,.],.]]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[[[.,[.,.]],.],[[.,.],.]]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[[[.,[.,.]],.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,.],[[.,[[[.,[.,.]],.],[[.,.],.]]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[[[.,[.,.]],.],[[.,.],.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[[[.,[.,.]],.],[[.,.],[[.,.],.]]]],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[[[.,[.,.]],.],[[.,.],.]]]],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[[[.,[.,.]],.],[[.,.],.]]],.]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.]],.]
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[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[.,[[.,.],[[[[.,[.,.]],.],[[.,.],.]],[.,.]]]],.]
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[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[[.,[.,.]],.],[[.,.],.]],[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[[[.,[.,.]],.],[[.,.],.]]],.]],.],[.,.]]
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[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],[[.,.],.]]],.],[[.,[.,.]],.]]
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[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[[.,[[.,[.,.]],.]],.],[[.,.],.]],[.,.]]],.]
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[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[[.,[[.,[.,.]],.]],.]],.],[[.,.],.]]],.]
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[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[[.,.],.]],.]]]]
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[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],.],[[.,[.,[.,.]]],.]]],[[[.,.],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],[[.,[.,[.,.]]],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]],[.,[.,.]]]
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[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[[[.,.],[.,.]],.],[.,[.,.]]],.]],.],.]]
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[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[[.,.],[[.,[[[.,.],.],.]],[.,.]]]],.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[[.,[[.,.],[[[[.,[.,.]],.],.],[.,.]]]],.],.]]
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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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[1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.]
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[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]
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[1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
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[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]=>[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],.],[[.,.],.]]]
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[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],.],.]]]
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[1,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],[[.,.],.]]]
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[1,1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],.],[.,.]]],.]
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[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,[.,.]]],[[[.,[.,.]],.],.]],.]
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[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],[.,.]]],[.,[.,.]]]],[.,[.,.]]]
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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
Francon's map from Dyck paths to binary trees.
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].
References
[1] Françon, J. Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique MathSciNet:0775838
[2] http://www-cs-faculty.stanford.edu/~knuth/programs/francon.w
[2] http://www-cs-faculty.stanford.edu/~knuth/programs/francon.w
Properties
bijective, graded
Sage code
def mapping(D): def LR_to_binary_tree(links, root=0): if links[root][0] != 0: left = LR_to_binary_tree(links, root=links[root][0]) else: left = None if links[root][1] != 0: right = LR_to_binary_tree(links, root=links[root][1]) else: right = None return BinaryTree([left, right]) n = D.semilength() d = list(D) + [0] l = [0]*(n) r = [0]*(n) h = [0]*(2*n+3) q = [0]*(n+1) qm = [0]*(n+1) h[1] = m = 1; k = 2; p = 0 while True: while h[k] != 0: k = k + 2 kk = h[k//2] p += 1 if d[p] == 1: l[kk-1] = m; m += 1; h[k] = m; else: l[kk-1] = 0 p += 1 if d[p] == 1: r[kk-1] = m; m += 1; h[k+1] = m; else: r[kk-1] = 0 if h[k] != 0: if h[k+1] != 0: continue else: kk = k elif h[k+1] != 0: kk = k+1 else: h[k//2] = 0; kk = (k//2) ^^ 1; k = kk & -2 if k == 0: return LR_to_binary_tree(list(zip(l, r))) j = 0; jj = 1; q[0] = kk; qm[0] = 1 while j < jj: kk = q[j] h[((kk//2)&(-qm[j]))+(kk&(qm[j]-1))] = h[kk] if h[2*kk] != 0: q[jj] = 2*kk q[jj+1] = 2*kk+1 qm[jj] = qm[jj+1] = qm[j]*2 jj = jj + 2 else: h[kk] = 0 j += 1
Created
Jan 31, 2020 at 19:19 by FindStatCrew
Updated
Jan 31, 2020 at 19:19 by Martin Rubey
searching the database
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